An analysis of the multiple model adaptive control algorithm

Abstract

The Multiple Model Adaptive Control algorithm has been used in applications of advanced control technology.However, in these applications, many undesirable characteristics of the method, such as high amplitude limit cycles, have been uncovered. In this thesis the basic types of behavior exhibited by the method are explored. This is done through the simulation and analysis of the method as applied to a sample system structure.This structure has been carefully chosen to exhibit the major phenomena of interest while remaining amenable to detailed analysis.Two major types of results are presented. First of all, detailed conditions for the existance of each of the types of behavior are developed for the special system structure under consideration.Of possibly greater significance are the qualitative insights which result from extrapolating the detailed conclusions to problems of more general structure.It is believed that the qualitative understandings developed in this thesis can form the basis for the introduction of design modifications (two of which are suggested in this thesis) and the development of a systematic methodology for the design of adaptive control systems using the Multiple Model Adaptive Control algorithms.

Issues on Robust Adaptive Feedback Control

“…Hence, it is naïve to expect foolproof global asymptotic stability results in the near future, because there does not, as yet, exists a solid mathematical theory for global (stochastic) nonlinear time-varying stability. Even in the simpler CMMAC, involving LQG controllers, attempts to prove global stability were not successful (Greene, 1975;Shomber, 1980;Greene and Willsky, 1980). Thus, it is the opinion of the authors, what is needed in the short run is additional pragmatic understanding of the different multiple-model approaches, their similarities and differences and consistent fair comparisons on performance improvement over non-adaptive designs.…”

“…1975; Shomber, 1980;Athans et al, 1977;Greene and Willsky, 1980;Schiller and Maybeck, 1997;Maybeck and Griffin, 1997;Schott and Bequette, 1997). In the context of this paper it is important to stress that no robustness to unmodeled dynamics was considered in early CMMAC designs (such robustness issues were unknown in the 1970s) and that performance specifications were generated by LQG "tricks" and not with the frequency-weight concepts widely adopted at present.…”

“…The second approach relied upon stochastic designs that generated on-line posterior probabilities reflecting which of the models was more likely. In the latter approach the controllers could be designed either by classical LQG methods (Willner, 1973;Greene, 1975;Athans et al, 1977;Shomber, 1980;Greene and Willsky, 1980;Schiller and Maybeck, 1997;Maybeck and Griffin, 1997;Schott and Bequette, 1997) or by more sophisticated methods (Fekri et al, 2004a,b,c;Fekri, 2005). In the latter approach one can deal with MIMO designs.…”

Detection of abrupt changes in dynamic systems

“…The MM method was originally developed for problems of system identification and adaptive control [12][13][14][15][16][17]24], and in the initial part of this section we follow these early treatments. Subsequently we will look more closely at the issues that arise and possible adaptations that may be necessary for the use of MM for the detection of abrupt events (see [1,2,5,10,18,19,22,23] for further developments).…”

“…We note here only one technical point which is that we will focus on a discretetime formulation of the MM method. Continuous-time versions can be found in the literature (see [24]), and they differ from their discrete-time counterparts only in a technical and not in a conceptual or structural manner.…”