Research On Fault Diagnosis And Fault Tolerant Control Theory Of Nonlinear Systems With Infinite Distributed Time Delay

Time delay is often encountered in various practical systems, such as communication systems, biology systems, power systems, chemistry processes. The existence of time delay is the main reason that causes instability of the dynamic systems, so many researchers contributed their ability to research the systems with time delay. In fact the systems with nonlinear infinite distributed time delay include many systems with time delay. The system with discrete time delay or finite distributed time delay is the special case of the nonlinear system with nonlinear infinite distributed time delay. So it is very important to research the analysis and synthesis of the nonlinear systems with infinite distributed time delay. Based on Lyapunov stability theory and linear matrix inequality technique, the problems of fault diagnosis and fault tolerant control which include the robust H∞filter design, non-fragile robust control method and fault tolerant synchronization control method are discussed in this dissertation for the nonlinear systems with infinite distributed time delay. The effectiveness and the feasibility of the presented approaches are demonstrated by some simulation examples. The main contributions of this dissereation consist of the following major parts:1. The problem of designing robust H∞filter for the nonlinear systems with infinite distributed time delay is researched. Nonlinear infinite distributed time delay is in the state and measurement equations of the systems with norm-bounded and time-varying parameter uncertainties. A new Lyapunov-Krasovskii functional is introduced during the design procedure of filter and a novel method of designing robust H∞filter is firstly proposed. Based on Lyapunov stability theory, delay-independent condition and delay-dependent condition of robust H∞filter have been acquired. The robust H∞filter can guarantee that the filter error system with parameter uncertainties is asymptotically stable and satisfies a prescribed H∞performance level.2. The problem of non-fragile control for the nonlinear systems with infinite distributed time delay is researched. During designing non-fragile controller, two typical kinds of disturbed gains in controller are considered, i.e., independent of the controller and dependent on the controller. Both the discrete time delay and nonlinear infinite distributed time delay are in the nonlinear systems. Two conditions are discussed. One is that the lower bound of discrete time delay is equal to zero, the other is that the lower bound of discrete time delay is greater than zero. When the min of discrete time delay is greater than zero, in other words, when the systems have an interval time-varying delay, a new analysis method of Lyapunov-Krasovskii functional is used to design the non-fragile controller. The less conservatisve result can be achieved. We use the Newton-Leibniz formula in the derivative of the Lyapunov function. The relationship among the terms of the nonlinear systems and the relationship among the terms in the Newton-Leibniz formula are expressed by some free weighting matrices. The non-fragile controller can guarantee that the nonlinear systems with infinite distributed time delay and discrete time delay is asymptotical stable and satisfies a prescribed H∞performance level.3. The problem of fault tolerant control for the nonlinear systems with infinite distributed time delay is researched. Firstly, the problem of fault tolerant synchronization for the nonlinear systems with infinite distributed time delay is researched. A more general model of fault function is used to describe the fault happened in the systems. The synchronization can be acquired under the fault tolerant controller no matter whether fault occurs or not. Fault tolerant controller contains two parts:a state feedback controller and a fault compensator. Secondly, it is proved that the nonlinear systems with infinite distributed time delay which have a kernel function kj(s)=ｎｊδ(s) is equivalent to a class of nonlinear system. Then the problem of fault tolerant synchronization for a class of chaotic system with multiple time-delays is researched based on the fault tolerant control method of nonlinear systems with infinite distributed time delay. The condition of fault tolerant synchronization controller is delay-dependent and can be solved by linear matrix inequalities. Using the fault tolerant controller, the chaotic synchronization error system is asymptotically stable and satisfies a prescribed H∞performance level.4. The problem of fault tolerant synchronization control and fault detection based on fuzzy model is researched for the nonlinear systems with infinite distributed time delay of which kernel function is kj(s)=n.6(s). Firstly, the problem of fault tolerant synchronization of chaotic systems based on T-S fuzzy model and sample data is researched. The problem of fault tolerant synchronization is formulated to study the global asymptotical stability of the chaotic error system with the fuzzy sampled-data controller. To acquire good performance and to produce a less conservative analysis result, a new parameter-dependent Lyapunov-Krasovksii functional and a relaxed stabilization technique are considered. Secondly, the problem of designing the fuzzy hyperbolic fault detection filter for a nonlinear system based on fuzzy hyperbolic model is researched. A reference residual model is used to formulate the fuzzy hyperbolic fault detection filter as a H∞model-matching problem. By using H∞optimization control technique, the conditions of the fuzzy hyperbolic fault detection filter for the nonlinear system are presented via a linear matrix inequality formulation and can be solved by tool box of Matlab.