Simultaneous Sensor and Actuator Selection/Placement through Output Feedback Control

Abstract

In most dynamic networks, it is impractical to measure all of the system states; instead, only a subset of the states are measured through sensors. Consequently, and unlike full state feedback controllers, output feedback control utilizes only the measured states to obtain a stable closed-loop performance. This paper explores the interplay between the selection of minimal number of sensors and actuators (SaA) that yield a stable closed-loop system performance. Through the formulation of the static output feedback control problem, we show that the simultaneous selection of minimal set of SaA is a combinatorial optimization problem with mixedinteger nonlinear matrix inequality constraints. To address the computational complexity, we develop two approaches: The first approach relies on integer/disjunctive programming principles, while the second approach is a simple algorithm that is akin to binary search routines. The optimality of the two approaches is also discussed. Numerical experiments are included showing the performance of the developed approaches.Index Terms-Sensor and actuator selection and placement, static output feedback control, mixed-integer nonlinear matrix inequality, disjunctive programming, binary search algorithm.

Combined $\mathcal{H}_{\infty}$ linear parameter varying control design and optimal sensor/actuator selection

“…Combining the system model (17) with weights ( 22) and ( 23) according to figure. 2, yields the generalized plant of the form (1), which is the used in the optimization problem (9). The control problem is formulated with objective (21) and is solved using 'LCToolbox' 1 , an open source toolbox for matlab MATLAB [18].…”

“…In general, heuristic techniques have slow convergence. Another approach explores the design of static output feedback H ∞ /H 2 feedback control [8] and [9] with sensors or actuator selection. [10] solves the combined problem by taking uncertainty into account using approximations of the 0 norm in terms of (weighted) 1 norms [11].…”

Algorithms for joint sensor and control nodes selection in dynamic networks

“…For this reason, we do not delve into the literature of separate sensor or actuator selection. Interested readers are referred to our recent work [24,31] for a summary on methods that solve the separate SA selection problems. The literature of addressing the simultaneous sensor and actuator selection problem (SSASP) is summarized in what follows.…”

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

“…Control allocation is often necessary in redundantly actuated systems, such as parallel manipulators or fault‐tolerant systems, where the dimension of the control signal is less than or equal to the number of actuators available . Furthermore, a system's sensors and actuators can simultaneously be combined or selected in an optimal manner to minimize closed‐loop performance metrics or the number of sensors and actuators needed for closed‐loop stability …”

“…30,31 Furthermore, a system's sensors and actuators can simultaneously be combined or selected in an optimal manner to minimize closed-loop performance metrics 32,33 or the number of sensors and actuators needed for closed-loop stability. 34 The novel contributions of this paper include techniques to linearly combine an LTI system's actuators and/or sensors in such a manner that the new system is interior conic with prescribed bounds and the difference between the new system and a specified desired system is minimized in a weighted  2 or  ∞ sense. The weighting of the  2 or  ∞ norm is crucial, as it allows for certain frequency bandwidths to be targeted for performance purposes while ensuring the new system is interior conic.…”