Optimal sensor location problem for a linear distributed parameter system

This paper studies an optimal sensor location problem for a linear distributed parameter system. It is assumed that a criterion for the optimal sensor location is to minimize the trace of the optimal filtering error covariance function. The existence and uniqueness theorem concerning a solution of the optimal filtering error covariance function for the pointwise observation case is considered. Then by using the existence and uniqueness theorem, the comparison theorem for the partial differential equations of Riccati type is proved. By using the theorems obtained here, the existence theorem concerning a solution of the optimal sensor location problem is proved and the necessary and sufficient conditions for optimality are derived. Finally, some numerical examples for the optimal sensor location problem are illustrated.