A Globally Stable Adaptive Controller for Multivariable Systems

摘要

Hermite normal forms of nonsingular transfer matrices play a central role in determining the class of model transfer matrices which the plant can follow. However, due to inherent complexity in specifying the Hermite form in general, it has been argued that adaptive control is practically feasible only for those plants which have diagonal Hermite forms, i.e., which can be decoupled by using state feedback only. The sign definiteness of the high frequency gain matrix KP has been found to be sufficient to generate stable adaptive laws. For 2x2 systems, the knowledge of relative degree of each scalar transfer function has been used in determining the Hermite form. A globally stable adaptive controller has been developed and it has been shown that all 2x2 stably invertible systems can be generically adaptively controlled subject to the definiteness condition on the gain matrix.