Theory of Input Driven Dynamical Systems
Theory of Input Driven Dynamical Systems
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发表时间：
2012
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通讯作者：
Manjunath Gandhi;P. Tiňo;H. Jaeger
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作者：
Manjunath Gandhi;P. Tiňo;H. Jaeger
机器学习、机器人学、人工智能或认知科学中感兴趣的大多数动态模型都是非自治的，是输入驱动的。在过去的几年里，非自治系统的数学研究出现了许多重要的创新。在理解非自治系统的长期行为时，吸引子的概念是基本的。对于时变输入，事实证明，要使吸引子的概念有用，吸引子不能是单个子集，而必须被设想为随时间变化的集合的序列。本教程的目的是阐明非自治系统的吸引子的有用概念，并介绍一些新出现的动力系统理论概念，这些概念特别与输入驱动系统有关。
Most dynamic models of interest in machine learning, robotics, AI or cognitive science are nonautonomous and input-driven. In the last few years number of important innovations have occurred in mathemati- cal research on nonautonomous systems. In understanding the long term behavior of nonautonomous systems, the notion of an attractor is fun- damental. With a time varying input, it turns out that for a notion of an attractor to be useful, the attractor cannot a single subset, but must be conceived as a sequence of sets varying with time as well. The aim of this tutorial is to illuminate useful notions of attractors of nonautonomous systems, and also introduce some newly emerging concepts of dynamical systems theory which are particularly relevant for input driven systems.