Robust learning-based MPC for nonlinear constrained systems

This paper presents a robust learning-based predictive control strategy for nonlinear systems subject to both input and output constraints, under the assumption that the model function is not known a priori and only input–output data are available. The proposed controller is obtained using a nonparametric machine learning technique to estimate a prediction model. Based on this prediction model, a novel stabilizing robust predictive controller without terminal constraint is proposed. The design procedure is purely based on data and avoids the estimation of any robust invariant set, which is in general a hard task. The resulting controller has been validated in a simulated case study.

[1]  David Muñoz de la Peña,et al.  Output feedback MPC based on smoothed projected kinky inference , 2019, IET Control Theory & Applications.

[2]  David Muñoz de la Peña,et al.  Offset free data driven control: application to a process control trainer , 2019, IET Control Theory & Applications.

[3]  I. J. Leontaritis,et al.  Input-output parametric models for non-linear systems Part II: stochastic non-linear systems , 1985 .

[4]  Riccardo Scattolini,et al.  A stabilizing model-based predictive control algorithm for nonlinear systems , 2001, Autom..

[5]  D. Limón,et al.  Input-to-State Stability: A Unifying Framework for Robust Model Predictive Control , 2009 .

[6]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[7]  G. Beliakov Interpolation of Lipschitz functions , 2006 .

[8]  Jaime F. Fisac,et al.  A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems , 2017, IEEE Transactions on Automatic Control.

[9]  Rahul Mangharam,et al.  Data-Driven Modeling, Control and Tools for Cyber-Physical Energy Systems , 2016, 2016 ACM/IEEE 7th International Conference on Cyber-Physical Systems (ICCPS).

[10]  S. Shankar Sastry,et al.  Provably safe and robust learning-based model predictive control , 2011, Autom..

[11]  Daniel Limon,et al.  Robust Data-Based Model Predictive Control for Nonlinear Constrained Systems , 2018 .

[12]  Rolf Findeisen,et al.  Stability of Gaussian Process Learning Based Output Feedback Model Predictive Control , 2018 .

[13]  Thomas D. Sandry,et al.  Probabilistic and Randomized Methods for Design Under Uncertainty , 2007, Technometrics.

[14]  Lukas Hewing,et al.  Learning-Based Model Predictive Control: Toward Safe Learning in Control , 2020, Annu. Rev. Control. Robotics Auton. Syst..

[15]  Dario Ambrosini,et al.  Data-driven model predictive control using random forests for building energy optimization and climate control , 2018, Applied Energy.

[16]  Biao Huang,et al.  System Identification , 2000, Control Theory for Physicists.

[17]  Jan-P. Calliess,et al.  Lazily Adapted Constant Kinky Inference for Nonparametric Regression and Model-Reference Adaptive Control , 2016, Autom..

[18]  A. G. Sukharev Optimal method of constructing best uniform approximations for functions of a certain class , 1978 .

[19]  E. F. Camacho,et al.  On the computation of convex robust control invariant sets for nonlinear systems , 2010, Autom..

[20]  Alberto Bemporad,et al.  Direct Data-Driven Control of Constrained Systems , 2018, IEEE Transactions on Control Systems Technology.

[21]  Massimo Canale,et al.  Nonlinear model predictive control from data: a set membership approach , 2014 .

[22]  Robert L. Smith,et al.  Optimal estimation of univariate black-box Lipschitz functions with upper and lower error bounds , 2003, Comput. Oper. Res..

[23]  K. S. Narendra,et al.  Identification of Nonlinear Dynamical Systems Using Neural Networks , 1997 .

[24]  Stephen J. Roberts,et al.  Conservative decision-making and interference in uncertain dynamical systems , 2014 .

[25]  Carlo Novara,et al.  Set Membership identification of nonlinear systems , 2004, Autom..