Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE

B. Talaei; Jagannathan Sarangapani; John R. Singler

doi:10.1109/ISIC.2015.7307299

Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE

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Abstract

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.

Original language	American English
Journal	Proceedings of the IEEE International Symposium on Intelligent Control (2015, Sydney, Australia)
DOIs	https://doi.org/10.1109/ISIC.2015.7307299
State	Published - Sep 1 2015

Disciplines

Electrical and Computer Engineering
Mathematics
Numerical Analysis and Scientific Computing
Statistics and Probability

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https://doi.org/10.1109/ISIC.2015.7307299

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title = "Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE",

abstract = " 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.",

author = "B. Talaei and Jagannathan Sarangapani and Singler, \{John R.\}",

year = "2015",

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doi = "10.1109/ISIC.2015.7307299",

language = "American English",

journal = "Proceedings of the IEEE International Symposium on Intelligent Control (2015, Sydney, Australia)",

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T1 - Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE

AU - Talaei, B.

AU - Sarangapani, Jagannathan

AU - Singler, John R.

PY - 2015/9/1

Y1 - 2015/9/1

N2 - 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.

AB - 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.

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DO - 10.1109/ISIC.2015.7307299

M3 - Article

JO - Proceedings of the IEEE International Symposium on Intelligent Control (2015, Sydney, Australia)

JF - Proceedings of the IEEE International Symposium on Intelligent Control (2015, Sydney, Australia)

ER -

Adaptive Dynamic Programming Boundary Control of Uncertain Coupled Semi-Linear Parabolic PDE

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