State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions.

Area of Science:

• Control systems engineering
• Applied mathematics
• Chemical engineering

Background:

• Distributed dynamic systems often require full state measurements for control, which is frequently unfeasible with physical sensors.
• Partial differential equations (PDEs), particularly coupled reaction-diffusion equations, model these systems.
• Boundary measurements are often the only available data for state estimation.

Purpose of the Study:

• To develop an observer for state estimation in distributed systems using only boundary measurements.
• To present a novel modulating function method that avoids online PDE solving.
• To verify the algorithm's real-time functionality and effectiveness in mitigating sensor noise.

Main Methods:

• Utilizes the modulating function method with an orthonormal function basis representation.
• Generates auxiliary systems through modulating functions and annihilation conditions, enhanced by a decoupling matrix.
• Applies calculated kernels to modulate input/output signals over a receding time window for basis expansion coefficients.

Main Results:

• Successfully reconstructs the system state using boundary measurements.
• Demonstrates real-time functionality via simulation of chemical tubular reactor dynamics.
• Effectively mitigates white noise introduced by sensors.
• Outperforms conventional backstepping observers in tested scenarios.

Conclusions:

• The modulating function approach provides an effective solution for distributed state estimation without requiring online PDE solutions.
• This method offers a robust alternative for systems where full spatial state information is inaccessible.
• The technique is validated for practical applications, including chemical process control.