Verifying Hybrid Systems Involving Transcendental Functions

Abstract

Abstract. We explore uses of a link we have constructed between the KeYmaera hybrid systems theorem prover and the MetiTarski proof engine for problems involving special functions such as sin, cos, exp, etc. Transcendental functions arise in the specification of hybrid systems and often occur in the solutions of the differential equations that govern how the states of hybrid systems evolve over time. To date, formulas exchanged between KeYmaera and external tools have involved polynomials over the reals, but not transcendental functions, chiefly because of the lack of tools capable of proving such goals.

Evaluating Model Checking Approaches to Verify Stability of Control Systems in Simulink

“…Control systems requirements such as stability via Lyapunov methods have been verified mostly through theorem proving by directly posing the problems in mathematical terms (e.g., inequalities of region intersections as in [18]) for continuous systems, or over controllers implemented in code [16], closer to discrete systems.…”

“…The restrictions on the continuous components of the hybrid systems, to piecewise affine dynamics, is shared by other tools for hybrid systems, such as the CheckMate model checker, and the theorem prover Keymaera [12,18]. Consequently, we hypothesised that this tool, and other similar ones, would not be suitable to model and consequently verify the stability requirements of the discrete systems in Section 3.…”