Linear Tracking MPC for Nonlinear Systems-Part II: The Data-Driven 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.2022.3166851
• 发表日期: 2022
• 页码: 4406-4421
• 关键词: trajectory; stability analysis; Linear systems; nonlinear dynamical systems; predictive models; Numerical stability; Noise measurement; Data-driven control; predictive control for linear systems; Nonlinear systems; time varying systems

摘要

In this article, we present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parameterization provided by the fundamental lemma of Willems et al. We use new input-output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints. As intermediate results of independent interest, we extend the fundamental lemma to affine systems and we derive novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor.