Primal–dual tests for safety and reachability

Authors:
Stephen Prajna;Anders Rantzer
Affiliations:
Control and Dynamical Systems, California Institute of Technology, Pasadena, CA;Department of Automatic Control, Lund Institute of Technology, Lund, Sweden
Venue:
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Year:
2005

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Abstract

A methodology for safety verification using barrier certificates has been proposed recently. Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety, in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i.e., the reachability problem, concerns proving the existence of a trajectory starting from the initial set that reaches another given set. Using insights from convex duality and the concept of density functions, in this paper we show that reachability can also be verified through convex programming. Several convex programs for verifying safety, reachability, and other properties such as eventuality are formulated. Some examples are provided to illustrate their applications.