Stability-Based Hybrid Automata for Safety Verification Using Continuation Methods

Abstract

The rapid development of increasingly autonomous systems has advanced the challenge of safety assurance beyond the capabilities of existing methods. Therefore, new means of verification and validation are required to ensure the safe operation of emerging systems. Numerical continuation characterizes system behavior as parameters are varied and can be used to facilitate a bifurcation analysis, where equilibria and their stability properties are identified. This paper introduces hybrid stability automata -- system models constructed using numerical continuation that capture stability properties within a series of dynamic modes. These automata readily support safety analyses by explicitly defining stable, i.e. safe, regions of the operational envelope. The processes to create hybrid stability automata for one-dimensional and multi-dimensional systems are discussed and prototypical examples are presented. Example safety analyses using hybrid stability automata are demonstrated on the space shuttle reentry dynamics.