Measurement optimization with sensitivity criteria for distributed parameter systems

We consider the problem of optimally designing sensors for observation of a class of distributed parameter systems. The design of sensors concerns the choice of measurement conditions so that the information provided by measurements is maximal. This problem has been posed as a deterministic optimal control problem for a system equation of the Riccati type which governs a filter covariance. In the present study we introduce a functional called a sensitivity criterion by extending the Fisher information matrix to function spaces. It is shown that maximizing this criterion leads to a suboptimal solution of the sensor design problem associated with an infinite-dimensional state estimation problem. The existence theorem for a type of measurement control problem is proved and some numerical results are presented.