Analysis And Control Of Hybrid Complex Dynamical Systems And Networks

Complex systems and complex networks are focal and hot topics of great interest recently in science and engineering. However, impulsive, jumping, switching and instantaneously changing phenomena can be found in fields of neural networks, communication networks, robotics, aeronautics and astronautics, telecommunications, economics and automatic control, especially in many fields of biology, ecology, medicine, physics and so on. These systems are characterized by abrupt changes and switches in the states at certain instants, which display a certain kind of dynamics in between continuous and discrete systems. The phenomenon, in the form of impulses and switches, cannot be well described by a pure continuous-time or pure discrete-time model. This type of systems is said to be hybrid complex systems (networks). Nonlinear complex systems in the real world are characterized by the fact that at certain moments of time they experience abrupt changes and switches of the states, so the dynamic behaviors of the systems will become more complicated and harder to cope with. Therefore, it is very important, and indeed necessary, to provide some theories and methods in practical applications for analysis and control of this kind of impulsive and switching systems and networks. In this dissertation, the stability, robustness, stabilization and control of some complex dynamical systems including common differential systems, singular systems, chaotic systems etc. and complex networks with impulses, model switches, time-delays and uncertain perturbations are investigated. Applying some new analysis and control methods, a series of new theoretical results are obtained.Many dynamical systems in practice, such as networked systems, manufacture systems, electrical networks, economical systems, etc., are generalized state-space systems (known also as differential algebraic systems, singular systems, descriptor systems, etc.). The stability, robust stabilization and robust H∞control of singular impulsive systems are discussed in this dissertation. Since there are many differences between singular impulsive systems and common differential systems, pure singular systems and impulsive systems, solution properties, exponential stability and E-exponential stability of singular systems with impulse effect have been derived. Some sufficient and necessary conditions for the equivalence between exponential stability and E-exponential stability are given. Based on the Riccati inequality approach and Lyapunov stability theory, robustness for singular impulsive systems with uncertain perturbations are investigated. Sufficient conditions for robust H∞criteria of singular impulsive systems via state feedback control are established. A simple approach to the design of a robust impulsive controller is then presented. For hybrid systems, it is not easy to obtain better performance by using single continuous or discrete control law. So in this dissertation switching control of singular impulsive systems is investigated. Applying the Lyapunov function theory, several sufficient conditions are established for exponential stability, robust stabilization and H∞control of the corresponding singular-impulsive closed-loop systems.In order to drive the system state to designed trajectory and obtain satisfactory performances, based on impulsive and switching dynamical systems theories, a new hybrid impulsive and switching control strategy for synchronization of nonlinear systems is developed. First, we have formulated and studied a hybrid impulsive and switching control problem for singular systems with nonlinear perturbations. Some simple sufficient conditions guaranteeing the global robust exponential stabilization of its equilibrium via stabilizing controller design are obtained together with upper-bound estimates of the system fundamental solutions. A systematic procedure for designing the robust impulsive and switching controllers has also been suggested. Second, a new hybrid impulsive and switching control strategy for control and synchronization of nonlinear systems is developed. Using switched Lyapunov functions, several new criteria for global exponential stability of hybrid impulsive and switching nonlinear systems are established and, particularly, some simple sufficient conditions for driving the synchronization error to zero exponentially are proposed.Combining conventional methods of adaptive control with switching control, a new adaptive switching control scheme is presented to solve control and synchronization problems. Selecting the controller parameters is fairly flexible and simple. It can be applied to systems with uncertain perturbations and unknown parameters. Based on Lyapunov stability theory, an adaptive control law is applied to globally stabilize chaotic systems and achieve states synchronization of two chaotic systems whose dynamics are subjected to the system disturbances and/or some unknown parameters.Since couplings and topologies (i.e. architectures) of hybrid complex dynamical networks, which directly impact on dynamic behaviors of networks, need to be considered in addition to their hybrid features, they are more complicated than hybrid systems. Some kinds of complex networks have time-varying topologies, so they are said to be complex network with switching topology. This dissertation formulates its model and studies its stability and control problems. First, the stabilization problem of the complex networks using impulsive control which has not been studied up to now is addressed. Furthermore, some real-world complex dynamical networks commonly have communication time-delays due to finite speed of information processing. Based on the hybrid control and Lyapunov function, the stabilization and robust H∞control of such systems with impulsive and switching effects, which have not been studied before, are addressed with some criteria derived. Then, we have investigated the synchronization problem for a time-varying uncertain dynamical network with switching topology and unknown bounded coupling strengths via adaptive control. The dynamics of the network nodes are also assumed to be unknown but satisfying certain bound conditions. Based on Lyapunov stability theory, global convergence criteria for the dynamical network synchronization are derived using update laws for estimating the unknown parameters in the controller designs.For general complex dynamical networks, impulsive control and synchronization of complex dynamical networks with coupling time-delays are addressed. Sufficient conditions are obtained in terms of solutions of linear matrix inequalities. Sufficient conditions guaranteeing the global exponential stabilization of its equilibrium and exponential synchronization of networks are obtained. Moreover, the passivity problem of linearized complex dynamical networks, present or lack of communication time-delays has been addressed. Passive control and synchronization issues are considered respectively. Some criteria have been derived such that their inputs and outputs satisfy passive conditions. It is said to be passive control and synchronization of complex dynamical networks.Finally, a summary has been done for all discussion in the dissertation. The research works in further study are presented.