Optimal control computation for nonlinear systems with state-dependent stopping criteria. (English) Zbl 1258.49051

Summary: In this paper, we consider a challenging optimal control problem in which the terminal time is determined by a stopping criterion. This stopping criterion is defined by a smooth surface in the state space; when the state trajectory hits this surface, the governing dynamic system stops. By restricting the controls to piecewise constant functions, we derive a finite-dimensional approximation of the optimal control problem. We then develop an efficient computational method, based on nonlinear programming, for solving the approximate problem. We conclude the paper with four numerical examples.


49M37 Numerical methods based on nonlinear programming
49K15 Optimality conditions for problems involving ordinary differential equations
90C30 Nonlinear programming


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