A reduced adaptive observer for multivariable systems

Abstract

An adaptive observer for multivariable systems is presented for which the dynamic order of the observer is reduced, subject to mild restrictions. The observer structure depends directly upon the multivariable structure of the system rather than a transformation to a single-output system. The number of adaptive gains is at most the sum of the order of the system and the number of input parameters being adapted. Moreover, for the relatively frequent specific cases for which the number of required adaptive gains is less than the sum of system order and input parameters, the number of these gains is easily determined by inspection of the system structure. This adaptive observer possesses all the properties ascribed to the single-input single-output adpative observer. Like the other adaptive observers some restriction is required of the allowable system command input to guarantee convergence of the adaptive algorithm, but the restriction is more lenient than that required by the full-order multivariable observer. This reduced observer is not restricted to cycle systems.