Robust stability and performance for multiple model switched adaptive control

Abstract

While the concept of switching between multiple controllers to achieve a control objective is not new, the available analysis to date imposes various structural and analytical assumptions on the controlled plant. The analysis presented in this thesis, which is concerned with an Estimation-based Multiple Model Switched Adaptive Control (EMMSAC) algorithm originating from Fisher-Jeffes (2003); Vinnicombe (2004), is shown not to have such limitations. As the name suggests, the key difference between EMMSAC and common multiple model type switching schemes is that the switching decision is based on the outcome of an optimal estimation process. The use of such optimal estimators is the key that allows for a simplified, axiomatic approach to analysis. Also, since estimators may be implemented by standard optimisation techniques, their construction is feasible for a broad class of systems.

The presented analysis is the first of its kind to provide comprehensive robustness and performance guarantees for a multiple model control algorithm, in terms of lp, 1 ? p ? ? bounds on the closed loop gain, and is applicable to the class of minimal MIMO LTI plants. A key feature of this bound is that it permits the on-line alteration of the plant model set (dynamic EMMSAC) in contrast to the usual assumption that the plant model set is constant (static EMMSAC). It is shown that a static EMMSAC algorithm is conservative whereas a dynamic EMMSAC algorithm, based on the technique of dynamically expanding the plant model set, can be universal. It is also shown that the established gain bounds are invariant to a refinement of the plant model set, e.g. as a successive increasing fidelity sampling of a continuum of plants. Dynamic refinement of the plant model set is considered with the view to increase expected performance.

Furthermore, the established bounds—which are also a measure of performance— have the property that they are explicit in the free variables of the algorithm. It is shown that this property of the bound forms the basis for a principled, performance-orientated approach to design. Explicit, performance-orientated design examples are given and the trade off between dynamic and static constructions of plant model sets are investigated with respect to prior information on the acting disturbances and the uncertainty.

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