Hysteresis switching adaptive control of linear multivariable systems

The authors present a model reference adaptive control scheme for deterministic continuous-time multivariable systems represented by square, strictly proper, minimum-phase transfer function matrices. A typical requirement of existing algorithms is to assume that the zero structure at infinity and the high-frequency gain matrix are fully (or at least partially) known. It is well known that these requirements are very restrictive, since in general both the zero structure at infinity and the high-frequency gain matrix depend on plant parameters. It is shown that these restrictive assumptions may be dispensed with by using a hysteresis switching control strategy recently introduced by A.S. Morse et al. (1992). This entails running a finite number of parameter estimators in parallel, and using a switching algorithm to select between candidate estimators based on their associated prediction errors. Hysteresis in the switching algorithm precludes switching arbitrarily rapidly between estimators, and all switching ceases within a finite time. The results represent a significant step forward in understanding the minimal amount of prior knowledge necessary to design a stabilizing controller for a linear multivariable system