Practical Synchronization And Control Of Lagrange Networks And Its Related Problems

Synchronization and control of the networked Lagrange systems (Lagrange networks) has recently attracted a great deal of attention from various fields of nonlinear dynamics and control. This is mainly because the classical Lagrange e-quations can well formulate a large variety of mechanical systems including robotic manipulators, flying spacecrafts, walking robots, etc. Moreover, Lagrange networks possess extensive applications in many engineering fields, especially involving com-plex and integrated production processes, such as coordination of multiple manip-ulators, formation of flying spacecrafts, mobile sensor networks and so on. This dissertation is mainly concerned with the issues of practical synchronization and control for Lagrange networks and its related problems from the view of nonlinear dynamics and control. The main contents and contributions of this dissertation are summarized as follows:1. Pinning practical synchronization of Lagrange networks with disturbances. By applying local linear feedback injections to a small fraction of nodes, the net-worked identical Lagrange systems with disturbances achieve practical tracking syn-chronization. The Lagrange networks with both undirect graph and direct graph are considered. Based on practical stability theory and matrix theory, some simple yet generic criteria are derived. Furthermore, we discuss the following two im-portant problems for the pinning control scheme:1) How many agents should be chosen to pin? 2) What kinds of agents should be selected to pin? Subsequently, we take a Lagrange network composing of eight two-link revolute identical manip-ulators for example, which demonstrates the effectiveness of the designed control technique.2. Impulsive practical tracking synchronization of Lagrange networks in the presence of parametric uncertainties. Impulsive control is designed to make the un-certain Lagrange networks achieve practical tracking synchronization, where each agent is allowed to be nonidentical. Some simple yet general algebraic criteria for practical tracking synchronization without and with communication delays are es-tablished respectively. These criteria can synchronize the Lagrange networks from any initial conditions to a time-varying target trajectory with a desired tracking error bound. As a direct application of the theoretical results, we take a net-work composing of four nonidentical mobile robots for example. Simulation results demonstrate that the four mobile robots can achieve practical tracking synchro-nization.3. Practical synchronization of master-slave second-order nonautonomous chaotic system with parameter mismatch. When the master-slave synchronization scheme is considered, PD feedback control and output feedback control are pro-posed to make a class of second-order nonautonomous chaotic systems with param-eter mismatch achieve practical synchronization. Some simple yet general algebraic synchronization criteria are derived based on practical stability theory. Without loss of generality, the parameter mismatch can not only be existed in the system, but also in the external excitation. Besides, the values of the parameter mismatch can be uncertain. In fact, it only needs to know their bounds. Subsequently, we take the horizontal platform system and Duffing-Van der pol oscillator for examples, which demonstrate the effectiveness and feasible of the proposed control techniques.