Adaptive dynamic programming for linear impulse systems  

作　　者：Xiao-hua WANG Juan-juan YU Yao HUANG Hua WANG Zhong-hua MIAO 

机构地区：[1]School of Mechatronics Engineering and Automation, Shanghai University [2]Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University

出　　处：《Journal of Zhejiang University-Science C(Computers and Electronics)》2014年第1期43-50,共8页浙江大学学报C辑（计算机与电子（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.61104006,51175319,and 11202121);the MOE Scientific Research Foundation for the Returned Overseas Chinese Scholars;the Natural Science Foundation of Shanghai(No.11ZR1412400);the Shanghai Education Commission(Nos.12YZ010,12JC1404100,and 11CH-05),China

摘　　要：We investigate the optimization of linear impulse systems with the reinforcement learning based adaptive dynamic programming(ADP)method.For linear impulse systems,the optimal objective function is shown to be a quadric form of the pre-impulse states.The ADP method provides solutions that iteratively converge to the optimal objective function.If an initial guess of the pre-impulse objective function is selected as a quadratic form of the pre-impulse states,the objective function iteratively converges to the optimal one through ADP.Though direct use of the quadratic objective function of the states within the ADP method is theoretically possible,the numerical singularity problem may occur due to the matrix inversion therein when the system dimensionality increases.A neural network based ADP method can circumvent this problem.A neural network with polynomial activation functions is selected to approximate the pre-impulse objective function and trained iteratively using the ADP method to achieve optimal control.After a successful training,optimal impulse control can be derived.Simulations are presented for illustrative purposes.We investigate the optimization of linear impulse systems with the reinforcement learning based adaptive dynamic programming （ADP） method. For linear impulse systems, the optimal objective function is shown to be a quadric form of the pre-impulse states. The ADP method provides solutions that iteratively converge to the optimal objective function. If an initial guess of the pre-impulse objective function is selected as a quadratic form of the pre-impulse states, the objective function iteratively converges to the optimal one through ADP. Though direct use of the quadratic objective function of the states within the ADP method is theoretically possible, the numerical singularity problem may occur due to the matrix inversion therein when the system dimensionality increases. A neural network based ADP method can circumvent this problem. A neural network with polynomial activation functions is selected to approximate the pr^impulse objective function and trained iteratively using the ADP method to achieve optimal control. After a successful training, optimal impulse control can be derived. Simulations are presented for illustrative purposes.

关 键 词：Adaptive dynamic programming(ADP) Impulse system Optimal control Neural network 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]