Robust model predictive control with sliding mode for constrained non‐linear systems

Abstract

This study proposes a tractable robust non-linear model predictive control for constrained continuous-time uncertain systems with stability guarantees. First, a sampled-data model predictive control for the nominal system is designed to provide a desired performance. Then, a sliding mode control is designed to recover the nominal performance for the uncertain system. The sampled-data model predictive control that is solved online includes the initial state of the model employed in the problem as a decision variable. By merging sampled-data model predictive control and sliding mode control in between samples, the effect of the uncertainty, which is matched with the input, is reduced efficiently. The computational complexity of the proposed robust model predictive control is the same as for the model predictive control while the input and state constraints satisfaction and asymptotic stability of the closed-loop system are achieved. To illustrate the effectiveness of the proposed approach, the controller is applied to a vehicle platooning system.