Parameter identification of linear systems with heat sensors subject to unknown space-varying parameters

Abstract

We extend existing works on control of (finite-dimensional) linear systems with (infinite-dimensional) heat sensors [6]. The extension lies on the one hand, in the fact that all system poles and zeros are unknown and, on the other, in the fact that sensor equations include unknown spatially-varying parameters. These uncertainties make the problem of parameter identification quite challenging. The existing adaptive observers for this type of systems prove not to be applicable in the presence of these uncertainties. Presently, we develop an identification method that involves multi-sine exciting input signals. Doing so, the inaccessible signal at the junction point, between the system and the sensor, can be given an affine parameterized form. It turns out that the identification problem of the sensor is decoupled from that of the system. Then, a parameter estimator involving K-filters is designed to get estimates of the sensor parameters as well as those of the inaccessible signal at the junction point. A new persistent excitation concept is introduced that ensures exponential convergence of the sensor parameter estimates and the estimated junction signal. The latter is then used to identify the parameters of the system dynamics.