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Zeitschriftenartikel zum Thema „Optimal control methods“

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Veröffentlicht am 15. März 2025

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1

Gammell, Jonathan D., und Marlin P. Strub. „Asymptotically Optimal Sampling-Based Motion Planning Methods“. Annual Review of Control, Robotics, and Autonomous Systems 4, Nr. 1 (03.05.2021): 295–318. http://dx.doi.org/10.1146/annurev-control-061920-093753.

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Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also optimize a cost function, such as path length. Formal path-quality guarantees for continuously valued search spaces are an active area of research interest. Recent results have proven that some sampling-based planning methods probabilistically converge toward the optimal solution as computational effort approaches infinity. This article summarizes the assumptions behind these popular asymptotically optimal techniques and provides an introduction to the significant ongoing research on this topic.

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2

Tsirlin, A. M. „Methods of Simplifying Optimal Control Problems, Heat Exchange and Parametric Control of Oscillators“. Nelineinaya Dinamika 18, Nr. 4 (2022): 0. http://dx.doi.org/10.20537/nd220801.

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Methods of simplifying optimal control problems by decreasing the dimension of the space of states are considered. For this purpose, transition to new phase coordinates or conversion of the phase coordinates to the class of controls is used. The problems of heat exchange and parametric control of oscillators are given as examples: braking/swinging of a pendulum by changing the length of suspension and variation of the energy of molecules’ oscillations in the crystal lattice by changing the state of the medium (exposure to laser radiation). The last problem corresponds to changes in the temperature of the crystal.

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3

Vinter, R. B. „PERTURBATION METHODS IN OPTIMAL CONTROL“. Bulletin of the London Mathematical Society 23, Nr. 6 (November 1991): 616–17. http://dx.doi.org/10.1112/blms/23.6.616.

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4

Kučera, Vladimír. „Optimal control: Linear quadratic methods“. Automatica 28, Nr. 5 (September 1992): 1068–69. http://dx.doi.org/10.1016/0005-1098(92)90166-d.

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5

Lang, J., und J. G. Verwer. „W-methods in optimal control“. Numerische Mathematik 124, Nr. 2 (19.02.2013): 337–60. http://dx.doi.org/10.1007/s00211-013-0516-x.

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6

Chalabi, Z., und W. Zhou. „OPTIMAL CONTROL METHODS FOR AGRICULTURAL SYSTEMS“. Acta Horticulturae, Nr. 406 (April 1996): 221–28. http://dx.doi.org/10.17660/actahortic.1996.406.22.

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7

Hou, T. „Mixed Methods for Optimal Control Problems“. Numerical Analysis and Applications 11, Nr. 3 (Juli 2018): 268–77. http://dx.doi.org/10.1134/s1995423918030072.

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8

Chen, Hong, Lulu Guo, Ting Qu, Bingzhao Gao und Fei Wang. „Optimal control methods in intelligent vehicles“. Journal of Control and Decision 4, Nr. 1 (18.11.2016): 32–56. http://dx.doi.org/10.1080/23307706.2016.1254072.

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9

Bochev, Pavel. „Least-squares methods for optimal control“. Nonlinear Analysis: Theory, Methods & Applications 30, Nr. 3 (Dezember 1997): 1875–85. http://dx.doi.org/10.1016/s0362-546x(97)00152-1.

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10

Sachs, Ekkehard W. „Quasi Newton Methods in Optimal Control“. IFAC Proceedings Volumes 18, Nr. 2 (Juni 1985): 240. http://dx.doi.org/10.1016/s1474-6670(17)69239-5.

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11

Fraser-Andrews, G. „Numerical methods for singular optimal control“. Journal of Optimization Theory and Applications 61, Nr. 3 (Juni 1989): 377–401. http://dx.doi.org/10.1007/bf00941825.

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12

Buldaev, A. S. „Perturbation methods in optimal control problems“. Ecological Modelling 216, Nr. 2 (August 2008): 157–59. http://dx.doi.org/10.1016/j.ecolmodel.2008.03.030.

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13

Hager, William W. „Multiplier Methods for Nonlinear Optimal Control“. SIAM Journal on Numerical Analysis 27, Nr. 4 (August 1990): 1061–80. http://dx.doi.org/10.1137/0727063.

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14

Papageorgiou, Nikolaos S., Vicenţiu D. Rădulescu und Dušan D. Repovš. „Relaxation methods for optimal control problems“. Bulletin of Mathematical Sciences 10, Nr. 01 (25.02.2020): 2050004. http://dx.doi.org/10.1142/s1664360720500046.

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We consider a nonlinear optimal control problem with dynamics described by a differential inclusion involving a maximal monotone map [Formula: see text]. We do not assume that [Formula: see text], incorporating in this way systems with unilateral constraints in our framework. We present two relaxation methods. The first one is an outgrowth of the reduction method from the existence theory, while the second method uses Young measures. We show that the two relaxation methods are equivalent and admissible.

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15

Baranov, V. V., und V. I. Salyga. „Methods of uniform optimal stochastic control“. Computational Mathematics and Modeling 5, Nr. 1 (1994): 98–105. http://dx.doi.org/10.1007/bf01128583.

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16

Marburger, Jan. „On Optimal Control Using Particle Methods“. PAMM 9, Nr. 1 (Dezember 2009): 605–6. http://dx.doi.org/10.1002/pamm.200910274.

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17

Belta, Calin, und Sadra Sadraddini. „Formal Methods for Control Synthesis: An Optimization Perspective“. Annual Review of Control, Robotics, and Autonomous Systems 2, Nr. 1 (03.05.2019): 115–40. http://dx.doi.org/10.1146/annurev-control-053018-023717.

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In control theory, complicated dynamics such as systems of (nonlinear) differential equations are controlled mostly to achieve stability. This fundamental property, which can be with respect to a desired operating point or a prescribed trajectory, is often linked with optimality, which requires minimizing a certain cost along the trajectories of a stable system. In formal verification (model checking), simple systems, such as finite-state transition graphs that model computer programs or digital circuits, are checked against rich specifications given as formulas of temporal logics. The formal synthesis problem, in which the goal is to synthesize or control a finite system from a temporal logic specification, has recently received increased interest. In this article, we review some recent results on the connection between optimal control and formal synthesis. Specifically, we focus on the following problem: Given a cost and a correctness temporal logic specification for a dynamical system, generate an optimal control strategy that satisfies the specification. We first provide a short overview of automata-based methods, in which the dynamics of the system are mapped to a finite abstraction that is then controlled using an automaton corresponding to the specification. We then provide a detailed overview of a class of methods that rely on mapping the specification and the dynamics to constraints of an optimization problem. We discuss advantages and limitations of these two types of approaches and suggest directions for future research.

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18

Ostapenko, Valentin V., A. P. Yakovleva, I. S. Voznyuk und V. M. Rogov. „Optimal Control Methods for an Electrochemical Sewage“. Journal of Automation and Information Sciences 28, Nr. 1-2 (1996): 85–92. http://dx.doi.org/10.1615/jautomatinfscien.v28.i1-2.90.

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19

Roberts, Adrian. „Polynomial Methods in Optimal Control and Filtering“. Computing & Control Engineering Journal 4, Nr. 3 (1993): 116. http://dx.doi.org/10.1049/cce:19930025.

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20

Kaczorek, Tadeusz. „Polynomial methods in optimal control and filtering“. Control Engineering Practice 3, Nr. 10 (Oktober 1995): 1508–9. http://dx.doi.org/10.1016/0967-0661(95)90046-2.

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21

Fleming, W. H. „Perturbation Methods in Optimal Control (Alain Bensoussan)“. SIAM Review 31, Nr. 4 (Dezember 1989): 693–94. http://dx.doi.org/10.1137/1031148.

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22

Carpentier, Pierre, Guy Cohen und Anes Dallagi. „Particle methods for stochastic optimal control problems“. Computational Optimization and Applications 56, Nr. 3 (01.08.2013): 635–74. http://dx.doi.org/10.1007/s10589-013-9579-y.

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23

Palazzolo, A. B., R. R. Lin, A. F. Kascak und R. M. Alexander. „Active Control of Transient Rotordynamic Vibration by Optimal Control Methods“. Journal of Engineering for Gas Turbines and Power 111, Nr. 2 (01.04.1989): 264–70. http://dx.doi.org/10.1115/1.3240246.

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Although considerable effort has been put into the study of steady-state vibration control, there are few methods applicable to transient vibration control of rotor-bearing systems. In this paper optimal control theory has been adopted to minimize rotor vibration due to sudden imbalance, e.g., blade loss. The system gain matrix is obtained by choosing the weighting matrices and solving the Riccati equation. Control forces are applied to the system via a feedback loop. A seven mass rotor system is simulated for illustration. A relationshp between the number of sensors and the number of modes used in the optimal control model is investigated. Comparisons of responses are made for various configurations of modes, sensors, and actuators. Furthermore, spillover effect is examined by comparing results from collocated and noncollocated sensor configurations. Results show that shaft vibration is significantly attenuated in the closed-loop system.

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24

Dellnitz, Michael, Julian Eckstein, Kathrin Flaßkamp, Patrick Friedel, Christian Horenkamp, Ulrich Köhler, Sina Ober-Blöbaum, Sebastian Peitz und Sebastian Tiemeyer. „Development of an Intelligent Cruise Control Using Optimal Control Methods“. Procedia Technology 15 (2014): 285–94. http://dx.doi.org/10.1016/j.protcy.2014.09.082.

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25

Gurman, Vladimir, Irina Rasina, Irina Guseva und Oles Fesko. „Methods for approximate solution of optimal control problems“. Program Systems: Theory and Applications 6, Nr. 4 (2015): 113–37. http://dx.doi.org/10.25209/2079-3316-2015-6-4-113-137.

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26

Skibitskiy, N. V. „Interval methods in the problems of optimal control“. Industrial laboratory. Diagnostics of materials 88, Nr. 5 (23.05.2022): 71–82. http://dx.doi.org/10.26896/1028-6861-2022-88-5-71-82.

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The problem of optimal control of a linear dynamic object in conditions of incomplete information about the initial data is considered. The approaches based on various models of the uncertainty description are analyzed. It is shown that the use of the approach based on a probabilistic model for describing uncertainty is advisable when the uncertainty is associated only with randomness, the description of other sources of uncertainty within this model is rather difficult and the formal application of the regression analysis provides the results that are far from true. Though the fuzzy model is suitable for describing a wide range of the uncertainty sources, application of the model faces methodological difficulties when comparing and ranking fuzzy numbers and smoothing fuzzy data. In this regard, it seems promising to use an approach based on an interval model which allows description of a wide class of uncertain and inaccurate initial data. To unify control algorithms for the systems described by equations of state of different types with interval-given parameters, we developed an algorithm of equivalent transformations that provides the transition to special forms of representing the state matrix while maintaining preservation of all the dynamic properties of the original system. The problems of constructing the range of values of the roots of the matrix of the system and its description by an approximation in the form of an interval vector are solved to ensure the implementation of the algorithm. An approach is proposed to solve the problems of terminal control and maximum performance, when the uncertainty of the initial data is described by the interval model and the apparatus of interval analysis is used to solve the problem. It is shown that in this case with the direct use of the classical formulation of the optimal control problem without taking the uncertainty into account, there is no single optimal control which guarantees the exact transfer of the object to the required final state for any value of the parameters from a given range of their possible values. Therefore, in the presence of the interval uncertainty of the initial data, the solution of the problem can’t be obtained in the sense in which it is understood with precisely known parameters and the approach to the formulation of the control problem itself should be revised in order to determine in the future a solution that ensures guaranteed accuracy of the system translation. In this regard, we propose to formulate the control problem in conditions of the interval uncertainty as a problem of determining the set of control actions that guarantee the solution with the accuracy set up to the interval, on the set of initial data known up to the interval. Using an example of the problem with an inaccurately known initial state, it is shown that if the set of possible initial states of an object belongs to a n-dimensional rectangular parallelepiped, then when implementing a control on an object calculated for any initial state from a given set, the set of final states is convex and represents a n-dimensional parallelepiped. To construct the parallelepiped, it is sufficient to determine the coordinates of the vertices corresponding to the vertices of the abovementioned n-dimensional rectangular parallelepiped. We propose a system of inequalities which determines the condition for the membership of a set of finite states of the object obtained upon implementation of control for any possible value of the initial state from a given set to the required set of finite states. On the basis of this system of inequalities, conditions are formulated that provide a priori determination of the solvability of the problem.

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27

Gong, Qi, Fariba Fahroo und I. Michael Ross. „Spectral Algorithm for Pseudospectral Methods in Optimal Control“. Journal of Guidance, Control, and Dynamics 31, Nr. 3 (Mai 2008): 460–71. http://dx.doi.org/10.2514/1.32908.

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28

Goncharova, E. V., und M. V. Staritsyn. „Gradient refinement methods for optimal impulse control problems“. Automation and Remote Control 72, Nr. 10 (Oktober 2011): 2188–95. http://dx.doi.org/10.1134/s0005117911100171.

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29

Hou, T. „Erratum to: Mixed Methods for Optimal Control Problems“. Numerical Analysis and Applications 11, Nr. 4 (Oktober 2018): 372. http://dx.doi.org/10.1134/s1995423918040092.

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30

Kelley, C. T., und E. W. Sachs. „Quasi-Newton Methods and Unconstrained Optimal Control Problems“. SIAM Journal on Control and Optimization 25, Nr. 6 (November 1987): 1503–16. http://dx.doi.org/10.1137/0325083.

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31

Baturin, V. A., und S. V. Cheremnykh. „Second Order Methods for the Optimal Control Problems“. Automation and Remote Control 79, Nr. 5 (Mai 2018): 919–39. http://dx.doi.org/10.1134/s0005117918050120.

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32

Betts,, JT, und I. Kolmanovsky,. „Practical Methods for Optimal Control using Nonlinear Programming“. Applied Mechanics Reviews 55, Nr. 4 (01.07.2002): B68. http://dx.doi.org/10.1115/1.1483351.

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33

Borzı̀, Alfio. „Multigrid methods for parabolic distributed optimal control problems“. Journal of Computational and Applied Mathematics 157, Nr. 2 (August 2003): 365–82. http://dx.doi.org/10.1016/s0377-0427(03)00417-5.

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34

Gornov, A. Yu, A. I. Tyatyushkin und E. A. Finkelstein. „Numerical methods for solving applied optimal control problems“. Computational Mathematics and Mathematical Physics 53, Nr. 12 (Dezember 2013): 1825–38. http://dx.doi.org/10.1134/s0965542513120063.

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35

Gornov, A. Yu, A. I. Tyatyushkin und E. A. Finkelstein. „Numerical methods for solving terminal optimal control problems“. Computational Mathematics and Mathematical Physics 56, Nr. 2 (Februar 2016): 221–34. http://dx.doi.org/10.1134/s0965542516020093.

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36

I. Seginer und R. W. McClendon. „Methods for Optimal Control of the Greenhouse Environment“. Transactions of the ASAE 35, Nr. 4 (1992): 1299–307. http://dx.doi.org/10.13031/2013.28733.

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37

Vikhansky, A. „Enhancement of laminar mixing by optimal control methods“. Chemical Engineering Science 57, Nr. 14 (Juli 2002): 2719–25. http://dx.doi.org/10.1016/s0009-2509(02)00122-7.

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38

Basting, Christopher, und Dmitri Kuzmin. „Optimal control for mass conservative level set methods“. Journal of Computational and Applied Mathematics 270 (November 2014): 343–52. http://dx.doi.org/10.1016/j.cam.2013.12.040.

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39

Tang, Xiaojun, Zhenbao Liu und Yu Hu. „New results on pseudospectral methods for optimal control“. Automatica 65 (März 2016): 160–63. http://dx.doi.org/10.1016/j.automatica.2015.11.035.

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40

Kucera, Vladimir. „Control system design: Conventional, algebraic and optimal methods“. Automatica 25, Nr. 2 (März 1989): 322–23. http://dx.doi.org/10.1016/0005-1098(89)90090-3.

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41

Vakhrameev, S. A. „Geometrical and topological methods in optimal control theory“. Journal of Mathematical Sciences 76, Nr. 5 (Oktober 1995): 2555–719. http://dx.doi.org/10.1007/bf02362893.

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42

Zeid, Samaneh Soradi, Sohrab Effati und Ali Vahidian Kamyad. „Approximation methods for solving fractional optimal control problems“. Computational and Applied Mathematics 37, S1 (27.02.2017): 158–82. http://dx.doi.org/10.1007/s40314-017-0424-2.

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43

El Baqqaly, El-Houcine, und Mondher Damak. „Numerical Methods for Fractional Optimal Control and Estimation“. Babylonian Journal of Mathematics 2023 (26.05.2023): 23–29. http://dx.doi.org/10.58496/bjm/2023/005.

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Fractional calculus has become a valuable mathematical tool for modeling various physical phenomena exhibiting anomalous dynamics such as memory and hereditary properties. However, the fractional operators lead to difficulties in analysis, optimization, and estimation that limit the application of fractional models. This paper develops numerical methods to solve fractional optimal control and estimation problems with Caputo derivatives of arbitrary order. First, fractional Pontryagin's maximum principle is used to formulate first-order necessary conditions for fractional optimal control problems. A fractional collocation method using polynomial basis functions is then proposed to discretize the resulting boundary value problems. This allows transforming an infinite-dimensional optimal control problem into a finite nonlinear programming problem. Second, for fractional estimation, a novel ensemble Kalman filter is proposed based on a Monte Carlo approach to propagate the fractional state dynamics. This provides a recursive fractional state estimator analogous to the classical Kalman filter. The capabilities of the proposed collocation and ensemble Kalman filter methods are demonstrated through applications including fractional epidemic control, thermomechanical oscillator control, and state estimation of viscoelastic mechanical systems. The results illustrate improved accuracy over prior discretization schemes along with the ability to handle complex system dynamics. This work provides a comprehensive framework for numerical solution of fractional optimal control and estimation problems. The methods enable applying fractional calculus to address challenges in robotics, biomedicine, mechanics, and other fields where systems exhibit non-classical dynamics.

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44

Carraro, Thomas, und Michael Geiger. „Multiple shooting methods for parabolic optimal control problems with control constraints“. PAMM 15, Nr. 1 (Oktober 2015): 609–10. http://dx.doi.org/10.1002/pamm.201510294.

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45

Lanzon, Alexander, und Hong Wang. „Special Issue onDirections, Applications and Methods in Robust Control Optimal Control, Applications and Methods (OCAM)“. Optimal Control Applications and Methods 28, Nr. 4 (2007): n/a. http://dx.doi.org/10.1002/oca.816.

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46

Kumar, Renjith R., und Hans Seywald. „Should controls be eliminated while solving optimal control problems via direct methods?“ Journal of Guidance, Control, and Dynamics 19, Nr. 2 (März 1996): 418–23. http://dx.doi.org/10.2514/3.21634.

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47

Nekrasov, Sergej A., und Vladimir S. Volkov. „Numerical methods for solving optimal control for Stefan problems“. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, Nr. 2 (2016): 87–100. http://dx.doi.org/10.21638/11701/spbu10.2016.209.

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48

Fonner, Robert, und Alok K. Bohara. „Optimal Control of Wild Horse Populations with Nonlethal Methods“. Land Economics 93, Nr. 3 (24.07.2017): 390–412. http://dx.doi.org/10.3368/le.93.3.390.

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49

Axelsson, Owe, Michal Béreš und Radim Blaheta. „Computational methods for boundary optimal control and identification problems“. Mathematics and Computers in Simulation 189 (November 2021): 276–90. http://dx.doi.org/10.1016/j.matcom.2021.02.019.

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50

Fahroo, Fariba, und I. Michael Ross. „Pseudospectral Methods for Infinite-Horizon Nonlinear Optimal Control Problems“. Journal of Guidance, Control, and Dynamics 31, Nr. 4 (Juli 2008): 927–36. http://dx.doi.org/10.2514/1.33117.

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