Learning-based optimal boundary control for parabolic distributed parameter system with actuator dynamics.

Area of Science:

• Control Theory
• Applied Mathematics
• Chemical Engineering

Background:

• Investigates coupled partial differential equation (PDE) and ordinary differential equation (ODE) systems, which are common in modeling complex processes.
• Addresses the challenge of actuator dynamics influencing boundary conditions, a difficult aspect in control design.
• Highlights the complexity of optimizing infinite-dimensional performance indexes in coupled Hilbert spaces.

Purpose of the Study:

• To develop a novel data-driven boundary optimal controller for coupled PDE-ODE systems incorporating actuator dynamics.
• To address the challenge of boundary input within ODE actuator dynamics and simplify boundary condition reduction.
• To solve the optimal control problem for coupled PDE-ODE systems with actuator dynamics under Neumann boundary conditions for the first time.

Main Methods:

• Reformulated the coupled PDE-ODE system into one with homogeneous boundary conditions and derived its infinite-dimensional singular perturbation form.
• Designed a model-free iterative learning optimal control algorithm using critic and actor networks with weighted residual techniques.
• Employed arbitrary control policies to enhance exploration and relax persistent excitation conditions.

Main Results:

• Successfully solved the optimal control problem for a coupled PDE-ODE system with actuator dynamics under Neumann boundary conditions.
• Demonstrated uniform asymptotic stability of the closed-loop system in an infinite-dimensional Hilbert space for each learning iteration.
• Verified the effectiveness of the proposed approach through simulations on a diffusion-reaction process.

Conclusions:

• The developed data-driven iterative learning optimal control algorithm effectively handles coupled PDE-ODE systems with actuator dynamics.
• The approach ensures uniform asymptotic stability, providing a robust control solution.
• This work represents a significant advancement in controlling complex systems with challenging dynamics and boundary conditions.