Stability and performance of time-varying adaptive systems: Analysis and applications.

摘要

In this thesis we consider the problems of identification, prediction and adaptive control of systems with unknown time-varying parameters, with an emphasis on obtaining performance bounds. While these issues have been extensively studied in the case of time invariant systems, time-varying systems have not received much attention. This thesis is divided into two parts, the first of which deals with the analytical derivation of performance bounds, and the second, which proposes solutions to real-life vibration control problems.; Using a stochastic model for plant variation, it is shown that it is possible to obtain tight bounds on parameter identification performance. These results require minimal assumptions on the statistics of the regression vector and directly lead to a performance bound for adaptive predictors. In the case of adaptive control, it is shown that a family of adaptive controllers is mean square stable. This stability result allows the application of the identification and prediction bounds to obtain bounds on the variance of the closed-loop system output. For each of the cases described, simulation results are presented, which verify that the bounds are indeed tight.; The second part of this thesis deals with the problem of vibration cancellation which is an important problem in numerous places such as in the aerospace industry and in the design of disk drives. In this part of the thesis, a new adaptive control solution is proposed for this problem. The algorithm is analyzed and compared with other existing solutions. Computer simulations using real-life helicopter models show the effectiveness of the adaptive control schemes. Implementations of this algorithm on some laboratory test beds also bear out its effectiveness.