Robust Stability for Multiple Model Adaptive Control: Part II—Gain Bounds

The axiomatic development of a wide class of Estimation based Multiple Model Switched Adaptive Control (EMMSAC) algorithms considered in the first part of this two part contribution forms the basis for the proof of the gain bounds given in this paper. The bounds are determined in terms of a cover of the uncertainty set, and in particular, in many instances, are independent of the number of candidate plant models under consideration. The full interpretation, implications and usage of these bounds within design synthesis are discussed in part I. Here in part II, key features of the bounds are also discussed and a simulation example is considered. It is shown that a dynamic EMMSAC design can be universal and hence non-conservative and hence outperforms static EMMSAC and other conservative designs. A wide range of possible dynamic algorithms are outlined, motivated by both performance and implementation considerations.