A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version

TL;DR

This paper introduces a computationally efficient robust nonlinear model predictive control framework that guarantees constraint satisfaction and stability for uncertain systems by using offline computed bounds and an online constructed tube.

Contribution

It proposes a novel robust MPC scheme that combines offline Lyapunov-based bounds with online optimization for efficient control of uncertain nonlinear systems.

Findings

Ensures robust constraint satisfaction and practical stability.

Achieves similar robustness with less online computational effort.

Demonstrates effectiveness on a nonlinear benchmark example.

Abstract

In this paper, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighbourhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state of the art robust MPC approaches with a nonlinear benchmark example. This paper is an extended version of [1], and contains further details and additional considers: continuous-time systems (App. A), more general nonlinear constraints (App. B) and special cases (Sec. IV).