Skip to main content
Article
Approximate Bisimulations for Nonlinear Dynamical Systems
Departmental Papers (ESE)
  • Antoine Girard, University of Pennsylvania
  • George J Pappas, University of Pennsylvania
Document Type
Conference Paper
Date of this Version
12-12-2005
Comments
Copyright 2005 IEEE. Reprinted from Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, December 2005, pages 684-689.

This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
Abstract

The notion of exact bisimulation equivalence for nondeterministic discrete systems has recently resulted in notions of exact bisimulation equivalence for continuous and hybrid systems. In this paper, we establish the more robust notion of approximate bisimulation equivalence for nondeterministic nonlinear systems. This is achieved by requiring that a distance between system observations starts and remains, close, in the presence of nondeterministic system evolution. We show that approximate bisimulation relations can be characterized using a class of functions called bisimulation functions. For nondeterministic nonlinear systems, we show that conditions for the existence of bisimulation functions can be expressed in terms of Lyapunov-like inequalities, which for deterministic systems can be computed using recent sum-of-squares techniques. Our framework is illustrated on a safety verification example.

Citation Information
Antoine Girard and George J Pappas. "Approximate Bisimulations for Nonlinear Dynamical Systems" (2005)
Available at: http://works.bepress.com/george_pappas/202/