Discrete system identification and iterative solutions of linear systems†

Abstract

A framework is illustrated for analysing and synthesizing parameter identification algorithms from the viewpoint of iterative solutions of linear algebraic equations. The Kudva-Narendra identification procedure is converted into an iterative vector scheme. This scheme is interpreted as being a Jacobi simultaneous over-relaxation method and then reformulated as a successive over-relaxation method. In these identification schemes, the coefficients are up-dated at each iteration based upon the latest measurements of the plant inputs and outputs. Through the framework advocated in this paper, numerical methods technology can potentially provide insights for developing improved identification algorithms and guidelines for their implementation. It is noted that stable adaptive observers can also be designed within this framework for the simultaneous estimation of both the plant state and parameters from input-output measurements.