Positive Invariance of Constrained Affine Dynamics and Its Applications to Hybrid Systems and Safety Verification
Links to Files
Author/Creator
Author/Creator ORCID
Date
Type of Work
Department
Program
Citation of Original Publication
Shen, Jinglai. “Positive Invariance of Constrained Affine Dynamics and Its Applications to Hybrid Systems and Safety Verification.” IEEE Transactions on Automatic Control 57, no. 1 (January 2012): 3–18. https://doi.org/10.1109/TAC.2011.2142570.
Rights
© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Abstract
Motivated by long-time dynamic analysis of hybrid systems and safety verification problems, this paper addresses fundamental positive invariance issues of an affine dynamical system on a general polyhedron and their applications. Necessary and sufficient algebraic conditions are established for the existence of a positively invariant set of an affine system on a polyhedron using the tools of lexicographic relation and long-time oscillatory dynamic analysis. A linear program based algorithm is proposed to verify these conditions, and its computational complexity is analyzed. The positive invariance results are applied to obtain an explicit characterization of global switching behaviors of piecewise affine systems. Further, the positive invariance techniques developed in this paper are exploited to show the decidability of safety verification of a class of affine dynamics on semialgebraic sets.