Shortest-prediction-horizon non-linear model-predictive control with guaranteed asymptotic stability

Abstract

This paper presents a continuous-time shortest-prediction-horizon model-predictive control method that provides optimal output regulation with guaranteed closed-loop asymptotic stability within an assessable domain of attraction. The closed-loop stability is ensured by requiring plant state variables to satisfy a hard, Lyapunov, inequality constraint. Whenever the output regulation alone cannot ensure asymptotic closed-loop stability, the closed-loop system evolves while being at the hard constraint. Once the closed-loop system enters a state-space region in which the output regulation can ensure asymptotic stability, the hard constraint becomes inactive. Consequently, the non-linear control method is applicable to stable and unstable plants, whether non-minimum- or minimum-phase. A major shortcoming of unconstrained, shortest-prediction-horizon model-predictive control, which is equivalent to input–output linearization, is its inapplicability to plants operating at a non-minimum-phase steady state. This work addresses the major shortcoming. The control method is implemented on a chemical reactor with multiple steady states, to show its application and performance. The simulation results demonstrate that the closed-loop system is asymptotically stable for all physically-meaningful initial conditions.