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

Area of Science:

• Control Theory
• Applied Mathematics
• Chemical Engineering

Background:

• Distributed parameter systems governed by partial differential equations (PDEs) present significant control challenges.
• Uncertainty in semilinear parabolic PDE dynamics complicates the design of effective boundary control strategies.
• Output feedback control is crucial for systems where full state information is unavailable.

Purpose of the Study:

• To develop a neurodynamic programming-based output feedback boundary control method for uncertain coupled semilinear parabolic PDEs.
• To design a novel neural network observer for state estimation in the presence of nonlinear dynamics.
• To ensure closed-loop stability and verify performance through simulations.

Main Methods:

• Formulation of the Hamilton-Jacobi-Bellman (HJB) equation in the PDE domain to derive the optimal control policy.
• Development of a neural network (NN)-based observer for state estimation using measured outputs.
• Online estimation of the value functional using an NN approximator and adaptive tuning laws for HJB equation satisfaction.
• Lyapunov stability analysis to verify local uniformly ultimate boundedness.

Main Results:

• An optimal control policy was derived from the HJB equation solution.
• A novel NN observer successfully estimated system states despite uncertain nonlinearities.
• Suboptimal boundary control was achieved through forward-in-time value functional estimation.
• Adaptive tuning laws ensured online learning of the value functional and closed-loop stability.

Conclusions:

• The proposed neurodynamic programming approach provides effective output feedback boundary control for uncertain distributed parameter systems.
• The developed NN observer and adaptive tuning laws are key to achieving robust control and stability.
• Simulations on an unstable coupled diffusion reaction process confirmed the controller's performance.