Abstract
Abstract : This project pertains to the development of a theory for adaptive control of nonlinear dynamic systems that are nonlinearly parameterized (NLP). Developments in NLP systems that have been carried out as a part of this project relax the ubiquitous assumption made in the context of adaptive control which is that the unknown parameters occur linearly. During the past year, we have derived several new results related to NLP systems, and can be grouped under two categories: (I) Control of nonlinear systems with a triangular structure, (ii) Parameter convergence in NLP systems. The class of systems considered in (i) includes high-dimensional nonlinear systems connected in chain and triangular forms, examples of which include Hammerstein-Uryson models and recurrent neural networks. Global stabilization and tracking can be guaranteed for such systems in the presence of unknown parameters that occur nonlinearly. The results related to (ii) pertain to conditions of persistent excitation (PE) under which parameter convergence occurs in a class of discrete and continuous NLP systems. It is shown that for different classes of transcendental functions, distinct PE conditions can be derived that guarantee parameter convergence. Applications to parameter estimation in sigmoidal functions and identification of unknown frequencies of a sinusoidal signal are presented.
Published Version
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