Exponential Boundary Control for 2-D Spatial Distributed Parameter Systems Under Boundary Collocated and Planar...

Area of Science:

• Control Theory
• Applied Mathematics
• Systems Engineering

Background:

• Challenges in controlling 2-D spatial distributed parameter systems (DPSs) with complex diffusivity.
• Need for reduced sensor/actuator requirements in complex system control.
• Existing methods often require full-domain measurements or extensive control actuation.

Purpose of the Study:

• To achieve exponential realization of desired profiles in 2-D spatial DPSs with space-dependent diffusivity.
• To develop a cost-effective control strategy by minimizing sensors and actuators.
• To validate the proposed control and measurement schemes through numerical and application examples.

Main Methods:

• Proposed a planar output feedback boundary control strategy.
• Combined boundary collocated measurement and planar linear measurement techniques.
• Utilized Poincaré-Wirtinger inequality and variable substitution for error system analysis.

Main Results:

• Successfully demonstrated exponential convergence criteria for the error system.
• The proposed strategy requires control on only two boundaries and minimal output information.
• Effectiveness and practicability validated via a general numerical example and a 2-D heat conduction system.

Conclusions:

• The developed boundary control strategy is effective for 2-D spatial DPSs with space-dependent diffusivity.
• The approach significantly reduces the need for extensive sensors and actuators.
• The method offers a practical solution for real-world applications like heat conduction systems.