Relevant bibliographies by topics / Optimization Calculus of Variations and Optimal Control

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Optimization Calculus of Variations and Optimal Control'

Author: Grafiati
Published: 28 July 2024
Last updated: 31 July 2025

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Journal articles on the topic "Optimization Calculus of Variations and Optimal Control"

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Lan, Tian-Syung. "Dynamic MRR Function Optimization Using Calculus of Variations." Mathematical Problems in Engineering 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/671062.

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A dynamic machining model to optimize the control of material removal rate (MRR) for a cutting tool undergoing the considerations of fixed tool life and maximum machining rate is established in this paper. This study not only applies material removal rate mathematically into the objective function, but also implements Calculus of Variations to comprehensively optimize the control of material removal rate. In addition, the optimal solution for the dynamic machining model to gain the maximum profit is provided, and the decision criteria for selecting the optimal solution of the dynamic machining
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McShane, E. J. "The Calculus of Variations from the Beginning Through Optimal Control Theory." SIAM Journal on Control and Optimization 27, no. 5 (1989): 916–39. http://dx.doi.org/10.1137/0327049.

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Carlier, G., and A. Lachapelle. "A Planning Problem Combining Calculus of Variations and Optimal Transport." Applied Mathematics & Optimization 63, no. 1 (2010): 1–9. http://dx.doi.org/10.1007/s00245-010-9107-8.

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Krastanov, Mikhail, and Nadezhda Ribarska. "Lagrange multipliers in dynamic optimization." Mathematics and Education in Mathematics 54 (March 27, 2025): 009–17. https://doi.org/10.55630/mem.2025.54.009-017.

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An approach for studying optimization problems in abstract setting is presented and a general Lagrange multiplier rule is formulated. It is described how to apply this result to the basic problem of calculus of variations with pure state constraints of equality- type, as well as to a Mayer optimal control problem with pure state constraints.
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Petit, Maria Luisa. "Dynamic optimization. The calculus of variations and optimal control in economics and management." International Review of Economics & Finance 3, no. 2 (1994): 245–47. http://dx.doi.org/10.1016/1059-0560(94)90037-x.

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Dolgopolik, Maksim. "Constrained nonsmooth problems of the calculus of variations." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 79. http://dx.doi.org/10.1051/cocv/2021074.

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The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric constraints. To derive optimality conditions, we study generalised concepts of differentiability of nonsmooth functions called codifferentiability and quasidifferentiability. Under some natural and easily verifiable assumptions we prove that a nonsmooth integral functional defined on the Sobolev space is continuously codifferentiable and compute its codifferential an
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Lei, Yang, Shurong Li, Xiaodong Zhang, Qiang Zhang, and Lanlei Guo. "Dynamic Optimization of a Polymer Flooding Process Based on Implicit Discrete Maximum Principle." Mathematical Problems in Engineering 2012 (2012): 1–23. http://dx.doi.org/10.1155/2012/281567.

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Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and some inequality constraints as polymer concentration and injection amount limitation. The optimal control model is discretized by full implicit finite-difference method. To cope with the discrete optimal control problem (OCP), the necessar
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Murray, J. M. "Existence Theorems for Optimal Control and Calculus of Variations Problems Where the States Can Jump." SIAM Journal on Control and Optimization 24, no. 3 (1986): 412–38. http://dx.doi.org/10.1137/0324024.

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Drivotin, Oleg I. "Оn momentum flow density of the gravitational field". Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 17, № 2 (2021): 137–47. http://dx.doi.org/10.21638/11701/spbu10.2021.204.

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Momentum is considered on the basis of the approach widely used in the calculus of variations and in the optimal control theory, where variation of a cost functional is investigated. In physical theory, it is the action functional. Action variation under Lie dragging can be expressed as a surface integral of some differential form. The momentum density flow is defined using this form. In this work, the momentum balance equation is obtained. This equation shows that the momentum field transforms into a momentum of a mass. Examples showing the momentum flow structure for a mass distribution repr
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Bouzaouache, Hajer. "Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching." Complexity 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/5308013.

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This paper investigates the optimal control problem of a particular class of hybrid dynamical systems with controlled switching. Given a prespecified sequence of active subsystems, the objective is to seek both the continuous control input and the discrete switching instants that minimize a performance index over a finite time horizon. Based on the use of the calculus of variations, necessary conditions for optimality are derived. An efficient algorithm, based on nonlinear optimization techniques and numerical methods, is proposed to solve the boundary-value ordinary differential equations. In
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Dissertations / Theses on the topic "Optimization Calculus of Variations and Optimal Control"

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Dymkou, Siarhei. "Approximations for some classes of optimal control problems with state constraints and repetitive control systems." Thesis, University of Ballarat, 2005. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/69220.

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This report presents the investigation on the research work "Approximations for some classes of optimal control problems with state constraints and repetitive control systems". This report mainly gives the theoretical part of the research which is based on the numerical methods that are developed. It is conjectured that the corresponding algorithms will be realized as computer programs after which they can be used in practical work.<br>Master of Information Technology
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Anderson, James David. "Dynamical system decomposition and analysis using convex optimization." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:624001be-28d5-4837-a7d8-2222e270e658.

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This thesis is concerned with investigating new methods for the analysis of large-scale dynamical systems using convex optimization. The proposed methodology is based on composite Lyapunov theory and is computationally implemented using polynomial programming techniques. The main result of this work is the development of a system decomposition framework that makes it possible to analyze systems that are of such a scale that traditional methods cannot cope with. We begin by addressing the problem of model invalidation. A barrier certificate method for invalidating models in the presence of unce
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Pearson, John W. "Fast iterative solvers for PDE-constrained optimization problems." Thesis, University of Oxford, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405.

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In this thesis, we develop preconditioned iterative methods for the solution of matrix systems arising from PDE-constrained optimization problems. In order to do this, we exploit saddle point theory, as this is the form of the matrix systems we wish to solve. We utilize well-known results on saddle point systems to motivate preconditioners based on effective approximations of the (1,1)-block and Schur complement of the matrices involved. These preconditioners are used in conjunction with suitable iterative solvers, which include MINRES, non-standard Conjugate Gradients, GMRES and BiCG. The sol
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Taha, Haithem Ezzat Mohammed. "Mechanics of Flapping Flight: Analytical Formulations of Unsteady Aerodynamics, Kinematic Optimization, Flight Dynamics and Control." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/24428.

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A flapping-wing micro-air-vehicle (FWMAV) represents a complex multi-disciplinary system whose analysis invokes the frontiers of the aerospace engineering disciplines. From the aerodynamic point of view, a nonlinear, unsteady flow is created by the flapping motion. In addition, non-conventional contributors, such as the leading edge vortex, to the aerodynamic loads become dominant in flight. On the other hand, the flight dynamics of a FWMAV constitutes a nonlinear, non-autonomous dynamical system. Furthermore, the stringent weight and size constraints that are always imposed on FWMAVs invoke d
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Chaturapruek, Sorathan. "A Mathematical Framework for Unmanned Aerial Vehicle Obstacle Avoidance." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/60.

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The obstacle avoidance navigation problem for Unmanned Aerial Vehicles (UAVs) is a very challenging problem. It lies at the intersection of many fields such as probability, differential geometry, optimal control, and robotics. We build a mathematical framework to solve this problem for quadrotors using both a theoretical approach through a Hamiltonian system and a machine learning approach that learns from human sub-experts' multiple demonstrations in obstacle avoidance. Prior research on the machine learning approach uses an algorithm that does not incorporate geometry. We have developed tool
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Luria, Gianvittorio. "Constrained Calculus of Variations and Geometric Optimal Control Theory." Doctoral thesis, Università degli studi di Trento, 2010. https://hdl.handle.net/11572/368036.

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The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on
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Luria, Gianvittorio. "Constrained Calculus of Variations and Geometric Optimal Control Theory." Doctoral thesis, University of Trento, 2010. http://eprints-phd.biblio.unitn.it/170/1/Constrained_Calculus_of_Variations_and_Geometric_Optimal_Control_Theory.pdf.

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The present work provides a geometric approach to the calculus of variations in the presence of non-holonomic constraints. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The usual classification of the evolutions into normal and abnormal ones is also discussed, showing the existence of a universal algorithm assigning to every admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. A gauge-invariant formulation of the variational problem, based on
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Pooseh, Shakoor. "Computational methods in the fractional calculus of variations and optimal control." Doctoral thesis, Universidade de Aveiro, 2013. http://hdl.handle.net/10773/11510.

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Doutoramento em Matemática<br>The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their effi
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Gouveia, Paulo D. F. "Computação de simetrias variacionais e optimização da resistência aerodinâmica newtoniana." Doctoral thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10198/1571.

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Neste trabalho exploram-se alguns dos actuais recursos de computação científica no contexto da optimização estática e dinâmica. Começa-se por propor um conjunto de procedimentos computacionais algébricos que permitem automatizar todo o processo de obtenção de simetrias e leis de conservação, quer no contexto clássico do cálculo das variações, quer no contexto mais abrangente do controlo óptimo. A utilidade do package de funções desenvolvido é demonstrada com a identificação de novas leis de conservação para alguns problemas do controlo óptimo conhecidos na literatura. Estabelece-se depois uma
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Chen, Chuei Yee. "Quasiminimality and coercivity in the calculus of variations." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d6daadfd-92fb-4fa6-9d5b-fd8403955079.

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Books on the topic "Optimization Calculus of Variations and Optimal Control"

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Mili͡utin, A. A. Calculus of variations and optimal control. American Mathematical Society, 1998.

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Clarke, Francis. Functional Analysis, Calculus of Variations and Optimal Control. Springer London, 2013.

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Davidovich, Ioffe Aleksandr, Reich Simeon, Shafrir I, and International Conference on the Calculus of Variations and Related Topics (1998 : Technion, Israel Institute of Technology), eds. Calculus of variations and optimal control: Technion 1998. Chapman & Hall/CRC, 2000.

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Troutman, John L. Variational calculus and optimal control: Optimization with elementary convexity. 2nd ed. Springer, 1996.

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service), SpringerLink (Online, ed. Calculus of Variations, Classical and Modern. Springer-Verlag Berlin Heidelberg, 2011.

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Gregory, John, and Cantian Lin. Constrained Optimization in the Calculus of Variations and Optimal Control Theory. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2918-3.

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Gregory, John A. Constrained optimization in the calculus of variations and optimal control theory. Chapman & Hall, 1992.

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Gregory, John. Constrained Optimization in the Calculus of Variations and Optimal Control Theory. Springer Netherlands, 1992.

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John, Gregory. Constrained optimization in the calculus of variations and optimal control theory. Van Nostrand Reinhold, 1992.

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Pardalos, P. M. (Panos M.), 1954-, Ėnkhbat R. (Rėnt͡sėngiĭn), Tseveendorj Ider, and SpringerLink (Online service), eds. Optimization and Optimal Control: Theory and Applications. Springer Science+Business Media, LLC, 2010.

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Book chapters on the topic "Optimization Calculus of Variations and Optimal Control"

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Gregory, John, and Cantian Lin. "Optimal Control." In Constrained Optimization in the Calculus of Variations and Optimal Control Theory. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2918-3_4.

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Troutman, John L. "Standard Optimization Problems." In Variational Calculus and Optimal Control. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0737-5_2.

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Troutman, John L. "Review of Optimization in ℝd." In Variational Calculus and Optimal Control. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0737-5_1.

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Sachs, Gottfried, Rainer Mehlhorn, and Michael Dinkelmann. "Efficient Convexification of Flight Path Optimization Problems." In Variational Calculus, Optimal Control and Applications. Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8802-8_32.

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Chudej, Kurt. "Accelerating Multiple Shooting for State-Constrained Trajectory Optimization Problems." In Variational Calculus, Optimal Control and Applications. Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8802-8_20.

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Roubíček, Tomáš. "Existence Results for Some Nonconvex Optimization Problems Governed by Nonlinear Processes." In Variational Calculus, Optimal Control and Applications. Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8802-8_10.

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Gregory, John, and Cantian Lin. "The Basic Theory of the Calculus of Variations." In Constrained Optimization in the Calculus of Variations and Optimal Control Theory. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2918-3_2.

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Gregory, John, and Cantian Lin. "The Finite Dimensional Problem." In Constrained Optimization in the Calculus of Variations and Optimal Control Theory. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2918-3_1.

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Gregory, John, and Cantian Lin. "Additional Topics." In Constrained Optimization in the Calculus of Variations and Optimal Control Theory. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2918-3_3.

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Gregory, John, and Cantian Lin. "Unconstrained Reformulations." In Constrained Optimization in the Calculus of Variations and Optimal Control Theory. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2918-3_5.

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Conference papers on the topic "Optimization Calculus of Variations and Optimal Control"

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Glizer, Valery Y., Vladimir Turetsky, and Emil Bashkansky. "Application of Pontryagin’s Maximum Principle to Statistical Process Control Optimization." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70104.

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The optimization of a statistical process control with a variable sampling interval is studied. A control performance index is the expected loss, caused by delay in detecting process change. It is to be minimized by a proper choice of a sampling interval. The mathematical model of this problem is a nonstandard variational calculus problem with two types of constraints, an isoperimetric constraint and two geometric constraints. The integrands in the cost functional and the isoperimetric constraint are independent of the derivative of the minimizing function. Therefore, the classical Euler-Lagra
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Arutyunov, Aram, Dmitry Karamzin, and Fernando Pereira. "On the extension of classical calculus of variations and optimal control to problems with discontinuous trajectories." In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6426145.

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Zlotnik, Anatoly, and Jr-Shin Li. "Optimal Asymptotic Entrainment of Phase-Reduced Oscillators." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-5923.

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We derive optimal periodic controls for entrainment of a self-driven oscillator to a desired frequency. The alternative objectives of minimizing power and maximizing frequency range of entrainment are considered. A state space representation of the oscillator is reduced to a linearized phase model, and the optimal periodic control is computed from the phase response curve using formal averaging and the calculus of variations. Computational methods are used to calculate the periodic orbit and the phase response curve, and a numerical method for approximating the optimal controls is introduced.
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El Yakine Kouba, Nour, Mohamed Menaa, Mourad Hasni, and Mohamed Boudour. "Optimal control of frequency and voltage variations using PID controller based on Particle Swarm Optimization." In 2015 4th International Conference on Systems and Control (ICSC). IEEE, 2015. http://dx.doi.org/10.1109/icosc.2015.7152777.

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Tangpong, X. W., and Om P. Agrawal. "Fractional Optimal Control of Distributed Systems." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43046.

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This paper presents a formulation and a numerical scheme for Fractional Optimal Control (FOC) for a class of distributed systems. The fractional derivative is defined in the Caputo sense. The performance index of a Fractional Optimal Control Problem (FOCP) is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE). The scheme presented rely on reducing the equations for distributed system into a set of equations that have no space parameter. Several strategies are pointed out for this t
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Ayoubi, Mohammad A., and Peiman Naseradinmousavi. "Open-Loop Minimum-Energy Maneuver of a Solar-Sail Using Magnetic Torques and Reaction Wheels." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9093.

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This paper presents an open-loop, minimum-energy control law for attitude maneuver of a solar-sail. The proposed control law utilizes the magnetic torques and reaction wheels to reorient the solar-sail for near-earth missions. Using the calculus of variations and Pontryagin’s minimum principle, the necessary and sufficient conditions were derived for the nonlinear model of the solar-sail. Then the optimal control problem was formulated as a two-point boundary-value problem and solved via the Shooting method. The computed control law can be utilized in a flight-computer and in a sampled-data fe
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Agrawal, Om P. "Fractional Optimal Control of a Distributed System Using Eigenfunctions." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35921.

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This paper presents a formulation and a numerical scheme for Fractional Optimal Control (FOC) for a class of distributed systems. The fractional derivative is defined in the Caputo sense. The performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equations (PFDEs). Eigenfunctions are used to eliminate the space parameter, and to define the problem in terms of a set of state and control variables. This leads to a multi FOCP in which each FOCP could be solved independently
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Henze, Gregor P., Anthony R. Florita, Michael J. Brandemuehl, Clemens Felsmann, and Hwakong Cheng. "Advances in Near-Optimal Control of Passive Building Thermal Storage." In ASME 2009 3rd International Conference on Energy Sustainability collocated with the Heat Transfer and InterPACK09 Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/es2009-90143.

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Using a simulation and optimization environment, this paper presents advances towards near-optimal building thermal mass control derived from full factorial analyses of the important parameters influencing the passive thermal storage process for a range of buildings and climate/utility rate structure combinations. Guidelines for the application of, and expected savings from, building thermal mass control strategies that can be easily implemented and result in a significant reduction in building operating costs and peak electrical demand are sought. In response to the actual utility rates impos
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Rahman, S. M. Mizanoor, Behzad Sadrfaridpour, and Yue Wang. "Trust-Based Optimal Subtask Allocation and Model Predictive Control for Human-Robot Collaborative Assembly in Manufacturing." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9850.

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We develop a one human-one robot hybrid cell for collaborative assembly in manufacturing. The selected task is to assemble a few LEGO parts into a final assembled product following specified instructions and sequence in collaboration between the human and the robot. We develop a two-level feedforward optimization strategy that determines the optimal subtask allocation between the human and the robot for the selected assembly before the assembly starts. We derive dynamics models for human’s trust in the robot and the robot’s trust in the human for the assembly and estimate the trusts. The aim i
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Malik, Arif, John Sanders, Ramana Grandhi, and Mark Zipf. "Reliability-Based Optimal Cluster Mill Pass Scheduling." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62565.

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Optimal pass-scheduling on cluster-type cold rolling mills, use to process flat metals, presents added challenges over conventional (vertical-stack) mills due to the complexity of roll arrangements. Cluster-type rolling mills not only pose difficulties in modeling deflections occurring in the multi-roll stack, they also impose the burden of modeling more sophisticated mechanisms used to adjust rolling force distribution and achieve desired strip flatness. In a competitive global market for very thin gauge strip, an advantage is gained through use of efficient mathematical set-up models that ca
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Reports on the topic "Optimization Calculus of Variations and Optimal Control"

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Chernyak, Vladimir Y., Michael Chertkov, Joris Bierkens, and Hilbert J. Kappen. Optimal Stochastic Control as Non-equilibrium Statistical Mechanics: Calculus of Variations over Density and Current. Office of Scientific and Technical Information (OSTI), 2013. http://dx.doi.org/10.2172/1086764.

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