|
|
|
| Adaptive Model Predictive Control for Linear Systems with Parametric Uncertainties and Time Delay |
| KONG Lingren1, QI Qingyuan2
|
1. Institute of Complexity Science, Qingdao University, Qingdao 266071, China;
2. Qingdao Innovation and Development Center, Harbin Engineering University, Qingdao 266000, China |
|
|
|
|
Abstract 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.
|
|
Received: 24 April 2023
Published: 07 November 2024
|
|
|
|
|
|
[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. |
|
|
|
