# Selective Strong Structural Minimum Cost Resilient Co-Design for Regular Descriptor Linear Systems

## TL;DR

This paper develops a framework for optimally deploying actuation, sensing, and communication in regular descriptor systems to ensure resilient decentralized control, extending strong structural systems theory to handle selective structures and robustness.

## Contribution

It introduces the concept of selective strong structural fixed modes and provides necessary and sufficient conditions for resilient decentralized control feasibility in descriptor systems.

## Key findings

- Derived conditions for resilient control feasibility.
- Proposed a minimum cost placement strategy for actuation, sensing, and communication.
- Validated the approach on an electric power grid example.

## Abstract

This paper addresses the problem of minimum cost resilient actuation-sensing-communication co-design for regular descriptor systems while ensuring selective strong structural system's properties. More specifically, the problem consists of determining the minimum cost deployment of actuation and sensing technology, as well as communication between the these, such that decentralized control approaches are viable for an arbitrary realization of regular descriptor systems satisfying a pre-specified selective structure, i.e., some entries can be zero, nonzero, or either zero/nonzero. Towards this goal, we rely on strong structural systems theory and extend it to cope with the selective structure that casts resiliency/robustness properties and uncertainty properties of system's model. Upon such framework, we introduce the notion of selective strong structural fixed modes as a characterization of the feasibility of decentralized control laws. Also, we provide necessary and sufficient conditions for this property to hold, and show how these conditions can be leveraged to determine the minimum cost resilient placement of actuation-sensing-communication technology ensuring feasible solutions. In particular, we study the minimum cost resilient actuation and sensing placement, upon which we construct the solution to our problem. Finally, we illustrate the applicability the main results of this paper on an electric power grid example.