The presence of uncertainty and disturbance can lead to asymmetric control of nonlinear systems, and this asymmetric control can lead to a decrease in the productivity of the engineered system. In order to improve the control speed of the improved nonlinear system, complete synchronization and partial anti-synchronization of complex Lü chaotic systems with uncertainty and disturbance are investigated in the present paper. First, a new UDE-based dynamic feedback control method is proposed for the complete synchronization problem of the system. The method unites the dynamic gain feedback control method and the uncertainty and perturbation estimator (UDE) control method, where the dynamic gain feedback controller is used to achieve asymptotic stability of the nominal system and the UDE controller is used to handle a given controlled system with uncertainty and disturbance. Second, for the partial desynchronization problem of this system, a new UDE-based linear-like feedback control method is proposed, which consists of two controllers: a linear-like feedback controller used to achieve the asymptotic stabilization of the nominal system and the other UDE controller is designed to handle the given controlled system with uncertainty and disturbance. Finally, numerical simulations are performed to verify the correctness and stability of the theoretical results.

This paper introduces the working principle of the underwater spherical detection robot BYSQ-3. Through the known kinematics and dynamic models of the underwater spherical robot, using the combination of dynamic feedback gain control and UDE control, several designs are designed. The simple physical controller realizes the stabilization control of the system, and ensures that the whole system can achieve global asymptotic stability quickly. It is simpler and simpler than the traditional nonlinear control method, and the simulation results show that the correctness and effectiveness of the theory are verified.

The projection synchronization issue of complex Lü chaotic systems is examined in this work. Firstly, the system is presented, the complex chaotic system is transformed into the equivalent real number system, on this basis, the existence of the projection synchronization problem is proved and solution is obtained by an algorithm. Secondly, combines feedback controller and uncertainty and disturbance estimator (UDE), where one is used to implement the projection synchronization of nominal complex chaotic systems and the UDE controller is used to remove uncertainty and disturbance. Finally, the validity of the proposed results is proved by numerical simulation.

This paper mainly studies the partial anti-synchronization of laser hyperchaos system. First, transform complex systems into real systems. Secondly, in order to realize the full synchronization and partial anti synchronization of the system, the dynamic gain feedback control method and the dynamic feedback method based on uncertainty and disturbance estimator (UDE) are used to design simple and physically feasible controllers respectively. Finally, through MATLAB numerical simulation, it is proved that the error system is asymptotically stable, and the master-slave system realizes partial anti synchronization.