Simultaneous Sensor and Actuator Selection/Placement through Output Feedback Control
For control engineers designing output feedback controllers, this work provides methods to minimize sensor and actuator usage while ensuring stability, though the problem is computationally challenging.
This paper addresses the problem of simultaneously selecting minimal sensors and actuators for stable output feedback control in dynamic networks. The authors formulate it as a combinatorial optimization problem and propose two approaches: one based on integer/disjunctive programming and a simpler binary-search-like algorithm, with numerical experiments demonstrating their performance.
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 mixed-integer 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.