Suboptimal and Reduced-Order MPC via Timescale Separation

Abstract: In this paper, we propose a generalized framework for the design and analysis of suboptimal and reduced-order nonlinear Model Predictive Control (MPC) architectures. The proposed framework manages real-time operation of MPC schemes by (i) computing the control action suboptimally, i.e., by running a generic optimal control algorithm for a finite number of iterations, and (ii) relying on a reduced-order model that neglects part of the plant dynamics (accounting for, e.g., unmodeled dynamics or a low-level compensator). To rigorously handle the interplay between optimization error and model mismatch, we treat the sampling time as a tunable design parameter. We analyze the resulting closed-loop system, comprising the full-order physical plant interconnected with the iterative optimization algorithm (treated as a dynamical system), by leveraging tools from timescale separation. We prove that operating at a sufficiently fast sampling rate ensures that the closed-loop system maintains recursive feasibility and achieves an exponentially stable equilibrium point. The effectiveness of the proposed framework is validated on an underactuated two-link robotic arm through virtual experiments in the high-fidelity MuJoCo physics engine.