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A Direct Probabilistic Optimization Method for Constrained Optimal Control Problem

Authors: Akbar Banitalebi, Mohd Ismail Abd Aziz, Rohanin Ahmad

Abstract:

A new stochastic algorithm called Probabilistic Global Search Johor (PGSJ) has recently been established for global optimization of nonconvex real valued problems on finite dimensional Euclidean space. In this paper we present convergence guarantee for this algorithm in probabilistic sense without imposing any more condition. Then, we jointly utilize this algorithm along with control parameterization technique for the solution of constrained optimal control problem. The numerical simulations are also included to illustrate the efficiency and effectiveness of the PGSJ algorithm in the solution of control problems.

Keywords: Optimal Control Problem, Constraints, Direct Methods, Stochastic Algorithm

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087844

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[1] A., Banitalebi, B. A. A., Mohd-Ismail, A., Rohanin, A probabilistic algorithm for optimal control problem, International Journal of Computer Applications, 46 (2012), 48-55.
[2] R. Bellman, Introduction to mathematical theory of control processes, vol. 2, Academic Press, New York, (1971).
[3] J. T., Betts, S. L., Campbell, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2nd ed., Advances in Design and Control 19, SIAM, Philadelphia, (2010).
[4] L., Biegler, Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation, Comput. Chem. Eng., 8 (1984), 243-248.
[5] L. T, Biegler, An overview of simultaneous strategies for dynamic optimization, Chem. Eng. Process., 46 (2007), 1043-1053.
[6] E., Bryson, Y. C., Ho, Applied Optimal Control: Optimization, Estimation and Control, Taylor & Francis, New York, (1975).
[7] R. T., Farouki, V. T., Rajan, Algorithms for polynomials in Bernstein form, Comput. Aided. Geom. D., 5 (l988), l-26.
[8] A., Ghosh, S., Das, A., Chowdhury, R., Giri, An ecologically inspired direct search method for solving optimal control problems with Bezier parameterization, Eng. Appl. Artif. Intel., 24 (2011), 1195-1203.
[9] C. J., Goh, K. L., Teo, Control parametrization: A unified approach to optimal control problems with general constraints, Automatica, 24 (1988), 3-18.
[10] M. Hafayed, S. Abbas, Filippov approach in necessary conditions of optimality for singular control problem, Int. J. Pure Appl. Math, 77 (2012), 667-680.
[11] R. F., Hartl, S. P., Sethi, R. G., Vickson, A Survey of the Maximum Principles for Optimal Control Problems with State Constraints, SIAM Review, 37 (1995), no. 2, 181-218.
[12] R. C., Loxton, K. L., Teo, V., Rehbock, K. F. C., Yiu, Optimal control problems with a continuous inequality constraint on the state and the control, Automatica, 45 (2009), 2250-2257.
[13] H., Modares, M. B. N., Solving nonlinear optimal control problems using a hybrid IPSO-SQP algorithm, Eng. Appl. Artif. Intel., 24 (2011), 476-484.
[14] L. S., Pontryagin, V. G., Boltyanskii, R. V., Gamkrelidze, E. F., Mischenko, The mathematical theory of optimal processes (Translation by L. W., Neustadt), Macmillan, New York, (1962).
[15] R. G., Regis, Convergence guarantees for generalized adaptive stochastic search methods for continuous global optimization, Eur. J. Oper. Res., 207 (2010), 1187-1202.
[16] I., Sadek, T., Abualrub, M., Abukhaled, A computational method for solving optimal control of a system of parallel beams using Legendre wavelets, Math. Comput. Model., 45 (2007), 1253-1264.
[17] M., Schlegel, K., Stockmann, T., Binder, W., Marquardt, Dynamic optimization using adaptive control vector parameterization, Comput. Chem. Eng., 29 (2005), 1731-1751.
[18] K. L., Teo, C. J., Goh, K. H., Wong, A unified computational approach to optimal control problems, Scientific & Technical, London, (1991).
[19] R., Vinter, Optimal Control, Birkhauser, Boston, (2010).
[20] J., Vlassenbroeck, A Chebyshev Polynomial Method for Optimal Control with State Constraints, Automatica, 24 (1988), 499-506.