A structured systems approach for optimal actuator-sensor placement in linear time-invariant systems

Abstract

Abstract-In this paper we address the actuator/sensor allocation problem for linear time invariant (LTI) systems. Given the structure of an autonomous linear dynamical system, the goal is to design the structure of the input matrix (commonly denoted by B) such that the system is structurally controllable with the restriction that each input be dedicated, i.e., it can only control directly a single state variable. We provide a methodology that addresses this design question: specifically, we determine the minimum number of dedicated inputs required to ensure such structural controllability, and characterize, and characterizes all (when not unique) possible configurations of the minimal input matrix B. Furthermore, we show that the proposed solution methodology incurs polynomial complexity in the number of state variables. By duality, the solution methodology may be readily extended to the structural design of the corresponding minimal output matrix (commonly denoted by C) that ensures structural observability.

A framework for actuator placement in large scale power systems: Minimal strong structural controllability

“…In general, finding such minimal placement to ensure controllability or to achieve pre-specified control performance is an NP-hard problem, see [3]. Alternative approaches that lead to efficient and scalable algorithms, i.e., with polynomial time complexity, have been proposed in [4]. The proposed approaches are based on structural systems reformulation (see [5]) and provide optimal placement of actuators to ensure structural controllability of the system.…”

Control principles of complex systems

“…The maximum assignability index of B(G) is the maximum number of top assignable SCCs that a maximum matching M * may lead to. The minimum set of actuators can be found with polynomial time complexity (Pequito et al, 2013(Pequito et al, , 2016. Consider, for example, the network shown in Fig.…”

“…Yet, if we need to guarantee only structural controllability, MCP1 can be easily solved (Pequito et al, 2013(Pequito et al, , 2016. For a directed network G with LTI dynamics the minimum number of dedicated inputs (or actuators), N da , required to assure structural controllability, is…”

The single-input Minimal Controllability Problem for structured systems

“…Due to complexity and cost constraints it is of interest to look for control laws acting on a reasonably small number of state variables. Such input selection strategies have been reported for controlling large scale systems or for leader selection of multi-agent systems [1,[5][6][7]. In [8], the authors analysed three variants for the problem of minimizing the number of control inputs:…”