探讨了一类含参数不确定和输入延迟的约束多输入多输出线性系统的自适应模型预测控制问题。提出了一种基于时变更新率的自适应更新律,实现了在输入延迟的情况下更新估计系统的不确定参数。为了处理约束,将优化问题转换为源自于min-max优化可解的简单结构。此外,从理论上证明了闭环系统的渐近稳定性,并证明了提出的自适应模型预测控制策略是递归可行的。最后,数值模拟验证了所提方法的有效性。
This paper investigates the adaptive model predictive control (MPC) for a class of constrained linear multiple-input multiple-output (MIMO) systems with parametric uncertainty and input delay. An adaptive update law based on time-varying updating rate is proposed, which enables the update of uncertain parameters in the presence of input delay. Consequently, to deal with the constraints, we convert the optimization problem into a solvable simple structure, which originates from the min-max optimization. Furthermore, theoretically, it is shown that the closed-loop system is asymptotically stable and the proposed adaptive MPC strategy is proved to be recursively feasible. Finally, numerical simulation is given to illustrate the efficacy of the proposed method.
[1] GARCIA C E, PRETT D M, MORARI M. Model predictive control: theory and practice—a survey[J]. Automatica, 1989, 25(3):335-348.
[2] LEE J H, MORARI M, et al. State-space interpretation of model predictive control[J]. Automatica, 1994, 30(4):707-717.
[3] MAYNE D Q, RAWLINGS J B, et al. Constrained model predictive control: stability and optimality[J]. Automatica, 2000, 36(6): 789-814.
[4] INCREMONA G P, FERRARA A, et al. MPC for robot manipulators with integral sliding modes generation[J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(3): 1299-1307.
[5] KUMAR A S, AHMAD Z. Model predictive control (MPC) and its current issues in chemical engineering[J]. Chemical Engineering Communications, 2012, 199(4): 472-511.
[6] MANZOOR T, SUN Z, XIA Y, et al. MPC based compound flight control strategy for a ducted fan aircraft[J]. Aerospace Science and Technology, 2020, 107: 106264.
[7] ADETOL V, DEHAAN D, GUAY M. Adaptive model predictive control for constrained nonlinear systems[J]. Systems & Control Letters, 2009, 58(5): 320-326.
[8] ZhANG K, SHI Y. Adaptive model predictive control for a class of constrained linear systems with parametric uncertainties[J]. Automatica, 2020, 117: 108-974.
[9] KARIMSHOUSHTARI M, NOVARA C. Design of experiments for nonlinear system identification: a set membership approach[J]. Automatica, 2020, 119: 109-036.
[10] TANASKOVIC M, FAGIANO L, SMITH R, et al. Adaptive receding horizon control for constrained MIMO systems[J]. Automatica, 2014, 50(12): 3019-3029.
[11] BUJARBARUAH M, ZHANG X, TANASKOVIC M, et al. Adaptive stochastic MPC under time-varying uncertainty[J]. IEEE Transactions on Automatic Control, 2020, 66(6): 2840-2845.
[12] LORENZEN M, CANNON M,AllGÖWER F. Robust MPC with recursive model update[J]. Automatica, 2019, 103: 461-471.
[13] TANASKOVIC M, FAGIANO L, GLIGOROVSKI V. Adaptive model predictive control for linear time varying MIMO systems[J].Automatica, 2019, 105: 237-245.
[14] AKPAN V A, HASSAPIS G D. Nonlinear model identification and adaptive model predictive control using neural networks[J]. ISA Transactions, 2011, 50(2): 177-194.
[15] REESE B M, COLLINS JR E G. A graph search and neural network approach to adaptive nonlinear model predictive control[J]. Engineering Applications of Artificial Intelligence, 2016, 55: 250-268.
[16] ZHU B, XIA X. Adaptive model predictive control for unconstrained discrete-time linear systems with parametric uncertainties[J]. IEEE Transactions on Automatic Control, 2015, 61(10): 3171-3176.
[17] ZHU B, ZHENG Z, XIA X. Constrained adaptive model-predictive control for a class of discrete-time linear systems with parametric uncertainties[J]. IEEE Transactions on Automatic Control, 2019, 65(5): 2223-2229.
[18] DHAR A, BHASIN S. Novel adaptivempc design for uncertain mimo discrete-time lti systems with input constraints[C]//2018 17th European Control Conference (ECC). Limassol, Gyprus: IEEE, 2018: 319-324.
[19] DHAR A, BHASIN S. Indirect adaptivempc for discrete-time lti systems with parametric uncertainties[J]. IEEE Transactions on Automatic Control, 2021, 66(11): 5498-5505.
[20] HU Y, GOU L, FAN D, et al. An adaptive model predictive control strategy for a class of discrete-time linear systems with parametric uncertainty[J]. International Journal of Adaptive Control and Signal Processing, 2021, 35(12): 2389-2405.
