Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE using Neurodynamic Programming


In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.


Electrical and Computer Engineering

Second Department

Mathematics and Statistics

Research Center/Lab(s)

Intelligent Systems Center


This work was supported in part by NSF under Grant ECCS1128281 and in part by the Intelligent Systems Center.

Keywords and Phrases

Closed loop systems; Continuous time systems; Control nonlinearities; Distributed computer systems; Distributed parameter control systems; Uncertainty analysis; Dirichlet boundary controls; Distributed parameter systems; Hamilton-Jacobi-Bellman equations; Neuro dynamic programming; Optimal control policy; Semi-linear parabolic PDE; Semilinear parabolic partial differential equations; Uniformly ultimate boundedness; Feedback; Distributed parameter systems; Dynamic programming; Output feedback; Partial differential equations

International Standard Serial Number (ISSN)

2162-237X; 2162-2388

Document Type

Article - Journal

Document Version


File Type





© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Apr 2018