Academic literature on the topic 'Linear stochastic dynamic systems'

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Journal articles on the topic "Linear stochastic dynamic systems"

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Klamka, Jerzy. "Stochastic Controllability of Linear Systems With State Delays." International Journal of Applied Mathematics and Computer Science 17, no. 1 (2007): 5–13. http://dx.doi.org/10.2478/v10006-007-0001-8.

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Stochastic Controllability of Linear Systems With State DelaysA class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.
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Klamka, Jerzy. "Stochastic Controllability of Systems with Multiple Delays in Control." International Journal of Applied Mathematics and Computer Science 19, no. 1 (2009): 39–48. http://dx.doi.org/10.2478/v10006-009-0003-9.

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Stochastic Controllability of Systems with Multiple Delays in ControlFinite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamic system. As a special case, relative stochastic controllability of dynamic systems with a single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamic systems are also presented.
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Zhang, Yingqi, Wei Cheng, Xiaowu Mu та Caixia Liu. "Stochasticℋ∞Finite-Time Control of Discrete-Time Systems with Packet Loss". Mathematical Problems in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/897481.

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This paper investigates the stochastic finite-time stabilization andℋ∞control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochasticℋ∞finite-time boundedness and then state feedback controllers are designed to guarantee stochasticℋ∞finite-time stabilization of the class of stochastic systems. The stochasticℋ∞finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.
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Long, Fei, Hongmei Huang, and Adan Ding. "Stochastic Stabilization of Itô Stochastic Systems with Markov Jumping and Linear Fractional Uncertainty." Journal of Control Science and Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/697849.

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For a class of Itô stochastic linear systems with the Markov jumping and linear fractional uncertainty, the stochastic stabilization problem is investigated via state feedback and dynamic output feedback, respectively. In order to guarantee the stochastic stability of such uncertain systems, state feedback and dynamic output control law are, respectively, designed by using multiple Lyapunov function technique and LMI approach. Finally, two numerical examples are presented to illustrate our results.
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Javadi, Ali, Mohammad Reza Jahed-Motlagh, and Ali Akbar Jalali. "Robust H∞ control of stochastic linear systems with input delay by predictor feedback." Transactions of the Institute of Measurement and Control 40, no. 7 (2017): 2396–407. http://dx.doi.org/10.1177/0142331217708241.

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This study investigates the prediction-based (dynamic) stabilization of linear systems with input delay in the presence of external disturbances and multiplicative noise modelled as Itô type stochastic differential equations. Conventional memory-less (static) controllers are widely used for the stabilization of both deterministic and stochastic delayed systems. However, using these methods the upper bound for delay is strongly restricted. Motivated by acceptable performances of dynamic controllers for deterministic delayed systems, the extension of these methods for stochastic delayed systems is considered in this paper. The structure of the dynamic controller for stabilization of stochastic delayed systems is firstly derived utilizing the prediction vector. Then two sufficient conditions are given in the form of linear matrix inequalities that in the case of feasibility provide the stabilizing gain of the controller. Finally, simulation results are given to illustrate the effectiveness of the proposed method.
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SUN, L., and B. S. GREENBERG. "DYNAMIC RESPONSE OF LINEAR SYSTEMS TO MOVING STOCHASTIC SOURCES." Journal of Sound and Vibration 229, no. 4 (2000): 957–72. http://dx.doi.org/10.1006/jsvi.1999.2519.

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Lukashiv, Taras, Igor V. Malyk, Ahmed Abdelmonem Hemedan, and Venkata P. Satagopam. "Optimal Control of Stochastic Dynamic Systems with Semi-Markov Parameters." Symmetry 17, no. 4 (2025): 498. https://doi.org/10.3390/sym17040498.

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This paper extends classical Markov switching models. We introduce a generalized semi-Markov switching framework in which the system dynamics are governed by an Itô stochastic differential equation. Of note, the optimal control synthesis problem is formulated for stochastic dynamic systems with semi-Markov parameters. Further, a system of ordinary differential equations is derived to characterize the Bellman functional and the corresponding optimal control. We investigate the case of linear dynamics in detail, and propose a closed-form solution for the optimal control law. A numerical example is presented to illustrate the theoretical results.
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Rathore, Sandhya, Shambhu N. Sharma, Dhruvi Bhatt, and Shaival Nagarsheth. "Non-linear filtering for bilinear stochastic differential systems: A Stratonovich perspective." Transactions of the Institute of Measurement and Control 42, no. 10 (2020): 1755–68. http://dx.doi.org/10.1177/0142331219895711.

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Bilinear stochastic differential equations have found applications to model turbulence in autonomous systems as well as switching uncertainty in non-linear dynamic circuits. In signal processing and control literature, bilinear stochastic differential equations are ubiquitous, since they capture non-linear qualitative characteristics of dynamic systems as well as offer closed-form solutions. The novelties of the paper are two: we weave bilinear filtering for the Stratonovich stochasticity. Then this paper unfolds the usefulness of bilinear filtering for switched dynamic systems. First, the Stratonovich stochasticity is embedded into a vector ‘bilinear’ time-varying stochastic differential equations. Then, coupled non-linear filtering equations are achieved. Finally, the non-linear filtering results are applied to an appealing bilinear stochastic Ćuk converter circuit. This paper also encompasses a system of coupled bilinear filtering equations for the vector input Brownian motion case. This paper brings the notions of systems theory, that is, bilinearity, Stratonovich stochasticity, non-linear filtering techniques and switched electrical networks together. Numerical simulation results are presented to demonstrate that the proposed bilinear filter can achieve much better and accurate filtering performance than the conventional Extended Kalman Filter (EKF).
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Zhang, Huasheng, Changan Shao, Han Geng, and Tingting Zhang. "A Precise Stabilization Method for Linear Stochastic Time-Delay Systems." Actuators 11, no. 11 (2022): 325. http://dx.doi.org/10.3390/act11110325.

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Based on ensuring the steady-state performance of the system, some dynamic performance indicators that have not yet been realized in linear stochastic systems with time-delay are discussed in this paper. First, in view of the relationship between system eigenvalues and system performances, the region stability is provided, which can reflect the dynamic performance of the systems. Second, the design scheme of the region stabilization controller is given based on the region stability, so that the closed-loop system has the corresponding dynamic performance. Third, this paper also designs an algorithm to deal with the situation in which the eigenvalues are located in the non-connected region in order to obtain more accurate control system dynamic performance. Finally, an example shows how the precise control method dominates the dynamic performance of the system.
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Chang, R. J. "Two-stage optimal stochastic linearization in analyzing of non-linear stochastic dynamic systems." International Journal of Non-Linear Mechanics 58 (January 2014): 295–304. http://dx.doi.org/10.1016/j.ijnonlinmec.2013.10.002.

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Dissertations / Theses on the topic "Linear stochastic dynamic systems"

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Erbes, Teodora. "Stochastic Learning Feedback Hybrid Automata for Dynamic Power Management in Embedded Systems." Thesis, Virginia Tech, 2004. http://hdl.handle.net/10919/9709.

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Dynamic Power Management (DPM) refers to the strategies employed at system level to reduce energy expenditure (i.e. to prolong battery life) in embedded systems. The trade-off involved in DPM techniques is between the reductions of energy consumption and latency incurred by the jobs to be executed by the system. Such trade-offs need to be decided at runtime making DPM an on-line problem. In this context, the contributions of this thesis are two-fold. Firstly, we formulate the DPM problem as a hybrid automaton control problem. We model a timed hybrid automaton to mathematically analyze various opportunities in optimizing energy in a given system model. Secondly, stochastic control is added to the automata model, whose control strategy is learnt dynamically using stochastic learning automata (SLA). Several linear and non-linear feedback algorithms are incorporated in the final Stochastic Learning Hybrid Automata (SLHA) model. Simulation-based experiments show the expediency of the feedback systems in stationary environments. Further experiments are conducted using real trace data to compare stochastic learning strategies to the outcomes of several former predictive algorithms. These reveal that SLHA attains better trade-offs than the other studied methods under certain trace data. Advanced characterization of trace sequences, which allows a better performance of SLHA, is a subject of further study.<br>Master of Science
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Ranganathan, Shyam. "Non-linear dynamic modelling for panel data in the social sciences." Doctoral thesis, Uppsala universitet, Tillämpad matematik och statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-261289.

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Non-linearities and dynamic interactions between state variables are characteristic of complex social systems and processes. In this thesis, we present a new methodology to model these non-linearities and interactions from the large panel datasets available for some of these systems. We build macro-level statistical models that can verify theoretical predictions, and use polynomial basis functions so that each term in the model represents a specific mechanism. This bridges the existing gap between macro-level theories supported by statistical models and micro-level mechanistic models supported by behavioural evidence. We apply this methodology to two important problems in the social sciences, the demographic transition and the transition to democracy. The demographic transition is an important problem for economists and development scientists. Research has shown that economic growth reduces mortality and fertility rates, which reduction in turn results in faster economic growth. We build a non-linear dynamic model and show how this data-driven model extends existing mechanistic models. We also show policy applications for our models, especially in setting development targets for the Millennium Development Goals or the Sustainable Development Goals. The transition to democracy is an important problem for political scientists and sociologists. Research has shown that economic growth and overall human development transforms socio-cultural values and drives political institutions towards democracy. We model the interactions between the state variables and find that changes in institutional freedoms precedes changes in socio-cultural values. We show applications of our models in studying development traps. This thesis comprises the comprehensive summary and seven papers. Papers I and II describe two similar but complementary methodologies to build non-linear dynamic models from panel datasets. Papers III and IV deal with the demographic transition and policy applications. Papers V and VI describe the transition to democracy and applications. Paper VII describes an application to sustainable development.
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Pridham, Brad A. Wilson John C. "State space modeling and identification of stochastic linear structural systems." *McMaster only, 2004.

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Hanowsky, Michael John. "A model to design a stochastic and dynamic ground delay program subject to non-linear cost functions." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43849.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Engineering Systems Division, 2008.<br>Includes bibliographical references (p. 245-247).<br>When inclement weather reduces the arrival capacity of a busy metropolitan airport, it may lead to significant airborne delays. Delaying aircraft in the air consumes additional fuel, increases overall air traffic congestion, and may lead to costly flight diversions. As a result, during periods of inclement weather, the FAA may implement a Ground Delay Program (GDP) to proactively delay flights on the ground before they depart and reduce the possibility of future airborne delays. However, in order to assign ground delays to flights, a GDP must be implemented before they depart, at a time when the future airport arrival capacity may be uncertain. This dissertation discusses two analyses in regards to the design of a GDP. The first analysis proposes a model that solves for the optimal assignment of ground delay to aircraft for a stochastic and dynamic forecast of the airport arrival capacity, with nonlinear delay cost functions, and a capacity of the airborne arrival queue. This model is applied to several hypothetical examples and, in comparison to prior models from the literature, identifies solutions with a lower total expected cost, a smaller maximum observed arrival queue, or both. The second analysis compares the salience, or importance, of various stakeholder groups to their roles in the design of a GDP in practice. Passengers, in particular, are shown to be an important, but under-represented stakeholder group. A second model is proposed that solves for an assignment of ground delay that minimizes the total passenger delay cost. A comparison of these results to those of the first model show that the total cost of delays to passengers could be reduced by more than 30% if the FAA were to directly consider the cost of delays to passengers during the design of a GDP.<br>by Michael J. Hanowsky.<br>Ph.D.
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Beri, Stefano. "Stochastic dynamics in non-linear systems and maps with applications to the polarization dynamics in vertical cavity surface emitting lasers." Thesis, Lancaster University, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.423909.

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Schick, Ä°rvin C. (İrvin Cemil). "Robust recursive estimation of the state of a discrete-time stochastic linear dynamic system in the presence of heavy-tailed observation noise." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14323.

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Kasinos, Stavros. "Seismic response analysis of linear and nonlinear secondary structures." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/33728.

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Understanding the complex dynamics that underpin the response of structures in the occurrence of earthquakes is of paramount importance in ensuring community resilience. The operational continuity of structures is influenced by the performance of nonstructural components, also known as secondary structures. Inherent vulnerability characteristics, nonlinearities and uncertainties in their properties or in the excitation pose challenges that render their response determination as a non-straightforward task. This dissertation settles in the context of mathematical modelling and response quantification of seismically driven secondary systems. The case of bilinear hysteretic, rigid-plastic and free-standing rocking oscillators is first considered, as a representative class of secondary systems of distinct behaviour excited at a single point in the primary structure. The equations governing their full dynamic interaction with linear primary oscillators are derived with the purpose of assessing the appropriateness of simplified analysis methods where the secondary-primary feedback action is not accounted for. Analyses carried out in presence of pulse-type excitation have shown that the cascade approximation can be considered satisfactory for bilinear systems provided the secondary-primary mass ratio is adequately low and the system does not approach resonance. For the case of sliding and rocking systems, much lighter secondary systems need to be considered if the cascade analysis is to be adopted, with the validity of the approximation dictated by the selection of the input parameters. Based on the premise that decoupling is permitted, new analytical solutions are derived for the pulse driven nonlinear oscillators considered, conveniently expressing the seismic response as a function of the input parameters and the relative effects are quantified. An efficient numerical scheme for a general-type of excitation is also presented and is used in conjunction with an existing nonstationary stochastic far-field ground motion model to determine the seismic response spectra for the secondary oscillators at given site and earthquake characteristics. Prompted by the presence of uncertainty in the primary structure, and in line with the classical modal analysis, a novel approach for directly characterising uncertainty in the modal shapes, frequencies and damping ratios of the primary structure is proposed. A procedure is then presented for the identification of the model parameters and demonstrated with an application to linear steel frames with uncertain semi-rigid connections. It is shown that the proposed approach reduces the number of the uncertain input parameters and the size of the dynamic problem, and is thus particularly appealing for the stochastic assessment of existing structural systems, where partial modal information is available e.g. through operational modal analysis testing. Through a numerical example, the relative effect of stochasticity in a bi-directional seismic input is found to have a more prominent role on the nonlinear response of secondary oscillators when compared to the uncertainty in the primary structure. Further extending the analyses to the case of multi-attached linear secondary systems driven by deterministic seismic excitation, a convenient variant of the component-mode synthesis method is presented, whereby the primary-secondary dynamic interaction is accounted for through the modes of vibration of the two components. The problem of selecting the vibrational modes to be retained in analysis is then addressed for the case of secondary structures, which may possess numerous low frequency modes with negligible mass, and a modal correction method is adopted in view of the application for seismic analysis. The influence of various approaches to build the viscous damping matrix of the primary-secondary assembly is also investigated, and a novel technique based on modal damping superposition is proposed. Numerical applications are demonstrated through a piping secondary system multi-connected on a primary frame exhibiting various irregularities in plan and elevation, as well as a multi-connected flexible secondary system. Overall, this PhD thesis delivers new insights into the determination and understanding of the response of seismically driven secondary structures. The research is deemed to be of academic and professional engineering interest spanning several areas including seismic engineering, extreme events, structural health monitoring, risk mitigation and reliability analysis.
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Calmon, Andre du Pin. "Variação do controle como fonte de incerteza." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259270.

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Orientador: João Bosco Ribeiro do Val<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-08-14T00:07:24Z (GMT). No. of bitstreams: 1 Calmon_AndreduPin_M.pdf: 862345 bytes, checksum: 122780715dca28ac7fa3199aa0586e7c (MD5) Previous issue date: 2009<br>Resumo: Este trabalho apresenta a caracterização teórica e a estratégia de controle para sistemas estocásticos em tempo discreto onde a variação da ação de controle aumenta a incerteza sobre o estado (sistemas VCAI). Este tipo de sistema possui várias aplicações práticas, como em problemas de política monetária, medicina e, de forma geral, em problemas onde um modelo dinâmico completo do sistema é complexo demais para ser conhecido. Utilizando ferramentas da análise de funções não suaves, mostra-se para um sistema VCAI multidimensional que a convexidade é uma invariante da função valor da Programação Dinâmica quando o custo por estágio é convexo. Esta estratégia indica a existência de uma região no espaço de estados onde a ação ótima de controle é de não variação (denominada região de não-variação), estando de acordo com a natureza cautelosa do controle de sistemas subdeterminados. Adicionalmente, estudou-se algoritmos para a obtenção da política ótima de controle para sistemas VCAI, com ênfase no caso mono-entrada avaliado através de uma função custo quadrática. Finalmente, os resultados obtidos foram aplicados no problema da condução da política monetária pelo Banco Central.<br>Abstract: This dissertation presents a theoretical framework and the control strategy for discrete-time stochastic systems for which the control variations increase state uncertainty (CVIU systems). This type of system model can be useful in many practical situations, such as in monetary policy problems, medicine and biology, and, in general, in problems for which a complete dynamic model is too complex to be feasible. The optimal control strategy for a multidimensional CVIU system associated with a convex cost functional is devised using dynamic programming and tools from nonsmooth analysis. Furthermore, this strategy points to a region in the state space in which the optimal action is of no variation (the region of no variation), as expected from the cautionary nature of controlling underdetermined systems. Numerical strategies for obtaining the optimal policy in CVIU systems were developed, with focus on the single-input input case evaluated through a quadratic cost functional. These results are illustrated through a numerical example in economics.<br>Mestrado<br>Automação<br>Mestre em Engenharia Elétrica
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Graham, Don. "A Comparative evaluation of FDSA,GA, AND SA NON-LINEAR PROGRAMMING ALGORITHMS and development OF SYSTEM-OPTIMAL METHODOLOGY FOR DYNAMIC PRICING ON I-95 Express." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5940.

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As urban population across the globe increases, the demand for adequate transportation grows. Several strategies have been suggested as a solution to the congestion which results from this high demand outpacing the existing supply of transportation facilities. High –Occupancy Toll (HOT) lanes have become increasingly more popular as a feature on today's highway system. The I-95 Express HOT lane in Miami Florida, which is currently being expanded from a single Phase (Phase I) into two Phases, is one such HOT facility. With the growing abundance of such facilities comes the need for in- depth study of demand patterns and development of an appropriate pricing scheme which reduces congestion.This research develops a method for dynamic pricing on the I-95 HOT facility such as to minimize total travel time and reduce congestion. We apply non-linear programming (NLP) techniques and the finite difference stochastic approximation (FDSA), genetic algorithm (GA) and simulated annealing (SA) stochastic algorithms to formulate and solve the problem within a cell transmission framework. The solution produced is the optimal flow and optimal toll required to minimize total travel time and thus is the system-optimal solution. We perform a comparative evaluation of FDSA, GA and SA non-linear programming algorithms used to solve the NLP and the ANOVA results show that there are differences in the performance of the NLP algorithms in solving this problem and reducing travel time. We then conclude by demonstrating that econometric forecasting methods utilizing vector autoregressive (VAR) techniques can be applied to successfully forecast demand for Phase 2 of the 95 Express which is planned for 2014.<br>Ph.D.<br>Doctorate<br>Civil, Environmental, and Construction Engineering<br>Engineering and Computer Science<br>Civil Engineering
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Roy, Sandip 1978. "Moment-linear stochastic systems and their applications." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/87904.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.<br>Includes bibliographical references (p. 263-271).<br>Our work is motivated by the need for tractable stochastic models for complex network and system dynamics. With this motivation in mind, we develop a class of discrete-time Markov models, called moment-linear stochastic systems (MLSS), which are structured so that moments and cross-moments of the state variables can be computed efficiently, using linear recursions. We show that MLSS provide a common framework for representing and characterizing several models that are common in the literature, such as jump-linear systems, Markov-modulated Poisson processes, and infinite server queues. We also consider MLSS models for network interactions, and hence introduce moment-linear stochastic network (MLSN) models. Several potential applications for MLSN-in such areas as traffic flow modeling, queueing, and stochastic automata modeling-are explored. Fur- ther, we exploit the quasi-linear structure of MLSS and MLSN to analyze their asymptotic dynamics, and to construct linear minimum mean-square-error estimators and minimum quadratic cost controllers. Finally, we study in detail two examples of MLSN, a stochastic automaton called the influence model and an aggregate model for air traffic flows.<br>by Sandip Roy.<br>Ph.D.
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Books on the topic "Linear stochastic dynamic systems"

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Huang, Jen-Kuang. Indirect identification of linear stochastic systems with known feedback dynamics. National Aeronautics and Space Administration, 1997.

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Huang, Jen-Kuang. Indirect identification of linear stochastic systems with known feedback dynamics. National Aeronautics and Space Administration, 1997.

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Costa, Oswaldo L. V. Continuous-Time Markov Jump Linear Systems. Springer Berlin Heidelberg, 2013.

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Wolfgang, Kliemann, ed. Dynamical systems and linear algebra. American Mathematical Society, 2014.

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Caines, Peter E. Linear Stochastic Systems. Society for Industrial and Applied Mathematics, 2018. http://dx.doi.org/10.1137/1.9781611974713.

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Lindquist, Anders, and Giorgio Picci. Linear Stochastic Systems. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-45750-4.

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G, Chen. Linear stochastic control systems. CRC Press, 1995.

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Wang, Hong. Bounded Dynamic Stochastic Systems. Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0481-0.

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Ziegler, F., and G. I. Schuëller, eds. Nonlinear Stochastic Dynamic Engineering Systems. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-83334-2.

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Klein Haneveld, Willem K. Duality in Stochastic Linear and Dynamic Programming. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-51697-9.

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Book chapters on the topic "Linear stochastic dynamic systems"

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Thygesen, Uffe Høgsbro. "Linear Dynamic Systems." In Stochastic Differential Equations for Science and Engineering. Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003277569-5.

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Schuëller, G. I. "Stochastic Dynamic Analysis of Linear Systems." In Stochastic Methods in Structural Dynamics. Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3681-2_2.

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Pardoux, Etienne, and Denis Talay. "Stability of Linear Differential Systems with Parametric Excitation." In Nonlinear Stochastic Dynamic Engineering Systems. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-83334-2_11.

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Kozin, F. "The Method of Statistical Linearization for Non-Linear Stochastic Vibrations." In Nonlinear Stochastic Dynamic Engineering Systems. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-83334-2_4.

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Isermann, Rolf, and Marco Münchhof. "Mathematical Models of Linear Dynamic Systems and Stochastic Signals." In Identification of Dynamic Systems. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-540-78879-9_2.

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Socha, Leslaw. "Moment Equations for Linear Stochastic Dynamic Systems (LSDS)." In Linearization Methods for Stochastic Dynamic Systems. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-72997-6_3.

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Muscolino, G. "Response of Linear and Non-Linear Structural Systems under Gaussian or Non-Gaussian Filtered Input." In Dynamic Motion: Chaotic and Stochastic Behaviour. Springer Vienna, 1993. http://dx.doi.org/10.1007/978-3-7091-2682-0_6.

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Ruszczynski, Andrzej. "Modern Techniques for Linear Dynamic and Stochastic Programs." In Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-21637-8_3.

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Loucks, Daniel P. "Modeling Stochastic Processes." In International Series in Operations Research & Management Science. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-93986-1_13.

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AbstractMany public systems must deal with uncertain inputs over time. This chapter illustrates how models incorporating uncertain inputs over time can be developed and solved. Stochastic linear and dynamic programming models are developed to show the difference in output that define optimal sequential conditional decision making strategies.
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de Oliveria, A. M., O. L. V. Costa, and J. Daafouz. "H2 Dynamic Output Feedback Control for Hidden Markov Jump Linear Systems." In Modeling, Stochastic Control, Optimization, and Applications. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25498-8_21.

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Conference papers on the topic "Linear stochastic dynamic systems"

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Mukaidani, Hiroaki, Ippo Ishibashi, and Shouhei Furuya. "Pareto Optimal Control for Uncertain Markov Jump Linear Stochastic Systems." In International Conference of Control, Dynamic Systems, and Robotics. Avestia Publishing, 2017. http://dx.doi.org/10.11159/cdsr17.102.

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Bian, Tao, and Zhong-Ping Jiang. "Robust adaptive dynamic programming for continuous-time linear stochastic systems." In 2014 IEEE International Symposium on Intelligent Control (ISIC). IEEE, 2014. http://dx.doi.org/10.1109/isic.2014.6967601.

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CHEN, CHUNG-WEN, JEN-KUANG HUANG, and JER-NAN JUANG. "Identification of linear stochastic systems through projection filters." In 33rd Structures, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 1992. http://dx.doi.org/10.2514/6.1992-2520.

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Whiteman, R. R., J. Diggins, V. Schöllmann, et al. "Non-linear quantum mechanical ground state SQUID magnetometer dynamics." In Applied nonlinear dynamics and stochastic systems near the millenium. AIP, 1997. http://dx.doi.org/10.1063/1.54234.

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Ramakrishnan, Subramanian, and Connor Edlund. "Stochastic Stability of a Piezoelectric Vibration Energy Harvester and Stabilization Using Noise." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9216.

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Vibration energy harvesters convert the energy of ambient, random vibration into electrical power often using piezoelectric transduction. The stochastic dynamics of a piezoelectric harvester with parameteric uncertainties is yet to be fully explored in the nonequilibrium regime. Motivated by mathematical results that establish the counterintuitive phenomenon of stabilization of response in certain nonlinear systems using noise, we investigate the stochastic stability of a generic harvester in the linear and the monostable nonlinear regimes excited by multiplicative noise characterized by both Brownian and the Lévy stable distributions. First, a lower bound on the magnitude of noise intensity that guarantees exponential stability almost surely, is obtained analytically as an inequality in terms of system parameters in the linear case. This result is validated numerically using the Euler-Maruyama scheme. Next, noise-induced stabilization in the harvester dynamics is demonstrated numerically for both the linear and nonlinear cases wherein Lévy noise was found to achieve stabilization at lower noise intensities than Brownian noise. Additionally, the inclusion of a nonlinear stiffness does not have an appreciable affect on the stabilization behavior. The results indicate that stabilization may be achieved using noise and are expected to be useful in harvester design.
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Mehr, Negar, and Roberto Horowitz. "Probabilistic Freeway Ramp Metering." In ASME 2016 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/dscc2016-9827.

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Ramp metering is proved to be an effective strategy for reducing or avoiding freeway traffic congestion. As a result, huge amount of research has been conducted on synthesizing effective ramp metering controls. In the previous works, freeway is assumed to be a deterministic system which is in contrast with the intrinsic stochastic nature and behavior of freeways. Our work focuses on bridging this gap, and we propose a framework for freeway ramp metering in a probabilistic setting. Our algorithm finds onramp flows in a freeway network while treating exogenous vehicular arrivals as random variables with known distributions, allowing for the network arrivals to conform with their stochastic nature. We use sampling techniques in a model predictive control setup to formulate a tractable approximation of our stochastic optimization. Furthermore, we demonstrate how to relax the non-linear constraints of our optimization to create a linear program with an augmented set of constraints. We prove that the solution of our linear program formulation is the same as the solution of the original mixed-integer formulation. We showcase the results of our algorithm on an exemplar freeway network and introduce multiple interesting future research directions that are important and can be pursued solely in a stochastic framework.
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Ghorbanian, Parham, Subramanian Ramakrishnan, Adam J. Simon, and Hashem Ashrafiuon. "Stochastic Dynamic Modeling of the Human Brain EEG Signal." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3881.

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The occurrence and risk of recurrence of brain related injuries and diseases are difficult to characterize due to various factors including inter-individual variability. A useful approach is to analyze the brain electroencephalogram (EEG) for differences in brain frequency bands in the signals obtained from potentially injured and healthy normal subjects. However, significant shortcomings include: (1) contrary to empirical evidence, current spectral signal analysis based methods often assume that the EEG signal is linear and stationary; (2) nonlinear time series analysis methods are mostly numerical and do not possess any predictive features. In this work, we develop models based on stochastic differential equations that can output signals with similar frequency and magnitude characteristics of the brain EEG. Initially, a coupled linear oscillator model with a large number of degrees of freedom is developed and shown to capture the characteristics of the EEG signal in the major brain frequency bands. Then, a nonlinear stochastic model based on the Duffing oscillator with far fewer degrees of freedom is developed and shown to produce outputs that can closely match the EEG signal. It is shown that such a compact nonlinear model can provide better insight into EEG dynamics through only few parameters, which is a step towards developing a framework with predictive capabilities for addressing brain injuries.
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Adhikari, Sondipon. "Joint Distribution of Eigenvalues of Linear Stochastic Systems." In 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-1988.

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HomChaudhuri, Baisravan. "Distributionally Robust Stochastic Model Predictive Control for Collision Avoidance." In ASME 2019 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/dscc2019-9160.

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Abstract This paper focuses on distributionally robust controller design for avoiding dynamic and stochastic obstacles whose exact probability distribution is unknown. The true probability distribution of the disturbance associated with an obstacle, although unknown, is considered to belong to an ambiguity set that includes all the probability distributions that share the same first two moment. The controller thus focuses on ensuring the satisfaction of the probabilistic collision avoidance constraints for all probability distributions in the ambiguity set, hence making the solution robust to the true probability distribution of the stochastic obstacles. Techniques from robust optimization methods are used to model the distributionally robust probabilistic or chance constraints as a semi-definite programming (SDP) problem with linear matrix inequality (LMI) constraints that can be solved in a computationally tractable fashion. Simulation results for a robot obstacle avoidance problem shows the efficacy of our method.
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Ramakrishnan, Subramanian, Collin Lambrecht, and Connor Edlund. "Stochastic Dynamics of a Piezoelectric Energy Harvester Subjected to Lévy Flight Excitations." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5404.

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Vibration energy harvesting seeks to exploit the energy of ambient random vibration for power generation, particularly in small scale devices. Piezoelectric transduction is often used as a conversion mechanism in harvesting and the random excitation is typically modeled as a Brownian stochastic process. However, non-Brownian excitations are of potential interest, particularly in the nonequilibrium regime of harvester dynamics. In this work, we investigate the averaged power output of a generic piezoelectric harvester driven by Brownian as well as (non-Brownian) Lévy stable excitations both in the linear and the Duffing regimes. First, a coupled system of stochastic differential equations that model the electromechanical system are presented. Numerical simulation results (based on the Euler-Maruyama scheme) that show the average power output from the system under Brownian and Lévy excitations are presented for the cases where the mechanical degree of freedom behaves as a linear as well as a Duffing oscillator. The results demonstrate that Lévy excitations result in higher expectation values of harvested power. In particular, increasing the noise intensity leads to significant increase in power output in the Levy case when compared with Brownian excitations.
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Reports on the topic "Linear stochastic dynamic systems"

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Perdigão, Rui A. P. New Horizons of Predictability in Complex Dynamical Systems: From Fundamental Physics to Climate and Society. Meteoceanics, 2021. http://dx.doi.org/10.46337/211021.

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Discerning the dynamics of complex systems in a mathematically rigorous and physically consistent manner is as fascinating as intimidating of a challenge, stirring deeply and intrinsically with the most fundamental Physics, while at the same time percolating through the deepest meanders of quotidian life. The socio-natural coevolution in climate dynamics is an example of that, exhibiting a striking articulation between governing principles and free will, in a stochastic-dynamic resonance that goes way beyond a reductionist dichotomy between cosmos and chaos. Subjacent to the conceptual and operational interdisciplinarity of that challenge, lies the simple formal elegance of a lingua franca for communication with Nature. This emerges from the innermost mathematical core of the Physics of Coevolutionary Complex Systems, articulating the wealth of insights and flavours from frontier natural, social and technical sciences in a coherent, integrated manner. Communicating thus with Nature, we equip ourselves with formal tools to better appreciate and discern complexity, by deciphering a synergistic codex underlying its emergence and dynamics. Thereby opening new pathways to see the “invisible” and predict the “unpredictable” – including relative to emergent non-recurrent phenomena such as irreversible transformations and extreme geophysical events in a changing climate. Frontier advances will be shared pertaining a dynamic that translates not only the formal, aesthetical and functional beauty of the Physics of Coevolutionary Complex Systems, but also enables and capacitates the analysis, modelling and decision support in crucial matters for the environment and society. By taking our emerging Physics in an optic of operational empowerment, some of our pioneering advances will be addressed such as the intelligence system Earth System Dynamic Intelligence and the Meteoceanics QITES Constellation, at the interface between frontier non-linear dynamics and emerging quantum technologies, to take the pulse of our planet, including in the detection and early warning of extreme geophysical events from Space.
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Perdigão, Rui A. P. Earth System Dynamic Intelligence with Quantum Technologies: Seeing the “Invisible”, Predicting the “Unpredictable” in a Critically Changing World. Meteoceanics, 2021. http://dx.doi.org/10.46337/211028.

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We hereby embark on a frontier journey articulating two of our flagship programs – “Earth System Dynamic Intelligence” and “Quantum Information Technologies in the Earth Sciences” – to take the pulse of our planet and discern its manifold complexity in a critically changing world. Going beyond the traditional stochastic-dynamic, information-theoretic, artificial intelligence, mechanistic and hybrid approaches to information and complexity, the underlying fundamental science ignites disruptive developments empowering complex problem solving across frontier natural, social and technical geosciences. Taking aim at complex multiscale planetary problems, the roles of our flagships are put into evidence in different contexts, ranging from I) Interdisciplinary analytics, model design and dynamic prediction of hydro-climatic and broader geophysical criticalities and extremes across multiple spatiotemporal scales; to II) Sensing the pulse of our planet and detecting early warning signs of geophysical phenomena from Space with our Meteoceanics QITES Constellation, at the interface between our latest developments in non-linear dynamics and emerging quantum technologies.
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Venkatachalapathy, Rajesh. Systems Isomorphisms in Stochastic Dynamic Systems. Portland State University Library, 2019. http://dx.doi.org/10.15760/etd.7283.

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McKeague, Ian W., and Tiziano Tofoni. Nonparametric Estimation of Trends in Linear Stochastic Systems. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada213741.

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Cruz, Jose B., Basar Jr., and Tamer. Stochastic Dynamic Systems with Multiple Decision Makers and Parametric Uncertainties. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada179382.

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Willsky, Alan S., and George C. Verghese. Asymptotic Methods for the Analysis, Estimation, and Control of Stochastic Dynamic Systems. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada166234.

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Tunc Aldemir, Don W. Miller, Brian k. Hajek, and Peng Wang. Development of a Probabilistic Technique for On-line Parameter and State Estimation in Non-linear Dynamic Systems. Office of Scientific and Technical Information (OSTI), 2002. http://dx.doi.org/10.2172/793324.

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Perdigão, Rui A. P., and Julia Hall. Spatiotemporal Causality and Predictability Beyond Recurrence Collapse in Complex Coevolutionary Systems. Meteoceanics, 2020. http://dx.doi.org/10.46337/201111.

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Causality and Predictability of Complex Systems pose fundamental challenges even under well-defined structural stochastic-dynamic conditions where the laws of motion and system symmetries are known. However, the edifice of complexity can be profoundly transformed by structural-functional coevolution and non-recurrent elusive mechanisms changing the very same invariants of motion that had been taken for granted. This leads to recurrence collapse and memory loss, precluding the ability of traditional stochastic-dynamic and information-theoretic metrics to provide reliable information about the non-recurrent emergence of fundamental new properties absent from the a priori kinematic geometric and statistical features. Unveiling causal mechanisms and eliciting system dynamic predictability under such challenging conditions is not only a fundamental problem in mathematical and statistical physics, but also one of critical importance to dynamic modelling, risk assessment and decision support e.g. regarding non-recurrent critical transitions and extreme events. In order to address these challenges, generalized metrics in non-ergodic information physics are hereby introduced for unveiling elusive dynamics, causality and predictability of complex dynamical systems undergoing far-from-equilibrium structural-functional coevolution. With these methodological developments at hand, hidden dynamic information is hereby brought out and explicitly quantified even beyond post-critical regime collapse, long after statistical information is lost. The added causal insights and operational predictive value are further highlighted by evaluating the new information metrics among statistically independent variables, where traditional techniques therefore find no information links. Notwithstanding the factorability of the distributions associated to the aforementioned independent variables, synergistic and redundant information are found to emerge from microphysical, event-scale codependencies in far-from-equilibrium nonlinear statistical mechanics. The findings are illustrated to shed light onto fundamental causal mechanisms and unveil elusive dynamic predictability of non-recurrent critical transitions and extreme events across multiscale hydro-climatic problems.
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Emiliano, Diaz, and Jaspreet Singh. From linear insights to systemic solutions: the future of behavioral science. Busara, 2024. https://doi.org/10.62372/cesi7494.

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Behavioral Science has traditionally focused on understanding and influencing human behavior by identifying factors driving specific and directly related decisions. This linear approach, simplifies complex scenarios into isolated variables, and has provided the foundational insights for developing targeted interventions. While this perspective has proven effective in many cases, it may only sometimes fully capture the broader context in which behaviors occur, as a linear understanding alone is insufficient to grasp the complexities of human behavior fully. It misses important considerations like ripple effects and second-order effects. This is where systems thinking emerges as a valuable complement to applied behavioral science. By shifting from a singular, cause-and-effect perspective to a multi-layered, multidimensional approach, systems thinking allows us to see behavior not as an isolated event but as part of a broader system influenced by many interconnected factors that interact in dynamic and often unpredictable ways.
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Chen, Xin, Yanfeng Ouyang, Ebrahim Arian, Haolin Yang, and Xingyu Ba. Modeling and Testing Autonomous and Shared Multimodal Mobility Services for Low-Density Rural Areas. Illinois Center for Transportation, 2022. http://dx.doi.org/10.36501/0197-9191/22-013.

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Recent developments in transformative technologies hold the promise to provide holistic solutions for affordable transportation services to rural areas and thus greatly alleviate existing social inequality through efficient planning and management of complex transportation systems and systemwide interactions among multiple modes. To realize the promise, many challenging research questions need to be addressed, which often leads to computationally intractable, large-scale, dynamic/stochastic, discrete optimization models. This project proposes to address some of the challenges by building a series of holistic and tractable models on the design of mobility services, capacity planning, dynamic matching, and routing, as well as pricing. The proposed project is expected to create a new series of planning and management models that can support strategical and operational decisions for large-scale autonomous and shared mobility systems in rural areas. The planned case study and simulation for the Village of Rantoul, Illinois, will lay the foundation for future field implementation.
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