Adaptive optimal control of highly dissipative nonlinear spatially distributed processes with neuro-dynamic programming

IEEE Transactions on Neural Networks and Learning Systems
Biao LuoHan-Xiong Li

Abstract

Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider the optimal control problem of the general highly dissipative SDPs, and propose an adaptive optimal control approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loève decomposition is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. These EEFs together with singular perturbation technique are then used to obtain a finite-dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the PDE system. Subsequently, the optimal control problem is reformulated on the basis of the slow subsystem, which is further converted to solve a Hamilton-Jacobi-Bellman (HJB) equation. HJB equation is a nonlinear PDE that has proven to be impossible to solve analytically. Thus, an adaptive optimal control method is developed via NDP that solves the HJB equation online using neural network (NN) for approximating the value function; and an online NN weight tuning law is proposed without requiring an initial stabilizing control policy. Mor...Continue Reading

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Citations

Jun 26, 2015·IEEE Transactions on Neural Networks and Learning Systems·Hamidreza ModaresZhong-Ping Jiang
Aug 16, 2015·IEEE Transactions on Neural Networks and Learning Systems·Biao LuoXiong Yang
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
Apr 1, 2017·IEEE Transactions on Neural Networks and Learning Systems·Huaguang ZhangHe Jiang
Apr 1, 2017·IEEE Transactions on Neural Networks and Learning Systems·Lei LiuHuaguang Zhang
Mar 10, 2017·IEEE Transactions on Neural Networks and Learning Systems·Behzad TalaeiJohn Singler
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
May 18, 2018·IEEE Transactions on Neural Networks and Learning Systems·Huaguang ZhangYang Cui
Sep 4, 2017·IEEE Transactions on Neural Networks and Learning Systems·Behzad TalaeiJohn Singler

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