H∞ tracking control problem for completely unknown nonlinear system based on augmented matrix

This paper addresses the H∞ to tracking control problem for unknown nonlinear system based on the online ADP structure. We first use an identifier NN to approximate the unknown system. In order to transform the tracking problem into the regulation problem, the augmentation system is then constructed based on the identifier. Another NN is used to approximate the cost function in the HJI equation, such that H∞ to tracking control pairs can be obtained without the solution of the HJI equation. Moreover, a novel estimation algorithm is developed to online update the NN weights simultaneously. Finally, a simulation is presented to demonstrate the validity of the proposed method.

[1]  Frank L. Lewis,et al.  $ {H}_{ {\infty }}$ Tracking Control of Completely Unknown Continuous-Time Systems via Off-Policy Reinforcement Learning , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Frank L. Lewis,et al.  Online actor critic algorithm to solve the continuous-time infinite horizon optimal control problem , 2009, 2009 International Joint Conference on Neural Networks.

[3]  Derong Liu,et al.  Data-Driven Neuro-Optimal Temperature Control of Water–Gas Shift Reaction Using Stable Iterative Adaptive Dynamic Programming , 2014, IEEE Transactions on Industrial Electronics.

[4]  J. Na,et al.  Online adaptive approximate optimal tracking control with simplified dual approximation structure for continuous-time unknown nonlinear systems , 2014, IEEE/CAA Journal of Automatica Sinica.

[5]  Paul J. Webros.  A menu of designs for reinforcement learning over time , 1990 .

[6]  F.L. Lewis,et al.  Reinforcement learning and adaptive dynamic programming for feedback control , 2009, IEEE Circuits and Systems Magazine.

[7]  F. Lewis,et al.  Online solution of nonquadratic two‐player zero‐sum games arising in the H ∞  control of constrained input systems , 2014 .

[8]  Huaguang Zhang,et al.  An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games , 2011, Autom..

[9]  Tingwen Huang,et al.  Off-Policy Reinforcement Learning for $ H_\infty $ Control Design , 2013, IEEE Transactions on Cybernetics.

[10]  Huai-Ning Wu,et al.  Simultaneous policy update algorithms for learning the solution of linear continuous-time H∞ state feedback control , 2013, Inf. Sci..

[11]  Huai-Ning Wu,et al.  Neural Network Based Online Simultaneous Policy Update Algorithm for Solving the HJI Equation in Nonlinear $H_{\infty}$ Control , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Luigi Fortuna,et al.  Reinforcement Learning and Adaptive Dynamic Programming for Feedback Control , 2009 .

[13]  Derong Liu,et al.  Neural Network H ∞ Tracking Control of Nonlinear Systems Using GHJI Method , 2013, ISNN.

[14]  J. Koenderink.  Q… , 2014, Les noms officiels des communes de Wallonie, de Bruxelles-Capitale et de la communaute germanophone.

[15]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[16]  Derong Liu,et al.  Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm , 2013, Neurocomputing.

[17]  Derong Liu,et al.  Online Synchronous Approximate Optimal Learning Algorithm for Multi-Player Non-Zero-Sum Games With Unknown Dynamics , 2014, IEEE Transactions on Systems, Man, and Cybernetics: Systems.