Extensions of Compatibility Theory and Compatibility-Guided Co-Design

Extend the compatibility principle for temporally degenerate linear parabolic systems beyond exact operator compatibility, establish analogous structural conditions for nonlinear temporally degenerate systems, and exploit compatibility conditions as a guideline for actuator–sensor co-design.

Background

The paper characterizes admissible feedback interconnections for temporally degenerate linear parabolic systems through the exact identity A_1 = B K_0 C, which removes the singular reaction term and yields a regularized evolution equation. The authors identify three directions that remain unresolved: treating situations in which exact compatibility fails or is only approximate, extending the structural theory from linear to nonlinear degenerate systems, and using compatibility requirements to inform the joint placement or design of actuators and sensors. These directions are presented as significant open questions defining the next stage of the theory.