Fundamental Research on Learning and Intelligence in System Control

本课题的研究重点有两个方面：一是学习控制方案的一般处理；二是从系统论的角度研究神经网络的学习机制。不用说，这两个问题是相互关联的。在一般学习控制方案的研究中，得到了频域稳定条件、对象摄动下的鲁棒稳定条件的结果。这些结果保证了在有限维系统已有方法的基础上，可以对改进的重复控制方案等学习方案进行鲁棒性分析，并阐明了神经网络的学习机制及其在控制系统中的应用可以统一为无组织记忆的联想和在各自参数空间中的优化。在神经网络的研究中，将网络视为动态系统的基本观点导致了以下主题：1)推导了具有反馈连接的一般网络的学习算法，2)它在模式识别中的应用，3)它对组合网络的进一步推广，4)更有效的算法的应用，如共轭梯度法，每种算法都得到了满意的结果。特别是，复合网络具有这样的特点：1)通过将问题分解成更小的部分来使学习更容易，2)适用于教学信号隐含的网络，并有望成为神经网络的各种构造的基础。另一方面，也清楚地表明，更多的理论分析是相当困难的，部分原因是基本的非线性。在这个方向上进行更详细的研究可能是未来的一个悬而未决的问题。

The focus of this research project is two fold: one is the general treatment of learning control scheme and the other is the study of learning mechanism of neural networks viewed from the system theoretic viewpoint. Needless to say, these two issues are mutually related.In the study of the general learning control scheme, results on stability conditions in the frequency domain, robust stability condition under plant perturbations are obtained. these results guaranteed that robustness analysis can be made for such learning schemes as modified repetitive control schemes based upon the methodology already employed for finite-dimensional systems.In relation to these, it is also clarified that the learning mechanism of neural networks and its application to control systems can be unified into the principle that the association of unorganized memories and the optimization in their respective parameter space. The notion of composite networks to be described below is the key to this development.In the study of neural networks, the fundamental standpoint of viewing networks as dynamical systems led to the following subjects: 1) derivation of a learning algorithm for general networks with feedback connections, 2) its application to pattern recognition, 3) its further generalization to composite networks, 4) application of more effective algorithms such as the conjugate gradient method, each leading to a satisfactory result. In particular, the composite networks enjoy such features as 1) making learning easier by decomposing the problem into smaller parts, 2) applicable to networks where teaching signals are implicit, and are expected to become more fundamental to various construction of neural networks.On the other hand, it has also become clear that more theoretical analysis is fairly difficult, partly due to the fundamental nonlinearity. More detailed research in this direction can be an open problem for the future.