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

Inseok Hwang, D.M. Stipanovic, C.J. Tomlin
Proceedings of the 2003 American Control Conference, 2003.  
This paper presents applications of polytopic a p proximation 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 a p proximation, computationally
more » ... mputationally efficient algorithms for overapproximative reachability analysis have been developed for linear dynmical systems [l]. In this paper, we show that these can be extended to feedback linearizable nonlinear systems, linear dynamic games, ancl norm-hounded nonlinear systems. Three illustrative examples are presented.
doi:10.1109/acc.2003.1242451 fatcat:j6j2tdno6rawda6sanseipzolu