Adaptive Optimal Control of Highly Dissipative Nonlinear Spatially Distributed Processes With Neuro-Dynamic Programming
Luo, Biao1,2; Wu, Huai-Ning1; Li, Han-Xiong3
2015-04-01
发表期刊IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
卷号26期号:4页码:684-696
文章类型Article
摘要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-Loeve 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. Moreover, by involving the NN estimation error, we prove that the original closed-loop PDE system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded. Finally, the developed method is tested on a nonlinear diffusion-convection-reaction process and applied to a temperature cooling fin of high-speed aerospace vehicle, and the achieved results show its effectiveness.
关键词Adaptive Optimal Control Empirical Eigenfunction (Eef) Highly Dissipative Partial Differential Equations (Pdes) Neuro-dynamic Programming (Ndp) Spatially Distributed Processes (Sdps)
WOS标题词Science & Technology ; Technology
关键词[WOS]DISCRETE-TIME-SYSTEMS ; HYPERBOLIC PDE SYSTEMS ; FINITE-DIMENSIONAL APPROXIMATION ; OPTIMAL TRACKING CONTROL ; OUTPUT-FEEDBACK CONTROL ; PARAMETER-SYSTEMS ; MODEL-REDUCTION ; ROBUST-CONTROL ; ITERATION ALGORITHM ; STABILIZATION
收录类别SCI
语种英语
WOS研究方向Computer Science ; Engineering
WOS类目Computer Science, Artificial Intelligence ; Computer Science, Hardware & Architecture ; Computer Science, Theory & Methods ; Engineering, Electrical & Electronic
WOS记录号WOS:000351835900004
引用统计
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/10738
专题复杂系统管理与控制国家重点实验室_平行控制
通讯作者Luo, Biao
作者单位1.Beihang Univ, Sci & Technol Aircraft Control Lab, Beijing 100191, Peoples R China
2.Chinese Acad Sci, Inst Automat, State Key Lab Management & Control Complex Syst, Beijing 100190, Peoples R China
3.City Univ Hong Kong, Dept Syst Engn & Engn Management, Hong Kong, Hong Kong, Peoples R China
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Luo, Biao,Wu, Huai-Ning,Li, Han-Xiong. Adaptive Optimal Control of Highly Dissipative Nonlinear Spatially Distributed Processes With Neuro-Dynamic Programming[J]. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS,2015,26(4):684-696.
APA Luo, Biao,Wu, Huai-Ning,&Li, Han-Xiong.(2015).Adaptive Optimal Control of Highly Dissipative Nonlinear Spatially Distributed Processes With Neuro-Dynamic Programming.IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS,26(4),684-696.
MLA Luo, Biao,et al."Adaptive Optimal Control of Highly Dissipative Nonlinear Spatially Distributed Processes With Neuro-Dynamic Programming".IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 26.4(2015):684-696.
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