Scenario optimization robust predictive control via Gaussian regression learning

doi:10.3785/j.issn.1008-973X.2023.04.006

Journal of ZheJiang University (Engineering Science)

2023, Vol. 57

Issue (4): 693-701 DOI: 10.3785/j.issn.1008-973X.2023.04.006

Scenario optimization robust predictive control via Gaussian regression learning

Wei-liang XIONG(

),De-feng HE*(

),Xiu-li WANG,Dan ZHOU

College of Information Engineering, Zhejiang University of Technology, Hangzhou 310012, China

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Abstract

A scenario optimization robust model predictive control algorithm based on Gaussian process regression was proposed for constrained linear systems with unknown additive uncertainty. The Gaussian regression was used to learn the uncertainty parameter from the empirical data in the offline stage, so that sufficient scenarios could be obtained. The finite-horizon optimal control problem constructed by extracted scenarios was solved in the online control stage, and the control law obtained by rolling optimization was used to control the system. The relaxation variable was introduced to ensure the feasibility of the optimization problem. Then the random convex optimization theory was used. It was proved that the closed-loop system satisfied the relaxed chance constraint and converged to the terminal set with certain confidence bound. The control simulation experiments of a DC-DC converter and a connected vehicle cruise system illustrated the feasibility and merits of the proposed algorithm.

Key words： robust model predictive control scenario optimization Gaussian regression learning chance constraint random convex optimization

Received: 26 April 2022 Published: 21 April 2023

CLC:

TP 273

Fund: 国家自然科学基金资助项目（62173303）；浙江省属高校基本科研业务费资助项目（RF-C2020003）

Corresponding Authors: De-feng HE E-mail: 17857102644@163.com;hdfzj@zjut.edu.cn

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Cite this article:

Wei-liang XIONG,De-feng HE,Xiu-li WANG,Dan ZHOU. Scenario optimization robust predictive control via Gaussian regression learning. Journal of ZheJiang University (Engineering Science), 2023, 57(4): 693-701.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.04.006 OR https://www.zjujournals.com/eng/Y2023/V57/I4/693

基于高斯回归学习的场景优化鲁棒预测控制

针对具有未知加性不确定性的约束线性系统，提出基于高斯过程回归学习的场景优化鲁棒模型预测控制算法. 在离线阶段使用高斯回归从经验数据中学习不确定性结构与参数，能够抽取大量随机场景. 在在线控制阶段中，求解抽取场景所构建的有限时域优化问题，将滚动优化得到的控制律作用于系统. 引入松弛变量保证优化问题的可行性，应用随机凸优化理论，证明所提算法使系统以一定的置信度满足松弛机会约束，收敛于终端域. 通过DC-DC转换器和网联车巡航控制仿真实验，验证了本文算法的有效性和优越性.

关键词： 鲁棒模型预测控制, 场景优化, 高斯回归学习, 机会约束, 随机凸优化

Fig.1 Fitting results and bilateral 0.8 confidence region of GP

Tab.1 Statistical results of 10 000 Monte Carlo simulations

Fig.2 State constraint set and one-step reachable set of initial state

Fig.3 10 000 Monte Carlo state trajectories of algorithm 1 at P_p = 0.1

Fig.4 10 000 Monte Carlo input trajectories of algorithm 1 at P_p = 0.1

Tab.2 Ideal acceleration data under two working conditions

Fig.5 Comparison of acceleration under decelerating condition

Fig.6 Comparison of speed under decelerating condition

Fig.7 Comparison of spacing error under decelerating condition

Fig.8 Comparison of state trajectory in decelerating condition

Fig.9 Comparison of acceleration under accelerating condition

Fig.10 Comparison of speed under accelerating condition

Fig.11 Comparison of spacing error under accelerating condition

Fig.12 Comparison of state trajectory under accelerating case


[1]	SCHWENZER M, AY M, BERGS T, et al Review on model predictive control: an engineering perspective[J]. The International Journal of Advanced Manufacturing Technology, 2021, 117 (5): 1327- 1349

[2]	MUNOZ-CARPINTERO D, CANNON M Convergence of stochastic nonlinear systems and implications for stochastic model-predictive control[J]. IEEE Transactions on Automatic Control, 2020, 66 (6): 2832- 2839

[3]	MAYNE D Q Model predictive control: recent developments and future promise[J]. Automatica, 2014, 50 (12): 2967- 2986 doi: 10.1016/j.automatica.2014.10.128

[4]	MAYNE D Robust and stochastic model predictive control: are we going in the right direction[J]. Annual Reviews in Control, 2016, 41: 184- 192 doi: 10.1016/j.arcontrol.2016.04.006

[5]	RAWLINGS J B, MAYNE D Q, DIEHL M. Model predictive control: theory, computation, and design [M]. Madison, WI: Nob Hill, 2017.

[6]	HEYDARI R, FARROKHI M Robust tube-based model predictive control of LPV systems subject to adjustable additive disturbance set[J]. Automatica, 2021, 129: 109672 doi: 10.1016/j.automatica.2021.109672

[7]	HANEMA J, LAZAR M, TÓTH R Heterogeneously parameterized tube model predictive control for LPV systems[J]. Automatica, 2020, 111: 108622 doi: 10.1016/j.automatica.2019.108622

[8]	ZHANG K, LIU C, SHI Y Self-triggered adaptive model predictive control of constrained nonlinear systems: a min–max approach[J]. Automatica, 2022, 142: 110424 doi: 10.1016/j.automatica.2022.110424

[9]	MESBAH A Stochastic model predictive control: an overview and perspectives for future research[J]. IEEE Control Systems Magazine, 2016, 36 (6): 30- 44 doi: 10.1109/MCS.2016.2602087

[10]	MUÑOZ-CARPINTERO D, HU G, SPANOS C J Stochastic model predictive control with adaptive constraint tightening for non-conservative chance constraints satisfaction[J]. Automatica, 2018, 96: 32- 39 doi: 10.1016/j.automatica.2018.06.026

[11]	ZIDEK R A E, KOLMANOVSKY I V, BEMPORAD A Model predictive control for drift counteraction of stochastic constrained linear systems[J]. Automatica, 2021, 123: 109304 doi: 10.1016/j.automatica.2020.109304

[12]	DHAR A, BHASIN S Indirect adaptive MPC for discrete-time LTI systems with parametric uncertainties[J]. IEEE Transactions on Automatic Control, 2021, 66 (11): 5498- 5505 doi: 10.1109/TAC.2021.3050446

[13]	CALAFIORE G C, FAGIANO L Robust model predictive control via scenario optimization[J]. IEEE Transactions on Automatic Control, 2012, 58 (1): 219- 224

[14]	CALAFIORE G C, FAGIANO L Stochastic model predictive control of LPV systems via scenario optimization[J]. Automatica, 2013, 49 (6): 1861- 1866 doi: 10.1016/j.automatica.2013.02.060

[15]	LORENZEN M, DABBENE F, TEMPO R, et al Stochastic MPC with offline uncertainty sampling[J]. Automatica, 2017, 81: 176- 183 doi: 10.1016/j.automatica.2017.03.031

[16]	SCHILDBACH G, FAGIANO L, MORARI M Randomized solutions to convex programs with multiple chance constraints[J]. SIAM Journal on Optimization, 2013, 23 (4): 2479- 2501 doi: 10.1137/120878719

[17]	ROSOLIA U, ZHANG X, BORRELLI F Data-driven predictive control for autonomous systems[J]. Annual Review of Control, Robotics, and Autonomous Systems, 2018, 1 (1): 259- 286 doi: 10.1146/annurev-control-060117-105215

[18]	CAMPI M C, GARATTI S The exact feasibility of randomized solutions of uncertain convex programs[J]. SIAM Journal on Optimization, 2008, 19 (3): 1211- 1230 doi: 10.1137/07069821X

[19]	HEWING L, WABERSICH K P, MENNER M, et al Learning-based model predictive control: toward safe learning in control[J]. Annual Review of Control, Robotics, and Autonomous Systems, 2020, 3 (1): 269- 296 doi: 10.1146/annurev-control-090419-075625

[20]	HEWING L, KABZAN J, ZEILINGER M N Cautious model predictive control using Gaussian process regression[J]. IEEE Transactions on Control Systems Technology, 2019, 28 (6): 2736- 2743

[21]	KLENSKE E D, ZEILINGER M N, SCHÖLKOPF B, et al Gaussian process-based predictive control for periodic error correction[J]. IEEE Transactions on Control Systems Technology, 2015, 24 (1): 110- 121

[22]	TERZI E, FARINA M, FAGIANO L, et al Robust multi-rate predictive control using multi-step prediction models learned from data[J]. Automatica, 2022, 136: 109852 doi: 10.1016/j.automatica.2021.109852

[23]	KÖHLER J, KÖTTING P, SOLOPERTO R, et al A robust adaptive model predictive control framework for nonlinear uncertain systems[J]. International Journal of Robust and Nonlinear Control, 2021, 31 (18): 8725- 8749 doi: 10.1002/rnc.5147

[24]	MANZANO J M, DE LA PENA D M, CALLIESS J P, et al Componentwise hölder inference for robust learning-based MPC[J]. IEEE Transactions on Automatic Control, 2021, 66 (11): 5577- 5583 doi: 10.1109/TAC.2021.3056356

[25]	WILLIAMS C K I, RASMUSSEN C E. Gaussian processes for machine learning [M]. Cambridge: MIT press, 2006.

[26]	LI F, LI H, HE Y Adaptive stochastic model predictive control of linear systems using Gaussian process regression[J]. IET Control Theory and Applications, 2021, 15 (5): 683- 693 doi: 10.1049/cth2.12070

[27]	GRANCHAROVA A, KOCIJAN J, JOHANSEN T A Explicit stochastic predictive control of combustion plants based on Gaussian process models[J]. Automatica, 2008, 44 (6): 1621- 1631 doi: 10.1016/j.automatica.2008.04.002

[28]	WANG Y, OCAMPO‐MARTINEZ C, PUIG V Stochastic model predictive control based on Gaussian processes applied to drinking water networks[J]. IET Control Theory and Applications, 2016, 10 (8): 947- 955 doi: 10.1049/iet-cta.2015.0657

[29]	BISHOP C M, NASRABADI N M. Pattern recognition and machine learning [M]. New York: Springer, 2006.

[30]	CLOETE J B, STANDER T, WILKE D N Parametric circuit fault diagnosis through oscillation-based testing in analogue circuits: statistical and deep learning approaches[J]. IEEE Access, 2022, 10: 15671- 15680 doi: 10.1109/ACCESS.2022.3149324

[31]	WANG J, JIANG C, HAN Z, et al Internet of vehicles: sensing-aided transportation information collection and diffusion[J]. IEEE Transactions on Vehicular Technology, 2018, 67 (5): 3813- 3825 doi: 10.1109/TVT.2018.2796443

[32]	ALI I, AHMEDY I, GANI A, et al Data collection in studies on Internet of things (IoT), wireless sensor networks (WSNs), and sensor cloud (SC): similarities and differences[J]. IEEE Access, 2022, 10: 33909- 33931 doi: 10.1109/ACCESS.2022.3161929

[33]	KOUVARITAKIS B, CANNON M. Model predictive control: classical, robust and stochastic [M]. Switzerland: Springer, 2016.

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