Fault tolerant shape control for output PDFs tracking of stochastic distribution systems

This paper investigates the fault-tolerant shape control (FTSC) problem for stochastic distribution systems. The available information for the addressed problem is the input and the measurable output Probability Density Function (PDF) of the system. The system is subject to actuator faults. In this case, the main objective is to achieve fault-tolerant shape control so that the output PDF can track a given target PDF shape even in the presence of faults. In this framework, an effective novel FTSC strategy is proposed based on the online estimation of the actuator faults, which includes a normal control law and an adaptive compensation control law simultaneously. The former can track the given output PDF with optimized performance index in the fault-free case, while the latter can automatically reduce (or even eliminate) the impact of faults for the given PDF shape. Finally, the effectiveness of the proposed design method is illustrated via a numerical example.