Gain Bounds for Multiple Model Switched Adaptive Control of General MIMO LTI Systems

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

Robust stability and performance analysis for multiple model adaptive controllers

Abstract—For an Estimation Based Multiple Model Switched Adaptive Control (EMMSAC) algorithm controlling a MIMO minimal LTI plant, $l_p,\ 1\le p\le \infty$ 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

Robust stability and performance for multiple model switched adaptive control

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

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

Robust stability for multiple model adaptive control: part I - the framework

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

Gain bounds for multiple model switched adaptive control of general MIMO LTI systems

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