Core Concepts
This paper develops computationally efficient criteria for structural functional observability (SFO) and structural output controllability (SOC) within the class of generically diagonalizable systems, and provides closed-form solutions for the associated minimal sensor and actuator placement problems.
Abstract
This paper investigates the structural functional observability (SFO) and structural output controllability (SOC) of a class of systems with generically diagonalizable state matrices. The key highlights and insights are:
The paper defines and characterizes generically diagonalizable matrices, referring to structured matrices for which almost all realizations are diagonalizable. It establishes that a graph is structurally diagonalizable if and only if each subgraph induced by every subset of strongly-connected components (SCCs) of this graph is so.
The paper develops simplified criteria for SFO in generically diagonalizable systems, which are significantly simpler compared to those for general systems. These criteria affirm the applicability of the criterion in prior work to the class of generically diagonalizable systems.
The paper identifies a class of systems for which the SOC can be verified in polynomial time, and highlights that generically diagonalizable systems fall into this class.
Leveraging the established criteria, the paper presents a closed-form solution and a weighted maximum matching based algorithm for the minimal sensor placement problem to achieve SFO in generically diagonalizable systems. For more general systems, it identifies a non-decreasing property of SFO with respect to a specific class of edge additions and proposes two algorithms to obtain an upper bound, proven optimal under certain circumstances.
The paper also proposes a weighted maximum flow algorithm to determine the minimal actuators needed for SOC in generically diagonalizable systems.