DESIGN OF ADAPTIVE CONTROL SYSTEM

Abstract

The thesis deals with the problem of designing model reference adaptive control systems from different points of view. It is divided into seven chapters. The first chapter contains an introduction to the problem of adaptive control and a review of the literature in this field. The second chapter contains an approach to the design of the overall system so as to guarantee its stabi lity. This is assured by imposing a Lyapunov function on the system and selecting the controls so that the deriva tive of this function is negative. The relation between this problem and the Lur'e problem of absolute stability is discussed and some conditions established to obtain a stable adaption algorithm using only the observed output variables. Different selections of Lyapunov functions are shown to lead to continuous or bang-bang controllers. Extensions of the method are obtained to nonlinear systems and to the identification problem. Finally, an alternative method employing an implicit model is discussed, for identification as well as adaption. A second method of adaption, based on optimal control theory, is discussed in the next three chapters. The third chapter discusses optimal model-following systems with known inputs, using a quadratic performance index, and also discusses time-orttimal and singular modelfollowing systems. "Perfect" model-following is seen to arise from the latter and also as a limiting case of "implicit" model-following with quadratic index. A suboptimal model following system is obtained when only output feedback is to be used. The fourth chapter formulates the model-following problem as a differential game. Existence of solutions to linear differential games is discussed in some detail and a dual of this game obtained as a game of estimation. The real and implicit model-following problems are discussed from this point of view and it is shown, that, for success ful model-following, the plant must be "more" controllable than the model. The problems of stochastic model-following and model-following with constraints on feedback strategies is discussed. The fifth chapter discusses the problem of obtain ing optimal adaptive systems, with model-following systems a particular case. A modified quasilinearization method is developed, so that the successive iterations for the optimal control can be carried out from the knowledge of the nominal solutions only. This obtains successive corrections to the nominal control in a series form, whieh is shown to be based on sensitivity functions and thus the same as suggested by Werner and Cruz. It is also shown that similar development is possible using the method of invariant imbedding. The sixth chapter contains two new identification methods based on orthonormal functions for identifying the parameters of linear systems. One method uses the integrals of orthonormal functions as "subsidiary" functions; the other uses the co-efficients of the expansions of the system output and its integrals in orthonormal series, both methods leading to an algebraic equation for the co-efficients. The seventh and last chapter contains a critical summary of the results and suggestions for further investigations.