Investigation Of Finite-Time Synchronization Of Networked Dynamical Systems And The Relevant Issues

The cooperation and coordinated control of networked dynamical systems has beenone of the cutting edge research topics in the field of complex dynamics and control dueto its widespread applications in mathematics, physics, computer science, informationscience, control science, neuroscience and biology, engineering, etc. Consensus and syn-chronization, as a fundamental form of coordinated motion of multi-agent systems, areused to describe the collective emerging dynamics of multiple interactional dynamicalsystems. A study of consensus and synchronization problems lays a fundamental ba-sis for the further investigation of the cooperation and coordinated control in networkedcomplex dynamical systems. Aiming to address one of the fundamental problems in theresearch filed, this thesis is mainly concerned with the finite-time synchronization of net-worked dynamical systems and the relevant issues from the perspective of dynamics andcontrol. In particular, the main contributions of the research work are summarized in thefollowing three aspects:1. Finite-time synchronization of chaotic systems with network topology. By de-veloping non-linear control strategies, it is shown that the coupled chaotic system canachieve fast synchronization exponentially with undirected network topology. The con-vergence conditions and settling times corresponding to diferent system parameters arerigorously established. It is found that the coupled chaotic system can achieve synchro-nization in finite time as long as the coupling strength is strong enough. For the syn-chronization of coupled chaotic systems with a leader, it is demonstrated that the statesof all chaotic systems can converge to the state of the leader. In addition, the finite-timesynchronization problems are studied and the corresponding convergence conditions areestablished for the coupled chaotic systems with directed network topology.2. Infinite-time and finite-time synchronization of networked harmonic oscilla-tors. Based on finite-time stability theory of dynamical systems, several criteria are an-alytically established to evaluate the infinite-time and finite-time synchronization of thecoupled harmonic oscillators with physics background and mechanics characteristics.Explicit expressions are derived analytically for the final trajectories that each harmonicoscillator must follow. The efects of non-linear factors, position measurement errors andexternal disturbances on the synchronization process of coupled harmonic oscillators arealso considered. In the presence of a leader, it is shown that the positions and velocitiesof all harmonic oscillators can track the position and velocity of the leader. Furthermore,it is found that settling times are not only mainly dependent on the algebraic connectivity of network graphs, but also the initial positions and velocities of all harmonic oscillators.3. Consensus of multiple non-identical second-order agent systems. Some controlprotocols ensuring multiple non-identical second-order agent systems achieve consensusare established with the help of construction of appropriate Lyapunov functions. Theexplicit expression of the final consensus state, which is characterized by the masses,velocity gains, initial positions and velocities of all agent systems, is also given. Forthe consensus of multiple agent systems with a leader, some sufcient conditions areproposed for the positions and velocities of all second-order agent systems to follow theposition and velocity of the leader. Theoretical results show that all time-varying, non-linear and non-identical second-order agent systems can reach consensus in the presenceor absence of a leader.