Design On Synchronization Of A Class Of Chaotic Systems And Consensus Of Second-Order Multi-agent Systems

As the nonlinear science and complexity science has a very wide range of applications in the real world, more and more domestic and foreign scientific research workers have begun to shift the focus to the nonlinear and complex work since 20th century. As a very important direction of nonlinear system theory, chaos phenomenon has received increasing attention. During the same period, the coordinated control of multi-agent system is a new subject in the field of complex engineering control, which reveals the inherent law of many natural phenomena. And more importantly, it can provide new ideas and methods to solve the complex realistic issues.In recent years, the theories and methods of chaos synchronization control have been proposed. However, because of the extremely sensitive to the initial value, the controller needs to be simpler, have better robustness and higher reliability. Therefore, it is necessary to improve and consummate the existing synchronization control methods, which makes it more practical. By combining terminal sliding mode control algorithm with adaptive technique, a novel synchronization control algorithm is proposed in the third chapter of this paper. This robust adaptive control algorithm is able to reduce the complexity of the controller and solve the singular problem caused by improper parameters in the traditional terminal sliding mode control. At the same time, it reduces the chattering amplitude caused by the variable structure, so as to improve the stability of the system. And it proved that the new algorithm can guarantee the two chaotic systems will be synchronized in the limited time.As social interaction is becoming more and more complex, the coordination control of multi-agent system (MAS) in complex network has been developed rapidly in recent decades. Since most of the coordination control problem can be obtained from the extension and variation of the consensus theory, it is necessary to study on this issue. Although the consensus control methods of the first-order MAS are very mature, the theory of the second-order system is still need to be improved. In the engineering application, the model errors, external disturbance and parameter perturbation would probably make the system appear uncertain term and cause the final states of the system unable to achieve the consistency. In this paper, the problem of the consistency of the second-order MAS with uncertainties is studied by using methods of algebraic graph theory, matrix theory, adaptive control, neural network and other techniques. The two proposed control methods have the advantages of simple structure, small computation and easily applied to engineering. Moreover, the rationality and validity of the designed methods are verified by computer simulation experiments.