A new control method of nonlinear systems based on impulse responses of universal learning networks

A new control method of nonlinear dynamic systems is proposed based on impulse responses of Universal Learning Networks (ULNs). ULNs form a superset of neural networks. They consist of a number of inter-connected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary (positive, zero, or even negative) time delays. A generalized learning algorithm is derived for the ULNs, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. The algorithm can also be used in a unified manner for almost all kinds of learning networks. In this paper, not only the controlled object but also its controller are described by the ULNs and the controller is constructed by using the higher order derivatives of ULNs. The main feature of the proposed control method is to use impulse response defined by the higher order derivatives as a criterion function of the network. By using the impulse response, nonlinear dynamics with not only quick response but also quick damping can be more easily obtained than the conventional nonlinear control systems with quadratic form criterion functions of control variables.