Masaru Koga

Forward propagation universal learning network

In this paper, a computing method of higher order derivatives of universal learning network (ULN) is derived by forward propagation, which models and controls large scale complicated systems such as industrial plants, economic, social and life phenomena. It is shown by comparison that forward propagation is preferable to backward propagation in computation time when higher order derivatives with respect to time invariant parameters should be calculated. It is also shown that first order derivatives of ULN with sigmoid functions and one sampling time delays correspond to the forward propagation learning algorithm of the recurrent neural networks. Furthermore, it is suggested that robust control and chaotic control can be realized if higher order derivatives are available.

Chaos control using second order derivatives of universal learning network

A method is proposed for controlling chaotic phenomena on a universal learning network (ULN). The chaos control method proposed here is a novel one. Generation and die-out of chaotic phenomena are controlled by changing the Lyapunov number of the ULN, which is accomplished by adjusting ULN parameters so as to minimize a criterion function that is the difference between the desired Lyapunov number and its actual value. Both a gradient method utilizing second order derivatives of the ULN and a random search method are adopted to optimize the parameters. Control of generation and die-out of chaotic phenomena are easily realized in simulations.

Stability theory of universal learning network

Higher order derivatives of the universal learning network (ULN) has been previously derived by forward and backward propagation computing methods, which can model and control the large scale complicated systems such as industrial plants, economic, social and life phenomena. In this paper, a new concept of nth order asymptotic orbital stability for the ULN is defined by using higher order derivatives of ULN and a sufficient condition of asymptotic orbital stability for ULN is derived. It is also shown that if 3rd order asymptotic orbital stability for a recurrent neural network is proved, higher order asymptotic orbital stability than 3rd order is guaranteed.