Nonlinear MPC for Feedback-Interconnected Systems: a Suboptimal and Reduced-Order Model Approach

TL;DR

This paper introduces a suboptimal, reduced-order Model Predictive Control architecture for feedback-interconnected systems, ensuring global exponential stability despite using simplified models and limited optimization iterations.

Contribution

It presents a novel MPC approach combining suboptimality and model reduction, with theoretical stability guarantees for complex interconnected systems.

Findings

Proves global exponential stability of the closed-loop system.

Validates the approach through numerical simulations on a mechatronic pendulum system.

Abstract

In this paper, we propose a suboptimal and reduced-order Model Predictive Control (MPC) architecture for discrete-time feedback-interconnected systems. The numerical MPC solver: (i) acts suboptimally, performing only a finite number of optimization iterations at each sampling instant, and (ii) relies only on a reduced-order model that neglects part of the system dynamics, either due to unmodeled effects or the presence of a low-level compensator. We prove that the closed-loop system resulting from the interconnection of the suboptimal and reduced-order MPC optimizer with the full-order plant has a globally exponentially stable equilibrium point. Specifically, we employ timescale separation arguments to characterize the interaction between the components of the feedback-interconnected system. The analysis relies on an appropriately tuned timescale parameter accounting for how fast the system dynamics are sampled. The theoretical results are validated through numerical simulations on a mechatronic system consisting of a pendulum actuated by a DC motor.