Approximate optimal control design for nonlinear one-dimensional parabolic PDE systems using empirical eigenfunctions and neural network

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
Biao Luo, Huai-Ning Wu

Abstract

This paper addresses the approximate optimal control problem for a class of parabolic partial differential equation (PDE) systems with nonlinear spatial differential operators. An approximate optimal control design method is proposed on the basis of the empirical eigenfunctions (EEFs) and neural network (NN). First, based on the data collected from the PDE system, the Karhunen-Loève decomposition is used to compute the EEFs. With those EEFs, the PDE system is formulated as a high-order ordinary differential equation (ODE) system. To further reduce its dimension, the singular perturbation (SP) technique is employed to derive a reduced-order model (ROM), which can accurately describe the dominant dynamics of the PDE system. Second, the Hamilton-Jacobi-Bellman (HJB) method is applied to synthesize an optimal controller based on the ROM, where the closed-loop asymptotic stability of the high-order ODE system can be guaranteed by the SP theory. By dividing the optimal control law into two parts, the linear part is obtained by solving an algebraic Riccati equation, and a new type of HJB-like equation is derived for designing the nonlinear part. Third, a control update strategy based on successive approximation is proposed to solve th...Continue Reading

References

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Citations

Aug 27, 2014·Neural Networks : the Official Journal of the International Neural Network Society·Shiping WenXinghuo Yu
Mar 21, 2015·IEEE Transactions on Neural Networks and Learning Systems·Biao LuoHan-Xiong Li
May 23, 2014·IEEE Transactions on Cybernetics·Long Jin, Yunong Zhang
Dec 23, 2014·IEEE Transactions on Cybernetics·Biao LuoTingwen Huang
Aug 16, 2015·IEEE Transactions on Neural Networks and Learning Systems·Biao LuoXiong Yang
Dec 8, 2014·Neural Networks : the Official Journal of the International Neural Network Society·Shiping WenPeng Li
Jul 15, 2016·IEEE Transactions on Neural Networks and Learning Systems·Biao LuoDing Wang
Jul 23, 2016·IEEE Transactions on Neural Networks and Learning Systems·Ruizhuo SongQinglai Wei
Mar 14, 2017·IEEE Transactions on Neural Networks and Learning Systems·Behzad TalaeiJohn Singler
Oct 6, 2017·IEEE Transactions on Neural Networks and Learning Systems·Biao LuoHuai-Ning Wu

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