Overapproximating the Reachable Values Set of Piecewise Affine Systems Coupling Policy Iterations with Piecewise Quadratic Lyapunov Functions
For control theorists and engineers, this provides a tighter overapproximation for safety verification of piecewise affine systems, though it is an incremental improvement over existing work.
The paper refines an overapproximation of the reachable values set for piecewise affine discrete-time systems by coupling policy iterations with piecewise quadratic Lyapunov functions, improving upon previous methods.
We have recently constructed a piecewise quadratic Lyapunov function to prove the boundedness of the reachable values set of piecewise affine discrete-time systems. The method developed also provided an overapproximation of the reachable values set. In this paper, we refine the latter overapproximation extending previous works combining policy iterations with quadratic Lyapunov functions.