Adaptive MPC for Constrained Trajectory Tracking of Uncertain LTI System with Input-Rate Limits

TL;DR

This paper develops an adaptive model predictive control approach for constrained trajectory tracking of uncertain LTI systems, ensuring recursive feasibility and stability despite input-rate limits and full parametric uncertainty.

Contribution

It introduces a systematic adaptive MPC framework that handles full parametric uncertainty, input-rate constraints, and guarantees recursive feasibility and stability.

Findings

The proposed MPC ensures recursive feasibility under input-rate constraints.

Stability and convergence of tracking error are proven via Lyapunov analysis.

Simulation results demonstrate the effectiveness of the adaptive MPC approach.

Abstract

This paper addresses the trajectory-tracking problem for discrete-time linear time-invariant systems with bounded parametric uncertainty, subject to hard constraints on system states, control inputs, and input rates. Unlike existing methods, which often consider only partial uncertainty, omit input-rate or state constraints, or focus on regulation problems, this work provides a systematic adaptive model predictive control (MPC) solution for constrained trajectory tracking under full parametric uncertainty. Determining the control input required to achieve zero tracking error under unknown parameters is challenging. Simultaneously, trajectory tracking under uncertainty with input-rate constraints induces temporal coupling in the control sequence, resulting in a time-varying admissible control set and rendering standard recursive feasibility arguments inapplicable. These challenges are overcome by systematically utilizing the estimated system parameters, coupled with a suitably designed adaptive learning process within a reformulated MPC framework. The recursive feasibility of the proposed MPC optimization routine is then rigorously established despite the time-varying admissible control set induced by input-rate constraints. Closed-loop stability is guaranteed via Lyapunov-based analysis, ensuring convergence of the tracking error and boundedness of system states. Simulation results validate the effectiveness of the pr