Mode Discerning Control Generation for Switched Systems with Unknown Exogenous Inputs

For switched systems, it is often crucial to identify which mode is currently activated. To achieve this, one could design specific control inputs, known as discerning controls, that force the system to reveal its active mode through its measured outputs. A system is said to be controlled mode discernible if such an input exists. Controlled mode discernibility for switched systems with unknown inputs has rarely been discussed, but it has important applications in active fault diagnosis. The objective of this paper is to investigate whether two modes of a switched system with unknown inputs can be distinguished by locally reconfiguring certain static or dynamic controllers. We formalize the idea by defining concepts stricter than controlled mode discernibility and characterizing them from a geometric perspective. Reconfiguration of controllers for generating discerning controls is formulated as three types of max-min problems for special cases, and the approaches for reducing the max-min problems to finite-dimensional optimization problems are provided. We further propose some design constraints for maintaining stability under the reconfigured controller, motivated by applications in active fault diagnosis. A demonstrative example is provided to explain the proposed concepts and formulations.