Contribuições ao problema de estimação de parâmetros de sistemas LPV

Abstract

This thesis is an investigation on time-varying parameter estimation in linear dynamic systems. Such systems, henceforth referred to as linear parameter-varying (LPV) systems, model many engineering problems, and are workable approximations to even more nonlinear problems. Treating parameter variation as uncertainty and applying robust analysis and control techniques to LPV systems, tempting as it may seem, is not an ideal approach: conservative, valid only for slowly varying parameters, and even then it may fail. Although some work in the literature try to sidestep those issues by introducing bounds on maximum parameter variation rates, it just becomes another piece of information that must be known or estimated a priori. This work is more in concert with the alternative, time-varying methods such as gain scheduling or adaptive control. System parameter values are a natural input to variable control structures, and when their actual values are not available, their estimates may be just as valuable. Parameter measurement for other purposes is a secondary concern here. The text begins with a brief review of system identification and the state estimation problem, for parameter estimation is an identification problem that may be posed as a nonlinear state estimation. From the perspective of linearizing the problem with respect to the parameters, evaluating LPV system bandwidth may be perceived as fundamental not only to discrete-time study of the sampled system, but also to continuous-time analysis. The results obtained in that area, regarding the LPV matrix's spectral radius,may be useful for other applications as well. Given a discrete or properly sampled continuous LPV system, parameter estimation is then posed as an optimization problem: some limits on what can and cannot be estimated are detected via the objective function's gradient. After that, a second approach is proposed: turning individual parameters' estimation into scalar problems. Another set of limitations is obtained. Finally, conclusions and suggestions of possible further work are listed and discussed. In particular, some pointers for a reinterpretation of the results in the differential geometry framework are presented in one of the appendices.