Stability Analysis And Fault-tolerant Control Of Constrained Systems Based On LMI Technique

With the development of aircraft control and navigation, saturation problem has ig-nited enormous attentions. There are two aspects on the problem of saturation. One is actuator saturation which is illustrated as the bounded output of actuator during the control process. Another is the state saturation of system. In the traditional designing, the satu-ration effects have not been considered, so when the saturation happens in the systems, which will result in the degradation of the system performance or system instability.For the first aspect, the global stability of closed-loop systems cannot be guaranteed when actuator saturation phenomena is considered for system analysis and design. That is to say stability can only be guaranteed in a bounded region. Based on this reason, two aspects are considered in recently. The fist one is how to estimate the domain of attraction of system. The other one is how to design controller to enlarge the domain of attraction. At the same time, the performance and the disturb tolerance ability of the closed-loop system are also interesting problems. In existing results, system analysis and controller design under actuator saturation is the main stream. However, in some complex systems such as aircrafts, space crafts, nuclear power plants, actuator saturation and actuator faults always happen at the same time. For a flying aircraft its rudder may be damnified which can lead to the fault of the actuator. On the other hand, the rudder(actuator) of the aircraft can only give a bounded input which can be seen as an actuator saturation phenomena. However, noting all above results, there is no work that deals with this problem.The other aspect is state saturation problem of systems. The material situation is illustrated as that states of systems are restricted in a bounded region forcibly. Then the linear structure of system is transformed to an unlinear system. However, in the traditional designing, this phenomena has not been considered, which will lead to that the global stability of systems cannot be guaranteed.Motivated by the above observations, and based on previous works of others, this paper studies a class of linear time-invariant systems with actuator saturation and actuator faults at the same time. Then, for state saturation systems we not only present new con- dition to estimate the domain of attraction but also consider the problem about controller design.The main contributions are as follows:Chapters 1-2 first summarize and analyze the development and main research meth-ods in saturation problem. Preliminaries about the considered problem are also given.Chapter 3, a dynamic output feedback controller design approach based on cone complementary linearisation procedure is proposed for linear time-invariant (LTI) sys-tems with actuator saturation. Firstly, the estimation of domain of attraction is given. Then, a design method to find a larger estimation of domain of attraction is presented. In the process of design, nonconvex conditions are obtained, so a cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. Two ex-amples are given to illustrate the efficiency of the design method.Chapter 4 studies the problem of stability analysis and dynamic output feedback controller design for continuous time linear systems under state saturation. In this paper, both full state saturation and partial state saturation are considered. In order to solve the key problem, a new system is constructed. Then, a new LMI based method is presented for estimating the domain of attraction of the origin for a closed-loop system under state saturation. Based on this method, LMI based algorithm is developed for constructing dynamic output-feedback controller which guarantee that the domain of attraction of the origin for closed-loop system is large as possible. An example is given to illustrate the efficiency of the design method.Chapter 5 studies the problem of designing adaptive fault-tolerant controllers for lin-ear time-invariant systems with actuator saturation. New methods for designing indirect adaptive fault-tolerant controllers are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller param-eters are updating automatically to compensate the fault effects on systems. The designs are developed in the framework of linear matrix inequality (LMI) approach, which can enlarge the domain of asymptotic stability of closed-loop systems in the cases of actuator saturation and actuator failures. Two examples are given to illustrate the efficiency of the design method.Chapter 6 studies the problem of designing adaptive fault-tolerant H∞controllers for linear time-invariant systems with actuator saturation. The disturbance tolerance abil-ity of the closed-loop system is measured by an optimal index. A notion of adaptive H∞performance index is proposed to describe the disturbance attenuation performances of closed-loop systems. New methods for designing indirect adaptive fault-tolerant con-trollers are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller parameters are updating automati-cally to compensate the fault effects on systems. The designs are developed in the frame-work of linear matrix inequality (LMI) approach, which can guarantee the disturbance tolerance ability and adaptive H∞performances of closed-loop systems in the cases of actuator saturation and actuator failures. An example is given to illustrate the efficiency of the design method.Finally, the results of the dissertation are summarized and further research topics are pointed out.