Relevant bibliographies by topics / Controlled invariant set

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Controlled invariant set'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Controlled invariant set"

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O’Dell, Brian D., and Eduardo A. Misawa. "Semi-Ellipsoidal Controlled Invariant Sets for Constrained Linear Systems." Journal of Dynamic Systems, Measurement, and Control 124, no. 1 (April 17, 2000): 98–103. http://dx.doi.org/10.1115/1.1434269.

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This paper investigates an alternative approximation to the maximal viability set for linear systems with constrained states and input. Current ellipsoidal and polyhedral approximations are either too conservative or too complex for many applications. As the primary contribution, it is shown that the intersection of a controlled invariant ellipsoid and a set of state constraints (referred to as a semi-ellipsoidal set) is itself controlled invariant under certain conditions. The proposed semi-ellipsoidal approach is less conservative than the ellipsoidal method but simpler than the polyhedral method. Two examples serve as proof-of-concept of the approach.
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Korda, Milan, Didier Henrion, and Colin N. Jones. "Convex Computation of the Maximum Controlled Invariant Set For Polynomial Control Systems." SIAM Journal on Control and Optimization 52, no. 5 (January 2014): 2944–69. http://dx.doi.org/10.1137/130914565.

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Németh, Balázs, Péter Gáspár, and Tamás Péni. "Nonlinear analysis of vehicle control actuations based on controlled invariant sets." International Journal of Applied Mathematics and Computer Science 26, no. 1 (March 1, 2016): 31–43. http://dx.doi.org/10.1515/amcs-2016-0003.

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Abstract In the paper, an analysis method is applied to the lateral stabilization problem of vehicle systems. The aim is to find the largest state-space region in which the lateral stability of the vehicle can be guaranteed by the peak-bounded control input. In the analysis, the nonlinear polynomial sum-of-squares programming method is applied. A practical computation technique is developed to calculate the maximum controlled invariant set of the system. The method calculates the maximum controlled invariant sets of the steering and braking control systems at various velocities and road conditions. Illustration examples show that, depending on the environments, different vehicle dynamic regions can be reached and stabilized by these controllers. The results can be applied to the theoretical basis of their interventions into the vehicle control system.
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Dambrine, M., J. P. Richard, and P. Borne. "Feedback control of time-delay systems with bounded control and state." Mathematical Problems in Engineering 1, no. 1 (1995): 77–87. http://dx.doi.org/10.1155/s1024123x95000081.

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This paper is concerned with the problem of stabilizing linear time-delay systems under state and control linear constraints. For this, necessary and sufficient conditions for a given non-symmetrical polyhedral set to be positively invariant are obtained. Then existence conditions of linear state feedback control law respecting the constraints are established, and a procedure is given in order to calculate such a controller. The paper concerns memoryless controlled systems but the results can be applied to cases of delayed controlled systems. An example is given.
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Isik, Leyla, Andrea Tacchetti, and Tomaso Poggio. "A fast, invariant representation for human action in the visual system." Journal of Neurophysiology 119, no. 2 (February 1, 2018): 631–40. http://dx.doi.org/10.1152/jn.00642.2017.

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Humans can effortlessly recognize others’ actions in the presence of complex transformations, such as changes in viewpoint. Several studies have located the regions in the brain involved in invariant action recognition; however, the underlying neural computations remain poorly understood. We use magnetoencephalography decoding and a data set of well-controlled, naturalistic videos of five actions (run, walk, jump, eat, drink) performed by different actors at different viewpoints to study the computational steps used to recognize actions across complex transformations. In particular, we ask when the brain discriminates between different actions, and when it does so in a manner that is invariant to changes in 3D viewpoint. We measure the latency difference between invariant and noninvariant action decoding when subjects view full videos as well as form-depleted and motion-depleted stimuli. We were unable to detect a difference in decoding latency or temporal profile between invariant and noninvariant action recognition in full videos. However, when either form or motion information is removed from the stimulus set, we observe a decrease and delay in invariant action decoding. Our results suggest that the brain recognizes actions and builds invariance to complex transformations at the same time and that both form and motion information are crucial for fast, invariant action recognition. NEW & NOTEWORTHY The human brain can quickly recognize actions despite transformations that change their visual appearance. We use neural timing data to uncover the computations underlying this ability. We find that within 200 ms action can be read out of magnetoencephalography data and that this representation is invariant to changes in viewpoint. We find form and motion are needed for this fast action decoding, suggesting that the brain quickly integrates complex spatiotemporal features to form invariant action representations.
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Romig, Swantje, Luc Jaulin, and Andreas Rauh. "Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System." Algorithms 12, no. 12 (December 6, 2019): 262. http://dx.doi.org/10.3390/a12120262.

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In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly accurate numerical computations over simulating guaranteed enclosures of all reachable states of a dynamic system model with bounded uncertainty in parameters and initial conditions, to the solution of global optimization tasks. By exploiting the fundamental enclosure properties of interval analysis, this paper aims at computing invariant sets of nonlinear closed-loop control systems. For that purpose, Lyapunov-like functions and interval analysis are combined in a novel manner. To demonstrate the proposed techniques for enclosing invariant sets, the systems examined in this paper are controlled via sliding mode techniques with subsequently enclosing the invariant sets by an interval based set inversion technique. The applied methods for the control synthesis make use of a suitably chosen Gröbner basis, which is employed to solve Bézout’s identity. Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets.
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Lakshmikantham, V., and Z. Drici. "Stability of conditionally invariant sets and controlled uncertain dynamic systems on time scales." Mathematical Problems in Engineering 1, no. 1 (1995): 1–10. http://dx.doi.org/10.1155/s1024123x95000020.

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A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.
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Leonessa, Alexander, Wassim M. Haddad, and Vijaysekhar Chellaboina. "Nonlinear robust hierarchical control for nonlinear uncertain systems." Mathematical Problems in Engineering 5, no. 6 (2000): 499–542. http://dx.doi.org/10.1155/s1024123x99001210.

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A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous) Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
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Awad, Osama Ali. "A SWITCHING GAIN CONTROLLER IN DRSIGNING OPTIMUM CONSTRAINT CONTROL PROBLEMS BASED ON GENETIC ALGORITHM." Iraqi Journal of Information & Communications Technology 4, no. 1 (May 3, 2021): 31–44. http://dx.doi.org/10.31987/ijict.4.1.142.

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This paper introduces an iterative approach for the design of an optimum switching gain controller for a linear time invariant single input/single output (SISO) systems. The controller parameters are determined at different switching instants so as to improve the dynamic characteristics of a closed loop system and satisfy a set of inequalities. The approach is based on solving a constrained parameter optimization problem. Optimization is carried out based on the genetic algorithm (GA) in order to find the optimum number of switching, optimum switching instants and optimum controller parameters vector. All that in the sense of minimizing a certain time based objective function and satisfying a set of parametric and operating constraints. Constraints imposed on the controlled system may be in the form of design specifications and/or performance requirements. The technique is applicable for any controller structure, and gives a set of an optimum parameter values switched at optimum switching instants. Parameter values are function of the system states at these instants. Different systems are examined to show the applicability of the presented approach.
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Dantas, Amanda Danielle O. da S., André Felipe O. de A. Dantas, João Tiago L. S. Campos, Domingos L. de Almeida Neto, and Carlos Eduardo T. Dórea. "PID Control for Electric Vehicles Subject to Control and Speed Signal Constraints." Journal of Control Science and Engineering 2018 (August 1, 2018): 1–11. http://dx.doi.org/10.1155/2018/6259049.

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A PID control for electric vehicles subject to input armature voltage and angular velocity signal constraints is proposed. A PID controller for a vehicle DC motor with a separately excited field winding considering the field current constant was tuned using controlled invariant set and multiparametric programming concepts to consider the physical motor constraints as angular velocity and input armature voltage. Additionally, the integral of the error, derivative of the error constraints, and λ were considered in the proposed algorithm as tuning parameters to analyze the DC motor dynamic behaviors. The results showed that the proposed algorithm can be used to generate control actions taking into account the armature voltage and angular velocity limits. Also, results demonstrate that a controller subject to constraints can improve the electric vehicle DC motor dynamic; and at the same time it protects the motor from overvoltage.
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Dissertations / Theses on the topic "Controlled invariant set"

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Gao, Yulong. "Stochastic Invariance and Aperiodic Control for Uncertain Constrained Systems." Licentiate thesis, KTH, Reglerteknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-236072.

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Uncertainties and constraints are present in most control systems. For example, robot motion planning and building climate regulation can be modeled as uncertain constrained systems. In this thesis, we develop mathematical and computational tools to analyze and synthesize controllers for such systems. As our first contribution, we characterize when a set is a probabilistic controlled invariant set and we develop tools to compute such sets. A probabilistic controlled invariantset is a set within which the controller is able to keep the system state with a certainprobability. It is a natural complement to the existing notion of robust controlled invariantsets. We provide iterative algorithms to compute a probabilistic controlled invariantset within a given set based on stochastic backward reachability. We prove that thesealgorithms are computationally tractable and converge in a finite number of iterations. The computational tools are demonstrated on examples of motion planning, climate regulation, and model predictive control. As our second contribution, we address the control design problem for uncertain constrained systems with aperiodic sensing and actuation. Firstly, we propose a stochastic self-triggered model predictive control algorithm for linear systems subject to exogenous disturbances and probabilistic constraints. We prove that probabilistic constraint satisfaction, recursive feasibility, and closed-loop stability can be guaranteed. The control algorithm is computationally tractable as we are able to reformulate the problem into a quadratic program. Secondly, we develop a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. In the particular case when there is no uncertainty, the design leads to a control system requiring minimum number of samples over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as mixed integer linear programs. The method is applied to a motion planning problem with temporal constraints.

QC 20181016

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Narasimhan, Bharat. "An automated virtual tool to compute the entire set of proportional integral derivative controllers for a continuous linear time invariant system." Texas A&M University, 2007. http://hdl.handle.net/1969.1/85831.

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This thesis presents the very practical and novel approach of using the Graphical User Interface (GUI) to compute the entire set of Proportional Integral Derivative (PID) controllers given the transfer function or the frequency response of the system under consideration. Though there is a wide spread usage of PID controllers in the industry, until recently no formal algorithm existed on determining a set of PID values that will stabilize the given system. The industry still relies on algorithms like the Ziegler- Nicholas or ad-hoc approaches in determining the value of PID controllers. Also when it comes to model free approaches, the use of Fuzzy logic and Neural network do not guarantee stability of the system. For a continuous Linear Time Invariant system Bhattacharyya and others have developed an algorithm that determines the entire set of PID controllers given the transfer function or just the frequency response of the system. The GUI has been developed based on this theory. The GUI also evaluates the user input performance specifications and generates a subset of stable controllers given the performance criteria for the system. This thesis presents an approach of automating the computation of entire set of stabilizing Proportional Integral Derivative (PID) controllers given the system transfer function or the frequency response data of the system. The Graphical User Interface (GUI) developed bridges the gap between the developed theory and the industry.
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Book chapters on the topic "Controlled invariant set"

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Olaru, Sorin, Nikola Stanković, Georges Bitsoris, and Silviu-Iulian Niculescu. "Low Complexity Invariant Sets for Time-Delay Systems: A Set Factorization Approach." In Low-Complexity Controllers for Time-Delay Systems, 127–39. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05576-3_9.

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Bayoumi, Ehab Hassan Eid, Hisham Soliman, and Farag El-Sheikhi. "Robust Decentralized Voltage Tracker of Islanded Multi-DG AC Microgrids Using Invariant Ellipsoids." In Advances in Environmental Engineering and Green Technologies, 1–35. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-7447-8.ch001.

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This chapter develops a robust decentralized voltage tracker for islanded MGs. The proposed controller is robust against the plug and play operation of the MG, loads, and line parameter uncertainties. The problem is solved in the framework of linear matrix inequality (LMI). The proposed robust control represents the load changes and the parameter variations of lines connecting the DGs as a norm-bounded uncertainty. The proposed controller utilizes local measurements from DGs (i.e., it is totally decentralized). Control decentralization is accomplished by decomposing the global system into subsystems. The effect of the rest of the system on a specific subsystem is considered as a disturbance to minimize (disturbance rejection control). The controller is designed by the invariant-sets (approximated by the invariant ellipsoids). Different time-domain simulations are carried out as connecting and disconnected one or more DGs, connecting and disconnecting local loads DGs and transmission line parameters variation.
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Haddad, Wassim M., and Sergey G. Nersesov. "Coordination Control for Multiagent Interconnected Systems." In Stability and Control of Large-Scale Dynamical Systems. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691153469.003.0007.

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This chapter describes a stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems. The framework is applied to the problem of coordination control for multiagent interconnected systems predicated on vector Lyapunov functions. In multiagent systems, several Lyapunov functions arise naturally where each agent can be associated with a generalized energy function corresponding to a component of a vector Lyapunov function. The chapter characterizes a moving formation of vehicles as a time-varying set in the state space to develop a distributed control design framework for multivehicle coordinated motion control by designing stabilizing controllers for time-varying sets of nonlinear dynamical systems. The proposed cooperative control algorithms are shown to globally exponentially stabilize both moving and static formations.
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Conference papers on the topic "Controlled invariant set"

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Ying Shang. "The maximal robust controlled invariant set of uncertain switched systems." In Proceedings of the 2004 American Control Conference. IEEE, 2004. http://dx.doi.org/10.23919/acc.2004.1384677.

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Korda, Milan, Didier Henrion, and Colin N. Jones. "Convex computation of the maximum controlled invariant set for discrete-time polynomial control systems." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6761016.

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Athanasopoulos, Nikolaos, and George Bitsoris. "A novel approach to the computation of the maximal controlled invariant set for constrained linear systems." In 2009 European Control Conference (ECC). IEEE, 2009. http://dx.doi.org/10.23919/ecc.2009.7074885.

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Pumhoessel, Thomas, Peter Hehenberger, and Klaus Zeman. "Preserving Stability Properties in Reduced Models of Time-Periodic Systems Using Proper Orthogonal Decomposition." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63435.

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The necessity of providing reduced models of dynamical systems is growing continuously. Model-based control and model-based design are exemplary fields of applications. In this contribution, the reduction of a controlled drivetrain of a rolling mill using the method of Proper Orthogonal Decomposition is investigated, where the specific choice of the control law leads to equations of motion with time-periodic coefficients. Depending on amplitudes and frequency parameters of the time-periodic coefficients, artificial damping is introduced, referred to as parametric control. The maximum damping effect depends on these parameters in a nonlinear manner, as it is shown by means of a stability-parameter from Floquet theory. The reduced model set-up approximates the stability-parameter of the full model in an appropriate way within a wide range of the parameters. A measure based on the linear time-invariant system is developed that gives insight into the effect of the simulated timeseries on the properties of the reduced model.
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Huang, Yiwen, and Yan Chen. "Switched Control Barrier Function With Applications to Vehicle Safety Control." In ASME 2020 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/dscc2020-3293.

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Abstract For safety-critical systems, the safety constraints are required to be satisfied through control design. To describe and apply system safety constraints, controlled invariant set (CIS) and control barrier function (CBF) are effective methods. In many applications, safety constraints may change dynamicly in operation environment and thus are not always continuous. However, such discontinuity and switching problems of CIS and CBF were well-addressed in the literature. In this paper, to tackle the issues, novel definitions of switched CIS (SCIS) and switched CBF (SCBF) are proposed. To address the undifferentiability issue in SCBF, a novel relaxation function that connects different SCISs is proposed. Sufficient conditions for selecting the relaxation function are proposed with a rigorous proof. In the application of vehicle safety control for an obstacle avoidance problem, a relaxation function is selected and demonstrated in the safety control design. To evaluate the effectiveness of the proposed definitions and control design, simulation results are presented and discussed.
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Wallace, Jon M., and Dimitri N. Mavris. "Simulation-Based Parametric Reliability Modeling Using Covariate Theory." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-43945.

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Reliability analysis methods used for preliminary safety assessments of complex systems typically assume a predetermined and invariant set of input variable statistical properties. However, during the product development phase of the system and especially during in service operation, the characteristics of the random variables can themselves be subject to variation. Thus, the resulting failure probability distribution can vary greatly from early predictions. The objective of this paper is to explore a technique used to create a general parametric failure probability distribution as a function of key variables. This technique is constructed around covariate theory which is the basis of the familiar Accelerated Life Testing and Proportional Hazards Modeling approaches. Where these approaches have traditionally been used with physical experiments, they are applied within this study to Monte Carlo simulation data generated using an available component modeling and simulation environment of a gas turbine airfoil limited by a single failure mode. Necessary modifications to the traditional from of the covariate approach are identified for application to controlled Monte Carlo simulation data. Implications to potential safety improvements early on in the product development phase are discussed.
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Diaz-Rodriguez, Ivan, Daniel N. Mohsenizadeh, and Shankar P. Bhattacharyya. "Experimental PID Controller Design: A New Frequency Domain Approach Based on Desired Performance." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6323.

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This paper presents an alternative approach to design PID controllers based on frequency response measurements. The proposed method does not require any mathematical model of the system and can handle the design process directly from a small set of frequency domain data. It is shown that for the class of Linear Time-Invariant (LTI) control systems, there exists a rational multilinear function for the frequency response between any two arbitrary breaking points in terms of the design controller. This function can be determined by conducting a small set of frequency response measurements and then will be used to synthesize a controller that guarantee a set of desired frequency-domain specifications. In this paper, we use this result to design a PID controller for a servomechanism control system. In particular, we show that such desirable PID controller can be calculated by solving an optimization problem.
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Gurriet, Thomas, Mark Mote, Andrew Singletary, Eric Feron, and Aaron D. Ames. "A Scalable Controlled Set Invariance Framework with Practical Safety Guarantees." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9030159.

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Pin, Gilberto, and Thomas Parisini. "Set invariance under controlled nonlinear dynamics with application to robust RH control." In 2008 47th IEEE Conference on Decision and Control. IEEE, 2008. http://dx.doi.org/10.1109/cdc.2008.4739484.

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C. C. Oliveira, Andreza, Fábio Leoli Júnior, and Carlos E.T. Dórea. "Cálculo de Conjuntos Invariantes Controlados Robustos com Complexidade Fixa usando Otimização Bilinear." In Congresso Brasileiro de Automática - 2020. sbabra, 2020. http://dx.doi.org/10.48011/asba.v2i1.1245.

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Neste trabalho uma metodologia numérica para o cálculo de poliedros invariantes controlados robustos de complexidade fixa, baseado em otimização bilinear, é proposta para sistemas lineares de tempo discreto, sujeitos a restrições nos estados e nas entradas de controle e a perturbações de amplitude limitada. Um conjunto é invariante controlado robusto se qualquer trajetória do estado iniciada dentro do conjunto pode ser mantido dentro dele por meio de uma ação de controle adequada, apesar das perturbações. Métodos convencionais de cálculo destes poliedros podem resultar em conjuntos de alta complexidade, definidos por um grande número de vértices. Por meio de exemplos numéricos, verifica-se que a metodologia proposta é capaz de calcular poliedros de volume maior do que os de métodos recentes que buscam também conjuntos com complexidade reduzida.
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