Viability, viscosity, and storage functions in model-predictive control with terminal constraints

Abstract

Under terminal constraints, the set of states such that a model-predictive control strategy is feasible, and thus stable, is equivalent to the viable-reachable set of the controlled system. We prove that viscosity and storage function approaches to viability theory are equivalent to each other. Based on these results we propose inner and outer bounds of the feasible set by storage functions, which for polynomial systems can be computed using sum-of-squares programmes. Numerical, discrete-time and continuous-time examples are given for lateral car dynamics and the forced Van der Pol oscillator, respectively.