An efficient computational approach to a class of minmax optimal control problems with applications

B. Li, Kok Lay Teo, G. H. Zhao, G. R. Duan

Abstract


In this paper, an efficient computational method is developed for solving a general class of minmax optimal control problems where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst.


doi:10.1017/S1446181110000040

Keywords


minmax optimal control, continuous state inequality constraints, constraint transcription, computational method, control parametrization, time scaling transform, root finding, obstacle avoidance, aircraft abort landing, windshear downburst



DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2917



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.