Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE
This paper develops an adaptive dynamic programming (ADP) based near optimal boundary control of distributed parameter systems (DPS) governed by uncertain coupled semi-linear parabolic partial differential equations (PDE) under Neumann boundary control condition. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated without any model reduction and the optimal control policy is derived. Subsequently, a novel identifier is developed to estimate the unknown nonlinearity in PDE dynamics. Accordingly, the sub-optimal control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN) online approximator and the identifier. Adaptive tuning laws are proposed for learning the value functional online. Local ultimate boundedness (UB) of the closed-loop system is verified by using Lyapunov theory. The performance of proposed controller is verified via simulation on an unstable coupled diffusion reaction process.
B. Talaei et al., "Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE," Proceedings of the IEEE International Symposium on Intelligent Control (2015, Sydney, Australia), Institute of Electrical and Electronics Engineers (IEEE), Sep 2015.
The definitive version is available at https://doi.org/10.1109/ISIC.2015.7307299
IEEE International Symposium on Intelligent Control (2015: Sep. 21-23, Sydney, Australia)
Electrical and Computer Engineering
Mathematics and Statistics
Center for High Performance Computing Research
Article - Conference proceedings
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