Nonlinear Dynamical System Modeling Via Recurrent Neural Networks and A Weighted State Space Search Algorithm

Given a task of tracking a trajectory, a recurrent neural network may be considered as a black-box nonlinear regression model for tracking unknown dynamic systems. An error function is used to measure the difference between the system outputs and the desired trajectory that formulates a nonlinear least square problem with dynamical constraints. With the dynamical constraints, classical gradient type methods are difficult and time consuming due to the involving of the computation of the partial derivatives along the trajectory. We develop an alternative learning algorithm, namely the weighted state space search algorithm, which searches the neighborhood of the target trajectory in the state space instead of the parameter space. Since there is no computation of partial derivatives involved, our algorithm is simple and fast. We demonstrate our approach by modeling the short-term foreign exchange rates. The empirical results show that the weighted state space search method is very promising and effective in solving least square problems with dynamical constraints. Numerical costs between the gradient method and our the proposed method are provided.