Title: Selective Strong Structural Minimum Cost Resilient Co-Design for Regular Descriptor Linear Systems,
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.