|
|
A type of distribution control method for nonlinear stochastic systems |
DING Yunfei, ZHU Chenxuan |
Electrical College, Shanghai Dianji University, Shanghai 201306, China |
|
|
Abstract Most nonlinear control systems are inevitably subject to random disturbances, such as systematic measurements and random noises(random vibrations or shocks)in practice, which affect the control of nonlinear systems. In this paper, a stochastic distributed control method is designed for nonlinear systems subject to random perturbations. In this method, the relationship between steady-state response probability density distribution and control target of a nonlinear stochastic system is studied. The control design is divided into two steps: firstly, the actual model with stochastic perturbation is transformed into the nonlinear system Hamiltonian model; then the output of the controlled system satisfies with a prescribed probability density distribution by using a technique for solving exact stationary solution of a nonlinear stochastic system. The convergence of control system is achieved by introducing the Lyapelov function in which the output of a closed-loop nonlinear stochastic system can converge to a pre-defined steady PDF to ensure the closed-loop stability of the controlled system. The results show that the proposed method is effective and can make the controlled system be able to track a pre-defined target steady probability distribution.
|
Received: 27 March 2017
|
|
|
|
[1]NISIO M. Stochastic control theory: dynamic programming principle[M]. Tokyo:Springer Japan,2015.[2]刘希昌, 莫秋云, 李帅帅,等. 小型垂直轴风力发电机的气动噪声数值模拟与试验验证[J]. 流体机械, 2016, 44(6):11-16. LIU Xichang,MO Qiuyun,LI Shuaishuai,et al. Numerical simulation and analysis of aerodynamic noise based on small vertical axis wind turbine [J]. Fluid machinery, 2016, 44(6):11-16.(in Chinese)[3]武赛,邓飞其,张成科,等. 一类Itö型随机非线性大系统分散自适应跟踪[J]. 江苏大学学报(自然科学版),2009,30(5):536-540. WU Sai, DENG Feiqi, ZHANG Chengke, et al. Decentralized adaptive tracking for a class of Itö stochastic nonlinear large-scale systems[J]. Journal of Jiangsu University(natural science edition), 2009, 30(5):536-540.(in Chinese)[4]WEI G, WANG Z, QIAN W. Nonlinear stochastic control and filtering with engineering-oriented complexities[J]. Atmospheric chemistry & physics, 2016, 10(13):6087-6096.[5]MIN Huifang, LU Junwei, XU Shengyuan, et al. Neural network-based output-feedback control for stochastic high-order non-linear time-delay systems with application to robot system[J]. IET control theory & applications, 2017, 11(10):1578-1588..[6]丛文,陈兵,闫绍新. 随机多输入多输出系统的自适应神经网络控制[J]. 青岛大学学报(工程技术版),2014,29(1):1-6,21. CONG Wen, CHEN Bing, YAN Shaoxin. Adaptive neural traching control for stochastic nonlinear MIMO systems[J]. Journal of Qingdao University(engineering & technology edition), 2014, 29(1):1-6,21.(in Chinese)[7]YI Y, ZHENG W X, SUN C, et al. DOB fuzzy controller design for non-gaussian stochastic distribution systems using two-step fuzzy identification[J]. IEEE transactions on fuzzy systems, 2016, 24(2):401-418.[8]殷利平,吴珂,朱鹏渭. 粒子群优化算法在随机分布控制中的应用[J]. 南京信息工程大学学报(自然科学版),2016,8(5):429-432. YIN Liping, WU Ke, ZHU Pengwei. Application of particle swarm optimization in stochastic distribution control[J]. Journal of Nanjing University of Information Science & Technology(natural science edition), 2016,8(5):429-432.(in Chinese)[9]杨恒占,钱富才,高嵩,等. 一类随机系统的概率密度函数形状控制[J]. 系统工程理论与实践,2016,36(9):2424-2431. YANG Hengzhan, QIAN Fucai, GAO Song, et al. The shape control of probability density function for a class of stochastic systems[J].Systems engineering-theory & practice, 2016, 36(9):2424-2431.(in Chinese)[10]许慧敏. 非线性系统迭代学习控制算法研究[D]. 北京:华北电力大学,2016.[11]SATOH S, KAPPEN H J, SAEKI M. An iterative method for nonlinear stochastic optimal control based on path integrals[J]. IEEE transactions on automatic control, 2016, 62(1):262-276.[12]朱建勇,桂卫华,阳春华,等. 基于泡沫尺寸随机分布的铜粗选药剂量控制[J]. 自动化学报, 2014, 40(10): 2089-2097. ZHU Jianyong, GUI Weihua, YANG Chunhua,et al. Reagent dosage control based on bubble size random distribution for copper roughing[J]. Acta automatica sinica, 2014, 40(10): 2089-2097.(in Chinese)[13]陈海永,孙鹤旭,王宏. 一类仿射非线性系统的概率密度函数形状控制[J]. 控制与决策,2011,26(8):1169-1174. CHEN Haiyong, SUN Hexu, WANG Hong. Probability density function shape control of a class of affine nonlinear stochastic systems[J]. Control and decision, 2011, 26(8):1169-1174.(in Chinese)[14]ZHOU J, YUE H, ZHANG J, et al. Iterative learning double closed-loop structure for modeling and controller design of output stochastic distribution control systems[J]. IEEE transactions on control systems technology, 2014, 22(6):2261-2276.[15]滕俊超,朱位秋. 谐和与宽带随机激励下拟可积哈密顿系统的最优时滞控制[J]. 振动工程学报,2016,29(2):207-213. TENG Junchao, ZHU Weiqiu. Optimal time-delay control of quasi integrable Hamiltonian systems under combined harmonic and wide-band random excitations[J]. Journal of vibration engineering, 2016, 29(2):207-213.(in Chinese)[16]李伯忍. 不确定随机时变时滞系统的记忆状态反馈控制[J]. 控制工程,2016, 23(9):1462-1468. LI Boren. Memory state feedback control of uncertain stochastic systems with time-varying delay[J]. Control engineering of China, 2016, 23(9):1462-1468.(in Chinese)[17]MESBAH A. Stochastic model predictive control: an overview and perspectives for future research[J]. IEEE control systems, 2016, 36(6): 30-44.[18]GUO L, WANG H. Stochastic distribution control system design: a convex optimization approach[M].London: Springer London, 2010.[19]WANG Y, LI C, CHENG D. New approaches to generalized Hamiltonian realization of autonomous nonlinear systems[J]. Science in China series F, 2003, 46(6): 431-444.[20]HUANG Z L, ZHU W Q. Exact stationary solutions of stochastically and harmonically excited and dissipated integrable hamiltonian systems[J]. Journal of sound & vibration, 2000, 230(3):709-720.[21]XU B, CHEN D, ZHANG H, et al. Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag[J]. Communications in nonlinear science and numerical simulation, 2017, 47: 35-47. |
|
|
|