Previous Articles    

Predictive Control of High-Order Fully Actuated Nonlinear Systems with Time-Varying Delays

LIU Guo-Ping   

  1. Department of Electronic and Electrical Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • Received:2021-11-20 Published:2022-04-13
  • Supported by:
    This research was supported in part by the National Natural Science Foundation of China under Grant Nos. 62173255 and 62188101.

LIU Guo-Ping. Predictive Control of High-Order Fully Actuated Nonlinear Systems with Time-Varying Delays[J]. Journal of Systems Science and Complexity, 2022, 35(2): 457-470.

This paper investigates the control problem of high-order fully actuated nonlinear systems with time-varying delays in the discrete-time domain. To make the compensation for time-varying delays concise, active and universal, a novel nonlinear predictive control method is proposed. The designed nonlinear predictive controller can achieve the same expected control performance as the nonlinear systems without delays. At the same time, the necessary and sufficient conditions for the stability of the closed-loop nonlinear predictive control systems are derived. Numerical examples show that the proposed nonlinear predictive controller design method can completely compensate for the time-varying delays of nonlinear systems.
[1] Liu K, Selivanov A, and Fridman E, Survey on time-delay approach to networked control, Annual Reviews in Control, 2019, 48: 57–79.
[2] Sun J and Chen J, A survey on Lyapunov-based methods for stability of linear time-delay systems, Frontiers of Computer Science, 2017, 11: 555–567.
[3] Ichikawa K, Frequency-domain pole assignment and exact model-matching for delay systems, International Journal of Control, 1985, 41(4): 1015–1024.
[4] Polyakov A, Efimov D, Perruquetti W, et al., Implicit Lyapunov-Krasovski functionals for stability analysis and control design of time-delay systems, IEEE Transactions on Automatic Control, 2015, 60(12): 3344–3349.
[5] Pepe P, On control Lyapunov-Razumikhin functions, nonconstant delays, nonsmooth feedbacks, and nonlinear sampled-data stabilization, IEEE Transactions on Automatic Control, 2017, 62(11): 5604–5619.
[6] Smith O J, A controller to overcome dead time, ISA Journal, 1959, 6(2): 28–33.
[7] Richalet J, Rault A, Testud J L, et al., Model predictive heuristic control: Applications to industrial processes, Automatica, 1978, 14(5): 413–428.
[8] Rouhani R and Mehra R K, Model algorithmic control: Basic theoretical properties, Automatica, 1982, 18: 401–414.
[9] Cutler C R and Ramaker B L, Dynamic matrix control — A computer control algorithm, Proceedings of the Joint Automatic Control Conference, San Francisco, 1980, WP5-B.
[10] Clarke D W, Mohtadi C, and Tuffs P S, Generalized predictive control — Part 1: The basic algorithm, Part 2: Extensions and interpretations, Automatica, 1987, 23: 137–160.
[11] Garca C E, Prett D M, and Morari M, Model predictive control: Theory and practice — A survey, Automatica, 1989, 25(3): 335–348.
[12] Liu G P, Mu J X, Rees D, et al., Design andstability analysis of networked control systems with random communication time delay using the modified MPC, International Journal of Control, 2006, 79(4): 287–296.
[13] Liu G P, Networked learning predictive control of nonlinear cyber-physical systems, Journal of Systems Science & Complexity, 2020, 33(6): 1719–1732.
[14] Pang Z H, Bai C D, Liu G P, et al., A novel networked predictive control method for systems with random communication constraints, Journal of Systems Science & Complexity, 2021, 34(4): 1364–1378.
[15] Isidori A, Nonlinear Control Systems, Springer, New York, 1989.
[16] Kanellakopoulos I, Kokotovic P V, and Morse A S, A toolkit for nonlinear feedback design, Systems & Control Letters, 1992, 18(2): 83–92.
[17] Liu L, Zheng W X, and Ding S, An adaptive sosm controller design by using a sliding-modebased filter and its application to buck converter, IEEE Transactions on Circuits and Systems I: Regular Papers, 2020, 67:(7) 2409–2418.
[18] Duan G R, High-order fully actuated system approaches — Part I: Models and basic procedure, Int. J. Systems Science, 2021, 52(2): 422–435.
[19] Duan G R, High-order fully actuated system approaches: Part III. Robust control and high-order backstepping, Int. J. Systems Science, 2021, 52(5): 952–971.
[20] Duan G R, High-order fully actuated system approaches: Part IV. Adaptive control and highorder backstepping, Int. J. Systems Science, 2021, 52(5): 972–989.
[1] WANG Tao · KANG Yu · LI Pengfei · ZHAO Yun-Bo · YU Peilong. Robust Approximation-Based Event-Triggered MPC for Constrained Sampled-Data Systems [J]. Journal of Systems Science and Complexity, 2021, 34(6): 2109-2124.
[2] LIU Xinmiao · XIA Jianwei · WANG Jing · SHEN Hao. Interval Type-2 Fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application [J]. Journal of Systems Science and Complexity, 2021, 34(6): 2195-2218.
[3] LIU Wei · HUANG Jie. Sampled-Data Semi-Global Robust Output Regulation for a Class of Nonlinear Systems [J]. Journal of Systems Science and Complexity, 2021, 34(5): 1743-1765.
[4] LIU Guo-Ping. Networked Learning Predictive Control of Nonlinear Cyber-Physical Systems [J]. Journal of Systems Science and Complexity, 2020, 33(6): 1719-1732.
[5] HU Qiong,FEI Qing,MA Hongbin,WU Qinghe,GENG Qingbo. Switching Control System Based on Robust Model Reference Adaptive Control [J]. Journal of Systems Science and Complexity, 2016, 29(4): 897-932.
[6] SU Wei. Perfect Adaptation of General Nonlinear Systems [J]. Journal of Systems Science and Complexity, 2016, 29(1): 61-73.
[7] SHANG Fang,LIU Yungang,ZHANG Guiqing. Adaptive Stabilization for a Class of Feedforward Systems with Zero-Dynamics [J]. Journal of Systems Science and Complexity, 2015, 28(2): 305-315.
[8] YAN Xuehua, LIU Yungang,WANG Qingguo. Global Output-Feedback Tracking for Nonlinear Cascade Systems with Unknown Growth Rate and Control Coefficients [J]. Journal of Systems Science and Complexity, 2015, 28(1): 30-46.
[9] REN Jingli , CHENG Zhibo , GUO Lei. FURTHER RESULTS ON LIMITATIONS OF SAMPLED-DATA FEEDBACK [J]. Journal of Systems Science and Complexity, 2014, 27(5): 817-835.
[10] Xuehua YAN, Yungang LIU. THE FURTHER RESULT ON GLOBAL PRACTICAL TRACKING FOR HIGH-ORDER UNCERTAIN NONLINEAR SYSTEMS [J]. Journal of Systems Science and Complexity, 2012, 25(2): 227-237.
[11] Lipo MO. ROBUST STABILIZATION FOR MULTI-INPUT POLYTOPIC NONLINEARSYSTEMS [J]. Journal of Systems Science and Complexity, 2011, 24(1): 93-104.
[12] Fang SHANG;Yungang LIU;Chenghui ZHANG. ADAPTIVE PRACTICAL TRACKING CONTROL BY OUTPUT FEEDBACK FOR ACLASS OF NONLINEAR SYSTEMS [J]. Journal of Systems Science and Complexity, 2010, 23(6): 1210-1220.
[13] Daizhan CHENG;Yupeng QIAO;Wei NI. DESIGN OF CONTROL INVARIANT SETS OF PLANAR SYSTEMS [J]. Journal of Systems Science and Complexity, 2009, 22(4): 614-626.
[14] Xiaohua LIU;Chunyan HAN. ROBUST MODEL PREDICTIVE CONTROL OF CONTINUOUS UNCERTAIN SYSTEMS [J]. Journal of Systems Science and Complexity, 2008, 21(2): 267-275.
[15] Yimin SUN;Shengwei MEI;Qiang LU. NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL CONTROLLABILITY OF A CLASS OF AFFINE NONLINEAR SYSTEMS [J]. Journal of Systems Science and Complexity, 2007, 20(4): 492-500.
Viewed
Full text


Abstract