Multivariable Adaptive Control

TLDR: This thesis treats the problem of direct adaptive control of linear multivariable systems and proposes a method for construction of Lyapunov functions for a class of single-input systems that relaxes a result by Elliott /et al./ where the interactor is required to be known.

Abstract: This thesis treats the problem of direct adaptive control of linear multivariable systems. The parametrization problem of adaptive control is discussed extensively. A pole-placement problem and a model-matching problem are formulated and interpreted in terms of model reference control. The problem is solved via a discussion on system invariants of multivariable systems as presented by Pernebo. The attention is then directed towards problems of identification and two different estimation schemes are formulated. Parameter convergence is guaranteed provided some conditions on /a priori/ information are satisfied. The requested prior knowledge is formulated in terms of the non-invertible system for the suggested prediction error identification algorithm. The second parameter adjustment law is shown to converge when a certain approximant of the left structure matrix, /i.e./, the system invariant is known. This result relaxes a result by Elliott /et al./ where the interactor is required to be known.The important question of stability of adaptive systems is also treated. The major result is a method for construction of Lyapunov functions for a class of single-input systems. Stability in the sense of Lyapunov and exponential convergence are shown. (Less)