Switching control of differential-algebraic equations with temporal logic specifications

This paper studies the switching control of differential-algebraic equations (DAEs). A specific problem concerned with switched DAEs is that jumps or impulses could be induced by mode switching, which is not well understood in many applications. We aim to find the control strategies that minimize the overall magnitude of undesirable jumps or impulses while rendering the systems achieve the expected behaviors. Applying an abstraction-based hybrid controller design framework, we extend formal methods to the control synthesis for switched DAEs with the specifications expressed in linear temporal logic. Abstractions are computed utilizing incrementally globally aymptotically stable property and Lyapunov-like functions. We illustrate the control synthesis procedure using a numerical example.