Viable set computation for hybrid systems

Abstract

In this paper, we revisit the problem of computing viability sets for hybrid systems with nonlinear continuous dynamics and competing inputs. As usual in the literature, an iterative algorithm, based on the alternating application of a continuous and a discrete operator, is employed. Different cases, depending on whether the continuous evolution and the number of discrete transitions are finite or infinite, are considered. A complete characterization of the reach-avoid computation (involved in the continuous time calculation) is provided based on dynamic programming. Moreover, for a certain class of automata, we show convergence of the iterative process by using a constructive version of Tarski’s fixed point theorem, to determine the maximal fixed point of a monotone operator on a complete lattice of closed sets. The viability algorithm is applied to a benchmark example and to the problem of voltage stability for a single machine-load system in case of a line fault.