Synchronization of classes of dynamical networks : analysis and control
Creators: name: Liu, Tao
Publisher: name: The Australian National University
Year: 2011
Subjects: subject: QA614.8.L58 2011
subject: Differentiable dynamical systems
subject: Synchronization
subject: System analysis

description: Dynamical networks composed of dynamical units are ubiquitous in many different contexts such as biology, ecology, sociology, technology, and even in our daily life. These networks bring us tremendous convenience and meanwhile provide us great challenges, which show the urgent need for research on the behavior, analysis and control of dynamical networks. Emerging from the interconnections of a population of coupled dynamical units, synchronization is a significant collective behavior of dynamical networks, and has received a great deal of attention due to its extensive applications. Actually, many phenomena encountered in natural sciences and engineering can be explained by synchronization in networks. This thesis is devoted to the analysis and control of synchronization for some classes of dynamical networks. The main contents and contributions of the thesis are summarized as follows. In the first part of the thesis, two different kinds of dynamical networks, namely, i) the networks with both delay free and time delay couplings, and ii) the networks with switching topology, are considered from a Lyapunov point of view. For the first type of networks, new criteria on asymptotic synchronization of a given network are derived from the stability analysis of an error dynamical system which is transformed into a large-scale system with different subsystems. For the second type of networks, multiple Lyapunov functionals are used to analyze exponential synchronization of a network with switching topology and time-varying coupling delay, and conditions on the "slow" switching signals specified by an average dwell time are given. Networks with switching topology in the absence of time delay are also discussed, and synchronization criteria for arbitrary switchings as well as designed switchings are proposed. In the second part of the thesis, synchronization analysis of a particular network motivated by cellular networks is carried out from an input-output point of view. The results are obtained by considering an input-output characterization of nonlinear operators based on dissipativity theory. The concept of dissipativity is extended to incremental-dissipativity, and input-output synchronization of the network which consists of incremental-dissipative nonlinear operators is proved to be equivalent to input-output stability of a large-scale system composed by dissipative subsystems, then synchronization of the network is guaranteed by the stability of the corresponding large-scale system. Finally, controlled synchronization of a network is studied by introducing a distributed controller as well as a more flexible switching distributed controller. The total control effort of the controller is constrained by a cost function. First, parameters of the constrained distributed controller which can synchronize the network and satisfies the control constraint simultaneously are solved by a nonlinear optimization problem. If such a single controller cannot be found, then a switching controller is considered. A new synchronization criterion for a network with a switching topology is established by using a single Lyapunov function method. With this new criterion, a synchronizing switching signal is identified, and candidate controllers are selected numerically, with both of which a switching controller can be constructed subsequently.