A System Level Approach to Robust Model Predictive Control

Robust tube-based model predictive control (MPC) methods address constraint satisfaction by leveraging an a-priori determined tube controller in the prediction to tighten the constraints. This paper presents a system level tube-MPC (SLTMPC) method derived from the system level parameterization (SLP), which allows optimization over the tube controller online when solving the MPC problem, which can significantly reduce conservativeness. We derive the SLTMPC method by establishing an equivalence relation between a class of robust MPC methods and the SLP. Finally, we show that the SLTMPC formulation naturally arises from an extended SLP formulation and show its merits in a numerical example.

[1]  Rolf Findeisen,et al.  Parameterized Tube Model Predictive Control , 2012, IEEE Transactions on Automatic Control.

[2]  SLSpy: Python-Based System-Level Controller Synthesis Framework , 2020, ArXiv.

[3]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[4]  Carmen Amo Alonso,et al.  Explicit Distributed and Localized Model Predictive Control via System Level Synthesis , 2019, 2020 59th IEEE Conference on Decision and Control (CDC).

[5]  Eric C. Kerrigan,et al.  Optimization over state feedback policies for robust control with constraints , 2006, Autom..

[6]  Tamal Mukherjee,et al.  System-Level Synthesis , 2003 .

[7]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

[8]  Nikolai Matni,et al.  Robust Closed-loop Model Predictive Control via System Level Synthesis , 2019, 2020 59th IEEE Conference on Decision and Control (CDC).

[9]  John C. Doyle,et al.  MPC Without the Computational Pain: The Benefits of SLS and Layering in Distributed Control , 2020, ArXiv.

[10]  Andrea Carron,et al.  Distributed Safe Learning using an Invariance-based Safety Framework , 2020, IFAC-PapersOnLine.

[11]  Eduardo F. Camacho,et al.  Robust tube-based MPC for tracking of constrained linear systems with additive disturbances , 2010 .

[12]  Nikolai Matni,et al.  Separable and Localized System-Level Synthesis for Large-Scale Systems , 2017, IEEE Transactions on Automatic Control.

[13]  Nikolai Matni,et al.  Distributed and Localized Closed Loop Model Predictive Control via System Level Synthesis , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[14]  J. Löfberg,et al.  Approximations of closed-loop minimax MPC , 2003, CDC.

[15]  Luigi Chisci,et al.  Systems with persistent disturbances: predictive control with restricted constraints , 2001, Autom..

[16]  Alberto Bemporad,et al.  The explicit solution of model predictive control via multiparametric quadratic programming , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[17]  SooJean Han,et al.  System Level Synthesis via Dynamic Programming , 2020, 2020 59th IEEE Conference on Decision and Control (CDC).

[18]  Nikolai Matni,et al.  Safely Learning to Control the Constrained Linear Quadratic Regulator , 2018, 2019 American Control Conference (ACC).

[19]  Stephen P. Boyd,et al.  CVXPY: A Python-Embedded Modeling Language for Convex Optimization , 2016, J. Mach. Learn. Res..

[20]  G. W. Stewart,et al.  Matrix Algorithms: Volume 1, Basic Decompositions , 1998 .

[21]  David Q. Mayne,et al.  Robust model predictive control using tubes , 2004, Autom..

[22]  Maryam Kamgarpour,et al.  Sparsity Invariance for Convex Design of Distributed Controllers , 2019, IEEE Transactions on Control of Network Systems.

[23]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .