Robust Control Of Polytopic Uncertain Systems And Its Applications To Networked Control Systems

Most practical systems might suffer uncertainties in different forms and robust con-trol theory is an effective method and tool for controlling such systems with uncertain-ties. Recently, considerable attention has been paid to study the robust stability analysis and controller synthesis problems for linear systems with uncertainties via parameter-dependent Lyapunov functions. It is commonly encountered in real world applications that some components of control systems (e.g., sensors, controllers, actuators) work out of order in practice. These failures can degrade the performance of system drastically, or even make the system out of control, which can result in serious consequence. For safety-critical systems, such as air vehicles, nuclear reactors, complex industrial control systems, etc, their safety and reliability are more important than their good performance. Reliable control is an effective novelty method to improve reliability of control systems. Conse-quently, the study of robust reliable control of uncertain systems has important practical value and theoretical meanings. On the other hand, the use of communication network in control systems connecting sensors/actuators to controllers more and more prevails in many control applications, including industrial process control, traffic control, satellite clusters, mobile robots. Based on previous work on robust stability for parameter uncer-tain systems via parameter-dependent Lyapunov functions, in this thesis, we systemati-cally and further study the problems of robust H∞performance analysis, state-feedback controller synthesis and filter design for a class of polytopic systems with time-varying uncertain parameters. The robust control approach developed in the thesis is applied to the study of robust reliable control and networked control in the framework of parameter-dependent Lyapunov stability theory. The main contents of the thesis are outlined as follows.Based on the previous work on parameter-dependent Lyapunov function stability, Chapter 2 develops robust H∞control for polytopic system with time-varying parameter uncertainties. The system under consideration is equivalently transformed into a descrip-tor form, and then H∞performance analysis is carried out for the descriptor system by employing parameter-dependent Lyapunov function with the introduction of two addi-tional slack matrices. As a result, robust/Ⅱ∞performance conditions are obtained, which do not involve the product between the Lyapunov matrix and the system matrix. The H∞performance conditions are applied to robust controller synthesis and filtering design. The descriptor system approach is further taken to explore robust H∞performance analysis and controller synthesis of affine parameter systems.Chapter 3 studies the reliable H∞controller design problem for a class of uncertain linear systems against actuator failures. The model of actuator failures is expressed as a polytopic uncertainty form, and then a parameter-dependent Lyapunov function is em-ployed to develop a novel procedure for designing a suboptimal reliable H∞controller. In the design, the H∞performance of the closed-loop system is optimized during normal operation (without failures) while the system satisfies a prescribed H∞performance level in the case of actuator failures. The suboptimal reliable H∞controller design procedure is applied to the design of state-feedback controllers for a linearized AV-8A Harrier VTOL aircraft model, and the effectiveness of the proposed design procedure is illustrated with simulation results. Furthermore, the necessity of the reliable control is demonstrated by the comparisons of the standard control system and the reliable control systems.Motivated by the work of Chapter 2 and Chapter 3, the idea of parameter-dependent Lyapunov approach is further extended in Chapter 4. to address the problem of robust re-liable tracking controller design against actuator failures for polytopic uncertain systems. A state feedback reliable tracking controller is designed by solving a set of linear matrix inequalities.Chapter 5 is concerned with the stabilization problem for a collection of continuous-time networked control systems (NCSs) with communication constraints and network-induced delays using parameter-dependent-Lyapunov-based robust control approach. Be-cause of the limitation of communication capacity, only a limited number of controller-plant connections can be accommodated at any time instant. Therefore, it is necessary to carefully determine a scheduling policy so as to achieve simultaneous stabilization for all these control loops. In the network setup, each of the feedback control systems with communication constraints is modelled as a switched system which switches between the open-loop and closed-loop models according to whether the feedback control loop gains access to the network or not. The modelling approach permits us to apply the ideas already developed in the switched system framework for the simultaneous stability anal-ysis for NCSs with communication constraints. The uncertain network-induced delays are expressed as polytopic uncertainties and robust control method based on parameter-dependent Lyapunov stability theory is applied to the polytopic uncertain systems. Fi-nally, a feedback control and scheduling co-design procedure is proposed for simultane-ous stabilization of the collection of NCSs.Motivated by the work of Chapter 5, a control and scheduling co-design strategy is further studied in Chapter 6 for a collection of discrete-time NCSs with communication constraints. The medium access constraint, network-induced delays, and packet-dropouts are simultaneously taken into account in the NCSs. A control and scheduling co-design strategy is proposed for simultaneous stabilization of the networked control systems with weighted L2 gain.Chapter 7 presents stability analysis for a networked reliable control system with controller failures. The control system under consideration is modelled as a discrete-time switched system with time-varying delays and polytopic uncertainties where the switched system is composed of both stable and unstable subsystems. Delay-dependent sufficient conditions for robust exponential stability are proposed for the delay switched system by employing parameter-dependent piecewise Lyapunov-like functional combined with the free-weighting matrix and average dwell time methods. These sufficient conditions are applied in the study of stability analysis for the networked reliable control system.The conclusions and perspectives are presented in the end of the thesis.