Combined minimum entropy and output PDFS control via neural networks

It is well known that entropy is a measure for uncertainties for stochastic systems. In the case that the system is represented by a probability density function, the entropy can be easily calculated. By combining the entropy with the recent developed control strategies on the shape control of the output probability density function for dynamic stochastic systems, in this paper a new control algorithm is formulated for a class of unknown dynamic stochastic systems. The obtained control input minimizes a combined performance function for the closed loop system and can thus realizes the control of the shape of the output probability density functions, and at the same time, minimizes the system entropy so as to reduce the uncertainties for the closed loop system. Since the system considered is unknown, a neural network model is used on-line to update the optimal control input. This leads to an adaptive control framework for the closed loop control of the system. A simulated example is included to show the effectiveness of the proposed algorithm and encouraging results have been obtained.