Maximum Likelihood Signal Matrix Model for Data-Driven Predictive Control

The paper presents a data-driven predictive control framework based on an implicit input-output mapping derived directly from the signal matrix of collected data. This signal matrix model is derived by maximum likelihood estimation with noise-corrupted data. By linearizing online, the implicit model can be used as a linear constraint to characterize possible trajectories of the system in receding horizon control. The signal matrix can also be updated online with new measurements. This algorithm can be applied to large datasets and slowly time-varying systems, possibly with high noise levels. An additional regularization term on the prediction error can be introduced to enhance the predictability and thus the control performance. Numerical results demonstrate that the proposed signal matrix model predictive control algorithm is effective in multiple applications and performs better than existing data-driven predictive control algorithm.

[1]  Matthew Brand,et al.  Incremental Singular Value Decomposition of Uncertain Data with Missing Values , 2002, ECCV.

[2]  Håkan Hjalmarsson,et al.  From experiment design to closed-loop control , 2005, Autom..

[3]  Pietro Tesi,et al.  Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness , 2019, IEEE Transactions on Automatic Control.

[4]  Mingzhou Yin,et al.  Maximum Likelihood Estimation in Data-Driven Modeling and Control , 2021, IEEE Transactions on Automatic Control.

[5]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[6]  John Lygeros,et al.  Data-Enabled Predictive Control: In the Shallows of the DeePC , 2018, 2019 18th European Control Conference (ECC).

[7]  Michail G. Lagoudakis,et al.  Least-Squares Policy Iteration , 2003, J. Mach. Learn. Res..

[8]  Benjamin Recht,et al.  A Tour of Reinforcement Learning: The View from Continuous Control , 2018, Annu. Rev. Control. Robotics Auton. Syst..

[9]  Bart De Moor,et al.  A note on persistency of excitation , 2005, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[10]  Basil Kouvaritakis,et al.  Model Predictive Control: Classical, Robust and Stochastic , 2015 .

[11]  Toshiharu Sugie,et al.  Adaptive model predictive control for a class of constrained linear systems based on the comparison model , 2007, Autom..

[12]  N. S. Khalid.  On-and off-line identification of linear state space models , 2012 .

[13]  M. Kanat Camlibel,et al.  Willems’ Fundamental Lemma for State-Space Systems and Its Extension to Multiple Datasets , 2020, IEEE Control Systems Letters.

[14]  John Lygeros,et al.  Regularized and Distributionally Robust Data-Enabled Predictive Control , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).

[15]  Paolo Rapisarda,et al.  Data-driven simulation and control , 2008, Int. J. Control.

[16]  Panos M. Pardalos,et al.  Approximate dynamic programming: solving the curses of dimensionality , 2009, Optim. Methods Softw..