Optimal measurement trajectories for distributed parameter systems

Abstract The paper deals with the optimal sensor location problem associated with minimax filtering for linear distributed parameter systems under the moving sensors. The problem of optimal choice of a measurement trajectory is treated here as an H ∞ - optimal control one under phase constraints with the objective to minimize a given ‘weak’ performance index under ‘worst’ possible disturbances. Existence of a solution to such a problem is established for the case of quadratic constraints on the disturbances and necessary conditions for optimally are derived on the basis of constructing a sequence of suboptimal solutions associated, in turn, with a sequence of finite-dimensional maximum principles.