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

TL;DR

This paper investigates optimal placement of actuators and sensors in time-varying systems over a finite horizon, focusing on control and estimation improvements using linear-quadratic and Kalman filtering techniques.

Contribution

It establishes existence and convergence results for optimal locations of actuators and sensors in Hilbert space systems, including dual problems for control and estimation.

Findings

Optimal actuator locations for control are characterized.

Optimal observation locations for final-time state estimation are identified.

Application to a linear advection-diffusion model demonstrates practical relevance.

Abstract

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