| The problem of stable adaptive control of a linear-time-invariant plant when no external distrubances are present was resolved in 1980. This case is termed the ideal case and requires assumptions on the plant that are quite restrictive and not generally valid in practice. The stability of adaptive control systems under assumptions that are practically more reasonable is therefore a subject of considerable importance. The work in this thesis examines some of the issues involved in this subject in the adaptive control of discrete-time plants, and forms part of a systematic research program at Yale aimed at developing a theory of adaptive control valid under reasonable practical assumptions. In particular, globally stable discrete-time adaptive control is shown to be possible without any prior knowledge on the high-frequency gain of the plant; the role of the degree of persistent excitation of the reference signal in assuring global stability for adaptive control in the presence of bounded external disturbances is resolved for the case of plants of arbitrary relative degree; the conditions for globally stable adaptive control of time-varying plants are established; and a unified treatment is presented for modified adaptive laws that result in globally stable adaptive control of a class of discrete-time plants that are only partially modeled. |
