Proper orthogonal decomposition based optimal neurocontrol synthesis of a chemical reactor process using approximate...

Area of Science:

• Control Systems Engineering
• Chemical Engineering
• Computational Neuroscience

Background:

• Optimal control of complex systems often requires advanced techniques.
• Systems governed by partial differential equations (PDEs) present significant control challenges.
• Approximate dynamic programming (ADP) and adaptive critic neural networks (ACNNs) offer powerful frameworks for optimal control.

Purpose of the Study:

• To extend ADP and ACNN-based optimal control to systems described by PDEs.
• To synthesize an optimal controller for a dispersion type tubular chemical reactor.
• To develop a general methodology for optimal control of nonlinear distributed parameter systems.

Main Methods:

• Proper Orthogonal Decomposition (POD) for basis function design.
• Galerkin projection to obtain a low-order lumped parameter system from PDEs.
• ADP in a discrete-time framework with dual ACNNs (adaptive critics) for control and costate estimation.
• Mapping lumped parameter control back to the spatial domain.

Main Results:

• Successful synthesis of an optimal neurocontroller for a nonlinear PDE-governed chemical reactor.
• Demonstration of the effectiveness of the POD and Galerkin projection for system reduction.
• Validation of the dual ACNN structure for capturing system dynamics and costate relationships.
• Numerical results illustrating the potential of the proposed control approach.

Conclusions:

• The presented approach effectively extends ADP and ACNNs for optimal control of PDE systems.
• The methodology is applicable to a general class of nonlinear distributed parameter systems.
• This work provides a robust framework for designing optimal controllers in complex engineering applications.