Applications of polytopic approximations of reachable sets to linear dynamic games and a class of nonlinear systems

This paper presents applications of polytopic approximation methods for reachable set computations using dynamic optimization. The problem of computing exact reachable sets can be formulated in terms of Hamilton-Jacobi partial differential equation (PDE). Numerical solutions, which provide convergent approximations of this PDE, have computational complexity, which is exponential in the continuous variable dimension. Using dynamic optimization and polytopic approximation, computationally efficient algorithms for overapproximative reachability analysis have been developed for linear dynamical systems by P. Varaiya (1998). In this paper, we show that these can be extended to feedback linearizable nonlinear systems, linear dynamic games, and norm-bounded nonlinear systems. Three illustrative examples are presented.