Abstract
A numerical method for solving a special class of optimal control problems is given. The solution is based on state parametrization as a polynomial with unknown coefficients. This converts the problem to a non-linear optimization problem. To facilitate the computation of optimal coefficients, an improved iterative method is suggested. Convergence of this iterative method and its implementation for numerical examples are also given.
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Fink, P.A., Stech, D.J.: Solution of optimal control problems on a parallel machine using the Epsilon method. Optim. Control Appl. Methods 16, 1–17 (1995)
Jaddu, H.M.: Numerical Methods for Solving Optimal Control Problems Using Chebyshev Polynomials, PhD thesis, School of Information Science, Japan Advanced Institute of Science and Technology, 1998
Jennings, L.S., Teo, K.L., Goh, C.J.: MISER3 optimal control software: Theory and user manual, Department of Mathematics, the University of Western Australia, 1997. [Online] Available: http://www.cado.uwa.edu.au/miser
Liu, Y., Teo, K.L., Jennings, L.S., Wang, S.: On a class of optimal control problems with state jumps. J. Optim. Theory Appl. 98, 65–82 (1998)
Mehne, H.H., Farahi, M.H., Kamyad, A.V.: MILP modelling for the time optimal control problem in the case of multiple targets. Optim. Control Appl. Methods 27, 77–91 (2006)
Pinch, E.R.: Optimal Control and the Calculus of Variations. Oxford University Press (1993)
Rehbock, V., Teo, K.L., Jenning, L.S., Lee, H.W.J.: A survey of the control parametrization enhancing methods for constrained optimal control problems. In: Eberhard, A., et al. (eds.) Progress in Optimization: Contributions from Australia, pp. 247–275. Kluwer (1999)
Rubio, J.E.: Control and Optimization: The Linear Treatment of Non-linear Problems. Manchester University Press, Manchester (1986)
Tang, G.-Y.: Suboptimal control for nonlinear systems: A successive approximation approach. Syst. Control Lett. 54, 429-434 (2005)
Teo, K.L., Goh, C.J., Wong, K.H.: A Unified Computational Approach to Optimal Control Problems. Longman Scientific and Technical (1991)
Teo, K.L., Jennings, L.S., Lee, H.W.J., Rehbock, V.: Control parametrization enhancing transform for constrained optimal control problems. J. Aust. Math. Soc. B 40, 314–335 (1999)
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Mehne, H.H., Borzabadi, A.H. A numerical method for solving optimal control problems using state parametrization. Numer Algor 42, 165–169 (2006). https://doi.org/10.1007/s11075-006-9035-5
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DOI: https://doi.org/10.1007/s11075-006-9035-5