@inbook{cea07f70b3894b4c8c07afbd8381fd3e,
title = "Polytopic approximations of reachable sets applied to linear dynamic games and a class of nonlinear systems",
abstract = "This chapter 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 algorithms for overapproximative reachability analysis have been developed for linear dynamical systems tikya[1]. In this chapter, we extend these to feedback linearizable nonlinear systems, linear dynamic games, and norm-bounded nonlinear systems. Three illustrative examples are presented.",
keywords = "Convex Polytope, Disturbance Input, Hybrid System, Linear Dynamical System, Protected Zone",
author = "Inseok Hwang and Stipanovi{\'c}, \{Du{\v s}an M.\} and Tomlin, \{Claire J.\}",
note = "★This research was supported by DARPA under the Software Enabled Control Program (AFRL contract F33615-99-C-3014), by ONR under MURI contract N00014-02-1-0720, and by an NSF Career Award (ECS-9985072).",
year = "2005",
doi = "10.1007/0-8176-4409-1\_1",
language = "English (US)",
series = "Systems and Control: Foundations and Applications",
publisher = "Birkh{\"a}user",
number = "9780817643850",
pages = "3--19",
booktitle = "Systems and Control",
address = "Switzerland",
edition = "9780817643850",
}