Adaptive Control of Time-Varying Systems Using Multiple Models

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ObjectiveThe objective of the research is to understand how a machine or an organism can adapt to a time-varying environment, particularly when it is rapidly time-varying. Under such conditions, conventional adaptation (based on incremental adjustments) may be too slow to cope with the changes. Obviously a new approach is needed, and the multiple-model method is an attractive candidate.Rapidly varying environments arise in medicine, neuroscience, vision, economics, and other disciplines. The world we live in is an excellent example, where sudden and discontinuous changes are possible. The multiple model based approach described in the proposal can be thought of as a method which attempts to classify (or identify) the different situations that might arise, and proposes the appropriate actions that should be taken.Intellectual MeritFrom a mathematical standpoint, the research proposed opens a new area of adaptive control. It attempts to answer an important theoretical question which will have significant impact on problems that arise in many other disciplines.To the non-expert it will provide some understanding of the limits to adaptive control. More specifically, it attempts to answer questions related to how fast the environment can change, if we are to adapt successfully to it.Broader ImpactsThe research, when completed, will provide both graduate and undergraduate students, much needed training in new areas of mathematics related to advanced control methods.Undergraduates at Yale, who are women and underrepresented minority students will be actively encouraged by the PI to participate in the projects during the summers as well as to work on them under this direction for their senior projects.The PI organizes seminars regularly at Yale, He also delivers both scientific and popular lectures (e.g. Peabody Museum, Whitney Senior Citizen Center) both in the United States and around the world, and organizes the bi-annual Yale Workshop on Adaptive and Learning Systems. The results of the research carried out will be widely disseminated at these different settings. Finally, the mathematical results will be published in leading control journals.