Abstract-A new approach of fault detection and diagnosis (FDD) for general stochastic systems in discrete-time is studied. Our work on this problem is motivated by the fact that most of the nonlinear control laws are implemented as digital controllers in reality. Different from the formulation of classical FDD problem, it is supposed that the measured information for the FDD is the probability density functions (PDFs) of the system output rather than its measured value. A radial basis function (RBF) neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighting of the RBFs neural network. Feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. An illustrated example is included to demonstrate the efficiency of the proposed algorithm, and satisfactory results are obtained.

Abstract-In this paper, a new algorithm for an adaptive PI controller for nonlinear systems subject to stochastic nonGaussian disturbance is studied. The minimum entropy control is applied to decrease the closed-loop tracking error on an ILC basis. The key issue here is to divide the control horizon into a number of equal time intervals called batches. Within each interval, there are a fixed number of sample points. The design procedure is divided into two main algorithms, within each batch and between any two adjacent batches. A D-type ILC law is employed to tune the PI controller coefficients between two adjacent batches. However, within each batch, the PI coefficients are fixed. A sufficient condition is established to guarantee the stability of the closed-loop system. An analysis of the ILC convergence is carried out. Two-link robot manipulator example is included to demonstrate the use of the control algorithm, and satisfactory results are obtained.

Abstract-A new design of a fault tolerant control (FTC)-based an adaptive, fixed-structure PI controller, with constraints on the state vector for nonlinear discrete-time system subject to stochastic non-Gaussian disturbance is studied. The objective of the reliable control algorithm scheme is to design a control signal such that the actual probability density function (PDF) of the system is made as close as possible to a desired PDF, and make the tracking performance converge to zero, not only when all components are functional but also in case of admissible faults. A Linear Matrix Inequality (LMI)-based FTC method is presented to ensure that the fault can be estimated and compensated for. A radial basis function (RBF) neural network is used to approximate the output PDF of the system. Thus, the aim of the output PDF control will be a RBF weight control with an adaptive tuning of the basis function parameters. The key issue here is to divide the control horizon into a number of equal time intervals called batches. Within each interval, there are a fixed number of sample points. The design procedure is divided into two main algorithms, within each batch, and between any two adjacent batches. A P-type ILC law is employed to tune the parameters of the RBF neural network so that the PDF tracking error decreases along with the batches. Sufficient conditions for the proposed fault tolerance are expressed as LMIs. An analysis of the ILC convergence is carried out. Finally, the effectiveness of the proposed method is demonstrated with an illustrated example.