Linear Tracking MPC for Nonlinear Systems-Part I: The Model-Based Case

• 成果类型: Article
• 署名作者: Berberich, Julian; Koehler, Johannes; Mueller, Matthias A.; Allgoewer, Frank
• 署名单位: University of Stuttgart; Swiss Federal Institutes of Technology Domain; ETH Zurich; Leibniz University Hannover
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3166872
• 发表日期: 2022
• 页码: 4390-4405
• 关键词: Predictive models; nonlinear dynamical systems; system dynamics; MANIFOLDS; steady-state; stability analysis; Target tracking; Nonlinear systems; predictive control for linear systems; time varying systems; tracking

摘要

In this article, we develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small, and hence, we can slide along the steady-state manifold toward the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix, which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Furthermore, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper.