Robust Adaptive MPC in the Presence of Nonlinear Time-Varying Uncertainties: An Uncertainty Compensation Approach

TL;DR

This paper presents a robust adaptive MPC framework that compensates for nonlinear time-varying uncertainties using an L1 adaptive controller and robust feedback, ensuring constraint satisfaction and improved performance.

Contribution

The paper introduces UC-MPC, a novel approach combining uncertainty compensation with adaptive and robust control to handle nonlinear time-varying uncertainties in linear systems.

Findings

Enhanced constraint satisfaction in uncertain systems

Improved control performance demonstrated in simulations

Effective compensation for matched and unmatched uncertainties

Abstract

This paper introduces an uncertainty compensation-based robust adaptive model predictive control (MPC) framework for linear systems with nonlinear time-varying uncertainties. The framework integrates an L1 adaptive controller to compensate for the matched uncertainty and a robust feedback controller, designed using linear matrix inequalities, to mitigate the effect of unmatched uncertainty on target output channels. Uniform bounds on the errors between the system's states and control inputs and those of a nominal (i.e., uncertainty-free) system are derived. These error bounds are then used to tighten the actual system's state and input constraints, enabling the design of an MPC for the nominal system under these tightened constraints. Referred to as uncertainty compensation-based MPC (UC-MPC), this approach ensures constraint satisfaction while delivering enhanced performance compared to existing methods. Simulation results for a flight control example and a spacecraft landing on an asteroid demonstrate the effectiveness of the proposed framework.