Abstract

In the first part of the lecture we recall classical results on selecting optimal input signals for parameter estimation in systems with temporal (or spatial) dynamics only and their generalizations to unbounded signals. As a motivation for studying input signals, which can influence our system both in space and in time, we provide several examples of new techniques emerged in high energy lasers and in micro- and nano-technologies. We also mention an increasing role of cameras as sensors. Then, we discuss extensions of optimality conditions for input signals, trying to reveal an interplay between their spatial and temporal behavior. We concentrate on open loop input signals for linear systems, described by partial differential equations (PDE) or their Green’s functions. Finally, we sketch the following open problems: (i) simultaneous optimization of sensor positions and input signals, (ii) experiment design for estimating spatially varying coefficients of PDEs.