Realization of Perfect Tracking

Abstract

In Chapters 1 and 2, several control algorithms have been described ([41, 42, 43]) on the control of the output probability density functions of the stochastic systems. Using the B-spline approximations, the dynamic part of the stochastic system has been logically decoupled from the output density function itself. This leads to a group offeedback control algorithms (2.5.10), (2.5.12), (2.5.20), (2.5.22), (3.3.15) and (3.4.18), where it has been shown that the control inputs are always related to the weighted integration of the measured probability density functions of the system. However, in these approaches, the design criteria has been set to minimize a finite indexed quadratic performance function which characterises the tracking performance of the output probability density function with respect to a given density function. Although the control algorithm obtained can minimise the performance function, it cannot always guarantee the perfect tracking of the output probability density function with respect to the given distribution.