Adaptive Control of Time-Varying Systems Using Multiple Models

研究的目的是了解机器或生物体如何适应时变环境，特别是当它是快速时变的环境时。在这种情况下，传统的适应（基于增量调整）可能太慢，无法应对变化。显然，需要一种新的方法，而多模型方法是一个有吸引力的候选方法。快速变化的环境出现在医学、神经科学、视觉、经济学和其他学科中。我们生活的世界就是一个很好的例子，在那里突然的和不连续的变化是可能的。建议中描述的基于多个模型的方法可以被认为是一种方法，它试图对可能出现的不同情况进行分类（或识别），并提出应该采取的适当行动。从数学的角度来看，该研究开辟了自适应控制的新领域。它试图回答一个重要的理论问题，这个问题将对许多其他学科中出现的问题产生重大影响。对于非专家来说，它将提供一些对自适应控制限制的理解。更具体地说，它试图回答与环境变化有多快有关的问题，如果我们要成功地适应它。更广泛的影响这项研究完成后，将为研究生和本科生在与先进控制方法相关的数学新领域提供急需的培训。耶鲁大学的本科生，女性和少数族裔学生将被PI积极鼓励在夏季参与这些项目，并在这个指导下为他们的高级项目工作。PI定期在耶鲁大学组织研讨会，他还在美国和世界各地举办科学和大众讲座（例如皮博迪博物馆，惠特尼老年公民中心），并组织两年一次的耶鲁适应性和学习系统研讨会。所进行的研究结果将在这些不同的环境中广泛传播。最后，数学结果将发表在领先的控制期刊上。

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.