Polytopic approximations of reachable sets applied to linear dynamic games and a class of nonlinear systems

Inseok Hwang, Dušan M. Stipanović, Claire J. Tomlin

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish (US)
Title of host publicationSystems and Control
Subtitle of host publicationFoundations and Applications
Number of pages17
StatePublished - 2005

Publication series

NameSystems and Control: Foundations and Applications
ISSN (Print)2324-9749
ISSN (Electronic)2324-9757


  • Convex Polytope
  • Disturbance Input
  • Hybrid System
  • Linear Dynamical System
  • Protected Zone

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Computer Science Applications
  • Control and Optimization
  • Computational Mathematics


Dive into the research topics of 'Polytopic approximations of reachable sets applied to linear dynamic games and a class of nonlinear systems'. Together they form a unique fingerprint.

Cite this