Identification and Adaptive Control of Multivariable Stochastic Linear Systems

Abstract

An increasingly applied concept for the design of parameteradaptive controllers for single-input single-output systems is the combination of a recursive system parameter estimation method and a controller design procedure according to the certainty equivalence principle. Making use of the same concept for the design of multivariable parameter-adaptive controllers the choice of an appropriate structural representation of the system for the identification procedure becomes important because this influences the amount of necessary a priori information about the system, the number of system parameters to be estimated and the types of controllers which can be combined with the system identification scheme. In this paper a minimal input-output description is proposed as a basis for the design of multi variable parameter-adaptive controllers which yields less parameters to be estimated than other input-output descriptions and which can be linked easily to state space controllers and to controller design procedures for a matrix polynomial input-output description of the system. A parameter-adaptive minimum variance state controller based on the minimal input-output description is compared by simulation with other multivariable parameteradaptive minimum variance controllers based on a matrix polynomial and a p-canonical input-output description of the system. It is shown that the state controller yields at least as good results as the other controllers and that it is computationally feasible.