Search

This paper investigates the structural functional observability (SFO) and structural output controllability (SOC) of a class of systems with generically diagonalizable state matrices and explores the associated minimal sensor and actuator placement problems. The verification of SOC and the corresponding sensor and actuator placement problems, i.e., the problems of determining the minimum number of outputs and inputs required to achieve SFO and SOC, respectively, are yet open for general systems, which motivates our focus on a class of systems enabling polynomial-time solutions. In this line, we first define and characterize generically diagonalizable systems, referring to structured systems for which almost all realizations of the state matrices are diagonalizable. We then develop computationally efficient criteria for SFO and SOC within the context of generically diagonalizable systems. Our work expands the class of systems amenable to polynomial-time SOC verification. Thanks to the simplicity of the obtained criteria, we derive closed-form solutions for determining the minimal sensor placement to achieve SFO and the minimal actuator deployment to achieve SOC in such systems, along with efficient weighted maximum matching based and weighted maximum flow based algorithms. For more general systems to achieve SFO, an upper bound is given by identifying a non-decreasing property of SFO with respect to a specific class of edge additions, which is shown to be optimal under certain circumstances., Comment: Under review in a Journal

In this paper, new characterizations for functional observability, functional detectability, and structural functional observability (SFO) are developed, and based on them, the related optimal sensor placement problems are investigated. A novel concept of modal functional observability coinciding with the notion of modal observability is proposed. This notion introduces necessary and sufficient conditions for functional observability and detectability in a unified way without resorting to system observability decomposition, and facilitates the design of a functionally observable/detectable system. Afterwards, SFO is redefined rigorously from a generic perspective, contrarily to the definition of structural observability. A complete graph-theoretic characterization for SFO is proposed. Based on these results, the problems of selecting the minimal sensors from a prior set to achieve functional observability and SFO are shown to be NP-hard. Nevertheless, supermodular set functions are established, leading to greedy heuristics that can find approximation solutions to these problems with provable guarantees in polynomial time. A closed-form solution along with a constructive procedure is also given for the unconstrained case on systems with diagonalizable state matrices. Notably, our results also yield a polynomial-time verifiable case for structural target controllability, a problem that may be hard otherwise., Comment: To appear in IEEE Transactions on Automatic Control as a full paper (2025 March issue)