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

This correspondence presents two robust solutions to the control of the output probability density function for general multiinput and multioutput stochastic systems. The control inputs of the system appear as a set of variables in the probability density functions of the system output, and the signal available to the controller is the measured probability density function of the system output. A new type of dynamic probability density model is formulated by using a B-spline neural network with all its weights dynamically related to the control input. It has been shown that the so-formed robust control algorithms can control the shape of the output probability density function and can guaranteed the closed-loop stability when the system is subjected to a bounded unknown input. An illustrative example is included to demonstrate the use of the developed control algorithms, and desired results have been obtained.