Research On Observer-based Robust Fault Detection For Discrete Time-varying Systems

With the increasing demands of safety and reliability for equipments and control systems, fault detection for complex systems has attracted more and more attention and becomes one of the most important aspects in automatic control. Meanwhile, due to the fact that digital information systems such as computer control systems, networked control systems, wireless communication systems are widely used, research on discrete-time control systems has been more and more significant. Furthermore, all the plants are intrinsically time-varying systems, and missing measurements, abrupt changes of system structures as well as nonlinear perturbations which can be modeled by switched systems or Markovian jump systems are frequently encountered in various engineering systems. These systems have essential differences with the usual linear time invariant systems. However, research on fault detection for linear discrete time-varying systems with missing measurements or stochastic uncertainties, for discrete-time switched linear systems or discrete-time linear Markovian jump systems has not been well developed. The main purpose of this dissertation is to investigate observer-based fault detection for some typical classes of discrete time-varying systems. The main works and contributions in the dissertation are given as follows:Chapter 2 deals with the problem of fault detection filter design for linear discrete time-varying systems with multiplicative noise. By introducing an observer-based robust H∞fault detection filter as a residual generator, the design of the filter is formulated in the framework of H∞filtering for a class of stochastic time-varying systems. A sufficient and necessary condition for the existence of the filter is derived in terms of a Riccati equation based on Lyapunov and adjoint operator approaches. An analytical solution of the parameter matrices is obtained by solving the Riccati equation.Chapter 3 studies the problem of designing fault detection filter for linear discrete time-varying systems under two different circumstances with incomplete measurements. One is called the multiple packet dropouts, and the other one is multiple missing measurements. By using an observer-based robust H∞, fault detection filter as a residual generator, the filter design problem is formulated in the framework of H∞filtering problem for a class of stochastic time-varying systems. Sufficient and necessary conditions for the existence of the filters are derived in terms of Riccati equations, and analytical solutions of the parameter matrices are obtained by solving the corresponding Riccati equations.Chapter 4 investigates the problem of fault detection filter design for a class of discrete-time Markovian jump systems with nonlinear perturbation and missing measurements. The nonlinearity is assumed to satisfy global Lipschitz conditions. An observer-based fault detection filter is employed as a residual generator, and the stochastic H∞filtering formulation is proposed. By introducing some slack matrices, sufficient existence conditions of the filter are given in terms of matrix inequalities for two cases. One is the complete known transition probabilities case while the other one is the partially known transition probabilities case. Moreover, the solutions to the parameter matrices are obtained by solving a set of linear matrix inequalities.Chapter 5 deals with the problem of optimal fault detection for discrete-time Markovian jump linear systems. By constructing an observer-based fault detection filter and by defining generalized transfer function operator that maps from fault or unknown input to residual, the problem of designing optimal fault detection filter is formulated in the framework of maximizing stochastic H∞/H∞or H_/H∞performance index. A new adjoint operator-based optimization scheme is proposed for solving the aforementioned optimization problem and a mode-dependent unified optimal solution is obtained by solving a coupled Riccati equation.Chapter 6 treats the active fault tolerant control problem for a class of discrete-time linear switched systems under arbitrary switching. For the purpose of constructing a mode-dependent active fault tolerant control strategy, the residual feedback control structure is employed based on a mode-dependent optimal fault detection filter. The design of the overall system is implemented in two steps. First, for residual generation, the optimal fault detection filter is proposed by maximizing H∞/H∞or H_/H∞performance index in terms of a coupled Riccati equation. Then, a residual feedback control law is given for compensating the influence of fault for stability and H∞performance. The parameter matrices of the controller are obtained by solving linear matrix inequalities using cone complementary algorithm.