Control, State Estimation and Parameter Identification of Nonlinear Distributed Parameter Systems Using Fixed Point Techniques: A Survey

摘要

Fixed point theorems have been an important tool used by mathematicians in the study of the existence of a solution of nonlinear differential equations, and nonlinear operator equations in general, since the beginning of the century. The last seven years has seen the appearance of some papers which extended the basic idea of this tool to solve problems of control, state estimation, and parameter identification of nonlinear systems, including distributed parameter systems. The present paper attempts to survey the fixed point techniques used in nonlinear distributed parameter systems in papers already published on this subject. The fact that most of these papers concentrate on theoretical results is emphasized. Though several of them bring creative ideas, they are poor in practical results or concrete examples of applications.