Matlab implementation of direct and indirect shooting methods to solve an optimal control problem with state constraints

• Autorzy: Karbowski Andrzej

Identyfikatory

DOI

10.14313/JAMRIS/1‐2021/6

• Języki publikacji: EN

Abstrakty

EN

The paper presents a general procedure to solve nume‐ rically optimal control problems with state constraints. It is used in the case, when the simple time discretization of the state equations and expressing the optimal cont‐ rol problem as a nonlinear mathematical programming problem is too coarse. It is based on using in turn two multiple shooting BVP approaches: direct and indirect. The paper is supplementary to the earlier author’s paper on direct and indirect shooting methods, presenting the theory underlying both approaches. The same example is considered here and brought to an end, that is two full listings of two MATLAB codes are shown.

Słowa kluczowe

EN

optimal control; numerical methods; state constraints; shooting method; multiple shooting method; boundary value problem; MATLAB

• Wydawca: Łukasiewicz Industrial Research Institute for Automation and Measurements PIAP
• Czasopismo: Journal of Automation Mobile Robotics and Intelligent Systems
• Rocznik: 2021
• Tom: Vol. 15, No. 1
• Strony: 43--50
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Karbowski Andrzej

• Institute of Control and Computation Engineering, Warsaw University of Technology, Warsaw, Poland, www: http://www.ia.pw.edu.pl/~karbowsk.

Bibliografia

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• [4] A. Karbowski, “Shooting Methods to Solve Optimal Control Problems with State and Mixed Control‑State Constraints”. In: R. Szewczyk, C. Zieliński, and M. Kaliczyńska, eds., Challenges in Automation, Robotics and Measurement Techniques, Springer: Cham, 2016, 189–205, 10.1007/978‑3‑319‑29357‑8_17.
• [5] H. Maurer and W. Gillessen, “Application of multiple shooting to the numerical solution of optimal control problems with bounded state variables”, Computing, vol. 15, no. 2, 1975, 105–126, 10.1007/BF02252860.
• [6] H. J. Oberle, “Numerical solution of minima optimal control problems by multiple shooting technique”, Journal of Optimization Theory and Applications, vol. 50, no. 2, 1986, 331–357, 10.1007/BF00939277.
• [7] R. Pytlak, J. Blaszczyk, A. Karbowski, K. Krawczyk, and T. Tarnawski, “Solvers chaining in the IDOS server for dynamic optimization”. In: 52nd IEEE Conference on Decision and Control, 2013, 7119–7124, 10.1109/CDC.2013.6761018.
• [8] S. Sager, Numerical methods for mixed‑integer optimal control problems, Ph.D. Thesis, University of Heidelberg, 2005.
• [9] J. Stoer and R. Bulirsch,Introduction to Numerical Analysis, Springer New York: New York, NY, 2002, 10.1007/978‑0‑387‑21738‑3.
• [10] O. von Stryk and R. Bulirsch, “Direct and indirect methods for trajectory optimization”, Annals of Operations Research, vol. 37, no. 1, 1992, 357–373, 10.1007/BF02071065.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).