Nonlinear dynamical system modeling viarecurrent neural networks and a weighted state space search algorithm
Leong-Kwan Li, Sally Shao, Ka Fai Cedric Yiu · Journal of Industrial and Management Optimization · 2011
Given a task of tracking a trajectory, a recurrent neural network may be consideredas a black-box nonlinear regression model for tracking unknowndynamic systems. An error function is used to measure the differencebetween the system outputs and the desired trajectory thatformulates a nonlinear least square problem with dynamicalconstraints. With the dynamical constraints, classical gradient typemethods are difficult and time consuming due to the involving of thecomputation of the partial derivatives along the trajectory. Wedevelop an alternative learning algorithm, namely the weighted statespace search algorithm, which searches the neighborhood of thetarget trajectory in the state space instead of the parameter space.Since there is no computation of partial derivatives involved, ouralgorithm is simple and fast. We demonstrate our approach bymodeling the short-term foreign exchange rates. The empiricalresults show that the weighted state space search method is verypromising and effective in solving least square problems withdynamical constraints. Numerical costs between the gradient methodand our the proposed method are provided.