摘要:
确定学习运用自适应控制和动力学系统的概念与方法, 研究未知动态环境下的知识获取、表达、存储和利用等问题. 针对产生周期或回归轨迹的连续 非线性动态系统, 确定学习可以对其未知系统动态进行局部准确建模, 其基本要 素包括: 1)使用径向基函数(Radial basis function, RBF)神经网络; 2)对于周期(或回归)状态轨迹 满足部分持续激励条件; 3)在周期(或回归)轨迹的邻域内实现对非线性系统动态的局部准确神经网络逼近(局部准确建模); 4)所学的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 并可在动态环境下用于动态模式的快速识别或者闭环神经网络控制. 本文针对离散动态系统, 扩展了确定学习理论, 提出一个根据时态数据序列对离散动态系统进行建模与控制的框架. 首先, 运用确定学习原理和离散系统的自适应辨识方法, 实现对产生时态数据的离散非线性系统的未知动态进行局部准确的神经网络建模, 并利用此建模结果对时态数据序列进行时不变表达. 其次, 提出时态数据序列的基于动力学的相似性定义, 以及对离散动态系统产生的时态数据序列(亦可称为动态模式)进行快速识别方法. 最后, 针对离散非线性控制系统, 实现了基于时态数据序列对控制系统动态的闭环辨识(局部准确建模). 所学关于闭环动态的知识可用于基于模式的智能控制. 本文表明确定学习可以为时态数据挖掘的研究提供新的途径, 并为基于数据的建模与控制等问题提供新的研究思路.
Abstract:
The deterministic learning theory aims at the area of knowledge acquisition, representation, and utilization in uncertain dynamical environments. Referred to as ``deterministic learning'' in comparison with the celebrated ``statistical learning'', the new learning theory is developed utilizing results from concepts and tools of adaptive control and dynamical systems. It provides systematic design approaches for nonlinear system identification, temporal/dynamical pattern recognition, and pattern-based control of nonlinear systems in uncertain dynamical environments. In this paper, the deterministic learning theory is extended to modeling and control of nonlinear discrete-time systems. Firstly, based on the temporal data sequences generated from discrete-time systems, locally-accurate approximation of the underlying system dynamics is achieved. Consequently, the temporal data sequences can be effectively represented by using the knowledge of approximated system dynamics. Secondly, definitions for similarity of temporal data sequences are given, and a method for rapid recognition of a temporal data sequence is proposed. Thirdly, deterministic learning of closed-loop system dynamics is implemented during neural network (NN) control of nonlinear discrete-time systems. The knowledge can be reused for pattern-based intelligent control. The deterministic learning theory will provide a new approach to data-based modeling, recognition, control of complex processes and systems.
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