Stable adaptive control of stochastic distributions and its application

This short paper presents a stable adaptive control algorithm for the control of the output probability density function for unknown time-invariant stochastic systems. An on-line parameter estimation algorithm is constructed using the measured output probability density functions of the system. Based upon the same type of dynamic model proposed by Wang (7, 8), a functional weighted type performance function is employed in the formulation of the adaptive control algorithm. It is shown that the stability of the closed loop system can be guaranteed under certain conditions. An applicability study of the proposed algorithm to the solid flocculation control in paper making is included, where a simulated example is employed to illustrate the use of the developed control algorithm.