Abstract of Thesis presented at COPPE/UFRJ as a partial fulfillment of the requirements for the degree of Doctor of Science (D.Sc.)

Multivariable Adaptive Control Using Factorization of the High Frequency Gain Matrix (HFGM)

Alvaro Koji Imai

March/2003

Advisors:

Liu Hsu Ramon Romankevicius Costa

Department:

Eletrical Engineering

      This dissertation concerns the design and analysis of the adaptive control of multi­variable linear time-invariant plants. In contrast to the monovariable case (single-input single-output), where the theory has reached quite a satisfactory level, the same can not be said about the multi variable case (multi-input multi-output). One major differ­ence between the two classes of systems is the concept of the sign of the high frequency gain of the plant which is simple in the first case since it is a simple scalar. However in the latter case such a gain is a matrix making the generalization of the sign concept far from immediate. The existing proposals to circumvent such a difficulty either led to restrictive assumptions about the prior knowledge of certain properties of the high frequency gain which involved symmetry conditions difficult to be satisfied in practice, or led to algorithms which did not require such assumptions but were extremely complicated to be useful in applications. We propose an approach to avoid restrictive prior knowledge assumptions about the high frequency gain while retaining a reason­able simplicity of the adaptive control law. To this end, the basic tool utilized is the appropriate factorization of the high frequency gain. A generalization of the sign of the scalar high frequency gain appears to be related with the signs of the leading principal minors of the high frequency gain matrix.