Robust control of the output probability density functions for multivariable stochastic systems

This paper presents two robust solutions to the control of the output probability density function for multi-input and multi-output stochastic systems, where the purpose of control input design is to minimise the difference between the probability density function of the system output and a given one. The probability density function of the system output is approximated by a B-spline neural network with all its weights dynamically related to the control input. The measured probability density function of the system output is directly used to construct two robust control algorithms which are insensitive to the unknown input. The stability of the closed loop system are proved under certain conditions. An illustrative example is included to demonstrate the use of the developed control algorithms and desired results have been obtained.