Abstract
Safety verification determines whether any trajectory starting from admissible initial states would intersect with a set of unsafe states. In this paper, we propose a numerical method for verifying safety of a network of interconnected hybrid dynamical systems with a state constraint based on bilinear sum-of-squares programming. The safety verification is conducted by the construction of a function of states called barrier certificate. We consider a finite number of interconnected hybrid systems satisfying the input-to-state property and the networked interconnections satisfying a dissipativity property. Through constructing a barrier certificate for each subsystem and imposing dissipation-inequality-like constraints on the interconnections, safety verification is formulated as a bilinear sum-of-squares feasibility problem. As a result, safety of the interconnected hybrid systems could be determined by solving an optimization problem, rather than solving differential equations. The proposed method makes it possible to verify the safety of interconnected hybrid systems, which is demonstrated by a numerical example.
Highlights
The problem of safety verification of hybrid dynamical systems has always been a fundamental issue within the systems, control, and computer communities
We concentrate on safety verification of a special kind of nonlinear hybrid dynamical system called polynomial hybrid system
We propose compositional barrier certificates for safety verification of interconnected hybrid systems
Summary
The problem of safety verification of hybrid dynamical systems has always been a fundamental issue within the systems, control, and computer communities. As an important numerical method of safety verification of dynamical systems, barrier certificates have been well developed under the frameworks of general nonlinear systems [9], time-delayed systems [10, 11], stochastic systems [12], interconnected continuous systems [13, 14], and hybrid systems [1, 15]. We propose compositional barrier certificates for safety verification of interconnected hybrid systems. Motivated by the above-mentioned reasons and the practical background, we consider the issue of developing compositional barrier certificates of interconnected hybrid systems for their safety verification. Numerical SOS programming solvers such as SOSTOOLS [21] and SOSOPT [22] are developed for such computations With this methodology, we are able to verify safety of interconnected hybrid systems without resorting exhaustive simulations.
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