Selection of Dynamic Sensors and Actuators in the Control of Linear Systems

This paper selects sensors and actuators (location, type, and number) from an admissible set. We seek an approximate solution to this integer programming problem. Given the optimal use of the entire admissible set of sensors and actuators, it is possible to decompose the quadratic cost function into contributions from each stochastic input and each weighted output. In the past, these suboptimal cost decomposition methods of sensor and actuator selection have been used to locate perfect (infinite bandwidth) sensors and actuators on large scale systems. This paper extends these ideas to the more practical case of imperfect actuators and sensors with dynamics of their own. Secondly, the old cost decomposition methods are discarded for improved formulas for sensor and actuator deletion (from the admissible set). These results show that there exists an optimal number of actuators (it is possible to use too few and too many). Preliminary attempts to solve this new research question are described. It is also shown that there exists optimal dynamics of the actuators. NASA’s SCOLE example demonstrates the concepts.