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Approximation of reachable sets using optimal control algorithms. (English) Zbl 1271.49021
Summary: We investigate and analyze a computational method for the approximation of reachable sets for nonlinear dynamic systems. The method uses grids to cover the region of interest and the distance function to the reachable set evaluated at grid points. A convergence analysis is provided and shows the convergence of three different types of discrete set approximations to the reachable set. The distance functions can be computed numerically by suitable optimal control problems in combination with direct discretization techniques which allows adaptive calculations of reachable sets. Several numerical examples with nonconvex reachable sets are presented.

MSC:
49M25 Discrete approximations in optimal control
49J15 Existence theories for optimal control problems involving ordinary differential equations
93B03 Attainable sets, reachability
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
90C30 Nonlinear programming
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