Abstract-An axiomatic framework providing robust stability and performance bounds for a wide class of Estimation based Multiple Model Switched Adaptive Control (EMMSAC) algorithms is developed. The approach decouples development of both the atomic control designs and the estimation processes thus permitting the usage of standard controller design and optimisation approaches for these components. The framework is shown to give tractable algorithms for MIMO LTI plants, and also for some classes of nonlinear systems (for example, an integrator with input saturation). The gain bounds obtained have the key feature that they are functions of the complexity of the underlying uncertainty as described by metric entropy measures. For certain important geometries, such as a compact parametric uncertainties, the gain bounds are independent of the number of plant models (above a certain threshold) which are utilized in the implementation. Design processes are described for achieving a suitable sampling of the plant uncertainty set to create a finite candidate plant model set (whose size is also determined by a metric entropy measure) which achieves a guaranteed robustness/performance.
Abstract-For an Estimation Based Multiple Model SwitchedAdaptive Control (EMMSAC) algorithm controlling a MIMO minimal LTI plant, lp, 1 ≤ p ≤ ∞ bounds on the gain from the input and output disturbances to the internal signals are obtained which are invariant to the number of models in the plant model set. For a compact uncertainty set it is shown that a realisable EMMSAC algorithm achieves robust stability for any plant within the uncertainty set.
Abstract-A wide class of MMAC with a finite lp (1 ≤ p ≤ ∞) closed loop gain are shown to have an unboundedly increasing lp closed loop gain for a simple set of plants under increasing parametric uncertainty. A modification is proposed which achieves a quadratic closed loop gain function which is independent of the size of the uncertainty set.
Abstract-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.
Abstract-For the class of MIMO minimal LTI systems controlled by an estimation based multiple model switched adaptive controller (EMMSAC), bounds are obtained for the closed loop lp gain, 1 ≤ p ≤ ∞, from the input and output disturbances to the internal signals.
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