Optimal Sensor and Actuator Locations in Linear Distributed Parameter Systems

A constructive method is developed to obtain optimal sensor and actuator locations for inverse optimal state estimation and control of a class of linear distributed parameter systems (DPSs). Given the inverse optimal state estimators and controllers for linear DPSs developed by the first author recently, it is shown that the performance index for optimal locations of sensors and actuators is the trace of the solution of the Bernoulli partial differential equations (PDEs), which are the optimal state estimation and control gain matrices. Thus, the optimal locations are designed so as to minimize the trace of the solution of the Bernoulli partial differential equations.