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Your search keyword '"Talaei, Behzad"' showing total 8 results
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8 results on '"Talaei, Behzad"'

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

Author

Talaei, Behzad, Jagannathan, S., Sarangapani, Jag, and Singler, John R.

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.

Published
2015

7. Boundary Control of 2-D Burgers’ PDE: An Adaptive Dynamic Programming Approach.

Author

Talaei, Behzad, Jagannathan, Sarangapani, and Singler, John

Subjects
*PARTIAL differential equations, *DYNAMIC programming
Abstract

In this paper, an adaptive dynamic programming-based near optimal boundary controller is developed for partial differential equations (PDEs) modeled by the uncertain Burgers’ equation under Neumann boundary condition in 2-D. Initially, Hamilton–Jacobi–Bellman equation is derived in infinite-dimensional space. Subsequently, a novel neural network (NN) identifier is introduced to approximate the nonlinear dynamics in the 2-D PDE. The optimal control input is derived by online estimation of the value function through an additional NN-based forward-in-time estimation and approximated dynamic model. Novel update laws are developed for estimation of the identifier and value function online. The designed control policy can be applied using a finite number of actuators at the boundaries. Local ultimate boundedness of the closed-loop system is studied in detail using Lyapunov theory. Simulation results confirm the optimizing performance of the proposed controller on an unstable 2-D Burgers’ equation. [ABSTRACT FROM AUTHOR]

Published
2018
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