Control for stochastic tracking error minimization based on state entropy with neural network

Abstract

It is well known that when the disturbance in the nonlinear system has whiteness, the error between the output of the system and the desired output does not show whiteness. Considering the adaptive system, the mean square evaluation function is often not sufficient for this problem. In recent years, entropy has been attracting attention as an evaluation function changing to the mean square criterion. Beginning with entropy of Shannon, its characteristics are related to higher-order statistics. When entropy is minimized, all moments of error are constrained. Especially in dynamic modeling, the entropy's criterion is more robust than that of MSE. In this research, we focus on correntrop, which has expanded Renyi's entropy more generally, consider controlling and updating the controller by the neural network. For state estimation of correntropy, state change of entropy of error is taken into account by explicitly using state quantity of control rather than time series data set. We confirm by simulation that the proposed method makes the probability density function of the error sharper.