一般化学習ネットワークにおけるカオス制御方式

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  • Chaos Control on Universal Learning Network

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A method is proposed for controlling of chaotic phenomena on Universal Learning Network (U.L.N.).<br>U.L.N. is a network which consists of arbitrary nonlinear functional nodes and arbitrary delay elements between the nodes, and can model and control various large-scale complicated systems like industrial plants as well as economical, social and life phenomena.<br>The chaos control method proposed here is a novel one. Generation and die-out of chaotic phenomena are controlled by changing Lyapunov Number of U.L.N., which is accomplished by adjusting U.L.N. parameters so as to minimize a criterion function that is the difference between the desired Lyapunov Number and its actual value.<br>A gradient method is developed for optimizing the parameters. The method utilizes second order derivetives and a method for calculating the second order derivetives is also proposed which is applicable to a wide range of systems with recurrent dynamics.<br>Nevertheless, it is difficult to optimeze the parameters sucusessfully by using the gradient method only because the Lyapunov Number is very sensitive to changes in the parameters and the criterion function is not convex. Therefore, a random search is combined with the gradient method.<br>Controlling of generation and die-out of chaotic phenomena are realized in simulations. In the simulations, sigmoid functions are adopted as U.L.N. node functions. Therefore, the U.L.N. is a fully recurrent neural network. And the weights, the thresholds and the slopes of the sigmoid functions are optimized.<br>The chaos control method could be the first step to a new paradigm of control system which makes use of chaotic phenomena positively.

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