Adaptive Fault-Tolerant Stochastic Shape Control With Application to Particle Distribution Control

This paper investigates the fault-tolerant shape control (FTSC) problem for stochastic distribution systems. For this problem, in addition to measurable input signals, it is assumed that the distribution function of the system output can be evaluated so that it is available. It is also assumed that the system is subject to actuator faults. In this case, the main control objective is for the output of the stochastic distribution system to track a given target distribution even in the presence of actuator faults. By estimating these actuator faults, an effective FTSC strategy is proposed, which consists of a normal control law and an adaptive compensation control law. The former can track the given output distribution with an optimized performance index in the fault-free case, while the latter can automatically reduce (or even eliminate) the adverse effects caused by the actuator faults. The proposed method can be applied to tracking control of output probability density functions. To demonstrate the effectiveness of the proposed scheme, simulation is performed on one numerical example with satisfactory results obtained. In addition, a practical example of soil particle gradation control in geotechnical applications is given in this paper, and the results show that the proposed fault-tolerant scheme is applicable to practical particle size distribution control.