Polytopic Approximations of Reachable Sets Applied to Linear Dynamic Games and a Class of Nonlinear Systems [chapter]

Inseok Hwang, Dušan M. Stipanović, Claire J. Tomlin
Systems and Control: Foundations & Applications  
This paper presents applications of polytopic approximation methods for reachable set computation using dynamic optimization. The problem of computing exact reachable sets can be formulated in terms of a 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
more » ... algorithms for overapproximative reachability analysis have been developed for linear dynamical systems [1] . In this paper, we extend these to feedback linearizable nonlinear systems, linear dynamic games, and norm-bounded nonlinear systems. Three illustrative examples are presented. ⋆
doi:10.1007/0-8176-4409-1_1 fatcat:fr4ntt27p5cg5g7s77h7s5mm5i