Adaptive Output Feedback Model Predictive Control

TL;DR

This paper introduces an adaptive output feedback MPC method combining an adaptive observer with robust MPC to handle uncertain systems without state measurements, ensuring recursive feasibility and robust constraint satisfaction.

Contribution

It proposes a novel two-tube approach with an adaptive observer and robust MPC, providing recursive feasibility and robustness in output feedback MPC for uncertain systems.

Findings

Ensures recursive feasibility of the control scheme.

Provides robustness against estimation errors.

Demonstrates effectiveness through simulation results.

Abstract

Model predictive control (MPC) for uncertain systems in the presence of hard constraints on state and input is a non-trivial problem, and the challenge is increased manyfold in the absence of state measurements. In this paper, we propose an adaptive output feedback MPC technique, based on a novel combination of an adaptive observer and robust MPC, for single-input single-output discrete-time linear time-invariant systems. At each time instant, the adaptive observer provides estimates of the states and the system parameters that are then leveraged in the MPC optimization routine while robustly accounting for the estimation errors. The solution to the optimization problem results in a homothetic tube where the state estimate trajectory lies. The true state evolves inside a larger outer tube obtained by augmenting a set, invariant to the state estimation error, around the homothetic tube sections. The proof for recursive feasibility for the proposed `homothetic and invariant' two-tube approach is provided, along with simulation results on an academic system.