分布参数切换系统保性能控制设计及仿真

doi:10.3778/j.issn.1002-8331.2412-0030

摘要/Abstract

摘要： 针对分布参数切换系统，设计反馈控制器和切换规则，使得相应闭环系统指数稳定且满足一定的性能指标。利用共同Lyapunov函数方法，通过Lyapunov稳定性定理、Poincare不等式和线性矩阵不等式（LMIs）等，得到分布参数切换系统保性能控制存在的充分条件。和已有结果相比较，将分布参数切换系统保性能控制概念进行了推广，并且充分考虑了分布切换参数系统中Laplace算子系数对系统性能的影响，降低了保守性。提出切换Lyapunov函数方法结合驻留时间方法，建立分布参数切换系统保性能控制存在的条件。通过计算机仿真验证所提出方法的有效性和优越性。

关键词: 分布参数系统, 切换系统, 保性能控制, 指数稳定, 切换Lyapunov函数, 驻留时间

Abstract: For distributed parameter switching systems, feedback control and switching signals are designed to ensure the corresponding closed-loop systems are exponentially stable and meet certain performance indicators. Firstly, using the common Lyapunov function method, by Lyapunov stability theorem, Poincare inequality, and linear matrix inequality (LMIs), sufficient conditions for the existence of guaranteed performance control in distributed parameter switching systems are obtained. Compared with existing results, the concept of guaranteed performance control for distributed parameter switching systems has been extended, and the influence of Laplace operator coefficients on system performance in distributed parameter switching systems has been fully considered which reduces conservatism. Next, the method of switching Lyapunov functions combined with the dwell-time method is proposed to establish the conditions for the existence of guaranteed performance control in distributed parameter switching systems. Finally, the effectiveness and superiority of the proposed method are verified through computer simulation.

Key words: distributed parameter systems, switched systems, guaranteed performance control, exponential stability, switching Lyapunov function, dwell time

鲍乐平, 黎曦. 分布参数切换系统保性能控制设计及仿真[J]. 计算机工程与应用, 2025, 61(11): 335-341.

BAO Leping, LI Xi. Design and Simulation of Guaranteed Performance Control for Distributed Parameter Switching Systems[J]. Computer Engineering and Applications, 2025, 61(11): 335-341.

参考文献

[1] OISHI M, TOMLIN C. Switched nonlinear control of a VSTOL aircraft [C]//Proceedings of the 38th IEEE Conference on Decision and Control, 1999: 685-2690.
[2] JEON D, TOMIZUKA M. Learning hybrid force and position control of robot manipulators[J]. IEEE Transactions on Robotics and Automation, 1993, 9(4): 423-431.
[3] VARAIYA P. Smart car on smart roads: problems of control[J]. IEEE Transactions on Automatic Control, 1993, 38(2): 195-207.
[4] LIBERZON D. Switching in systems and control [M]. Boston: Birkhauser, 2003.
[5] SUN Z D. Feedback stabilization of third-order switched linear control systems[J]. IEEE Control Systems Letters, 2020, 4(4): 857-861.
[6] 王强, 聂宏. 多时滞离散切换系统的动态输出反馈H∞控制[J]. 计算机工程与应用, 2015, 51(22): 214-217.
WANG Q, NIE H. Robust H∞ dynamic output feedback control for a class of discrete time switched systems with multi-delay[J]. Computer Engineering and Applications, 2015, 51(22): 214-217.
[7] SONG X, WANG M, AHN C K, et al. Finite-time H-infinity asynchronous control for nonlinear Markov jump distributed parameter systems via quantized fuzzy output-feedback approach[J]. IEEE Transactions on Cybernetics, 2019, 50(9): 4098-4109.
[8] WANG J W, WU H N. Exponential pointwise stabilization of semilinear parabolic distributed parameter systems via the Takagi Sugeno fuzzy PDE model[J]. IEEE Transactions on Fuzzy Systems, 2018, 26(1): 155-173.
[9] QIAN X, CUI B T. Mobile sensor networks for finite-time distributed H∞ consensus filtering of 3d nonlinear distributed parameter systems with randomly occurring sensor saturation[J]. Mathematics, 2022, 10(17): 3134.
[10] 李延波, 陈超洋, 张晶华, 等. 分布时滞随机偏微分系统的均方指数稳定性[J]. 控制理论与应用, 2022, 39(11): 2185-2192.
LI Y B, CHEN C Y, ZHANG J H, et al, Mean-square exponential stability of stochastic partial differential systems with distributed time-delay[J]. Control Theory and Technology, 2022, 39(11): 2185-2192.
[11] 周笔峰, 罗毅平, 时滞分布参数系统间歇非周期中和控制器设计[J]. 计算机工程与应用, 2020, 56(8): 220-225.
ZHOU B F, LUO Y P. Aperiodically intermittent neutrali-
zation control of distributed parameter systems with delay [J]. Computer Engineering and Applications, 2020, 56(8): 220-225.
[12] 付焕森, 崔宝同. 时滞分布参数系统的移动传感器/执行器防碰撞控制[J]. 控制理论与应用, 2020, 37(2): 245-252.
FU H S, CUI B T. Collision avoidance control of mobile sensor and actuator networks for distributed parameter systems with time-delay[J]. Control Theory & Applications, 2020, 37(2): 245-252.
[13] ZHANG X W, WU H N. Fuzzy stabilization design for semilinear parabolic PDE systems with mobile actuators and sensors[J]. IEEE Transactions on Fuzzy Systems, 2020, 28(3): 474-486.
[14] SASANE A, Stability of switching infinite-dimensional systems[J]. Automatica, 2005, 41(1): 75-78.
[15] AMIN S, HANTE F, BAYEN A. Exponential stability of switched linear hyperbolic initial-boundary value problems [J]. IEEE Transactions on Automatic Control, 2012, 57(2): 291-301.
[16] YANG H, JIANG B. On stability of nonlinear and switched parabolic systems[J]. IET Control Theory and Applications, 2013, 7(5): 749-756.
[17] 董学平, 温锐, 刘红亮. 一类时滞分布参数切换系统的鲁棒容错控制[J]. 控制与决策, 2012, 27(2): 232-236.
DONG X P, WEN R, LIU H L. Robust fault-tolerant control for a class of distributed parameter switched system with time-delay[J]. Control and Decision, 2012, 27(2): 232-236.
[18] BAO L P, HUANG P, FEI S M. Exponential stability and L2 gain analysis of switched distributed parameter systems with time delay[J]. Journal of Control and Decision, 2021, 8(4): 385-393.
[19] 鲍乐平. 分布参数切换系统稳定性研究 [D]. 南京: 东南大学, 2014.
BAO L P. Study on stability of distributed parameter switched systems[D]. Nanjing: Southeast University, 2014.
[20] GUAN Y, YANG H, JIANG B. Fault tolerant time optimization for a class of time-varying switched infinite dimensional linear systems[J]. Systems & Control Letters, 2022, 168: 105-361.
[21] HAN X X, WU K N, DING X. Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control[J]. Applied Mathematics and Computation, 2020, 385: 125422.
[22] LE C A, VACHER J, KERGRENE K. Formal stabilization of a coupled ODE-PDE switched system[C]//Proceedings of the 42nd Chinese Control Conference, 2023: 24-26.
[23] SONG X, PENG Z, SONG S, et al. Interval observer design for unobservable switched nonlinear partial differential equation systems and its application[J]. International Journal of Robust and Nonlinear Control, 2024, 34(16): 10990-11009.
[24] CHANG S, PENG T. Adaptive guaranteed cost control of systems with uncertain parameters[J]. IEEE Transactions on Automatic Control, 1972, 17(4): 474-483.
[25] 罗毅平, 刘欢. 时滞复杂动态网络的保性能控制[J]. 计算机工程与应用, 2013, 49(20): 48-51.
LUO Y P, LIU H. Guaranteed cost control of complex network with delay[J]. Computer Engineering and Applications, 2013, 49(20): 48-51.
[26] ZONG G, WANG X, ZHAO H. Robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay[J]. International Journal of Control, Automation and Systems, 2017, 15(1): 113-121.
[27] 李同彬, 高娟. 异步切换下切换时变时滞系统的保成本控制[J]. 工程数学学报, 2022, 4(39): 571-588.
LI T B, GAO J. Guaranteed cost control of switched time-varying delay systems under asynchronous switching[J]. Chinese Journal of Engineering Mathematics, 2022, 4(39): 571-588.
[28] WU H N, LI H X. A Galerkin/neural-network-based design of guaranteed cost control for nonlinear distributed parameter systems[J]. IEEE Transactions on Neural Networks, 2008, 19(5): 795-807.
[29] 董学平, 徐霄翔, 苏瑜田. 一类分布参数切换系统的保成本控制[J]. 合肥工业大学学报(自然科学版), 2012, 35(5): 606-699.
DONG X P, XU X X, SU Y T. Guaranteed cost control for a class of distributed parameter switched systems[J]. Journal of Hefei University of Technology (Natural Science), 2012, 35(5): 606-699.
[30] 周笔锋, 罗毅平, 李安平. 基于变时滞分布参数系统模型的宽厚板热加工控制炉温稳定间隙控制方法: CN 117518832A[P]. 2024-02-06.
ZHOU B F, LUO Y P, LI A P. Control method for furnace temperature stability gap in wide and thick plate hot processing based on variable delay distributed parameter system model: CN117518832A[P]. 2024-02-06.