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The choice of the location of controllers and observations is of greatimportance for designing control systems and improving the estimations invarious practical problems. For time-varying systems in Hilbert spaces, theexistence and convergence of the optimal location based on linear-quadraticcontrol on a finite-time horizon is studied. The optimal location ofobservations for improving the estimation of the state at the final time, basedon Kalman filter, is considered as the dual problem to the LQoptimal problem ofthe control locations. Further, the existence and convergence of optimallocations of observations for improving the estimation at the initial time,based on Kalman smoother is discussed. The obtained results are applied to alinear advection-diffusion model.

Optimal Actuator and Observation Location for Time-Varying Systems on a Finite-Time Horizon