Static and adaptive feedback control for synchronization of different chaotic oscillators with mutually Lipschitz nonlinearities

This paper addresses the control law design for synchronization of two different chaotic oscillators with mutually Lipschitz nonlinearities. For analysis of the properties of two different nonlinearities, an advanced mutually Lipschitz condition is proposed. This mutually Lipschitz condition is more general than the traditional Lipschitz condition. Unlike the latter, it can be used for the design of a feedback controller for synchronization of chaotic oscillators of different dynamics. It is shown that any two different Lipschitz nonlinearities always satisfy the mutually Lipschitz condition. Applying the mutually Lipschitz condition, a quadratic Lyapunov function and uniformly ultimately bounded stability, easily designable and implementable robust control strategies utilizing algebraic Riccati equation and linear matrix inequalities, are derived for synchronization of two distinct chaotic oscillators. Furthermore, a novel adaptive control scheme for mutually Lipschitz chaotic systems is established by addressing the issue of adaptive cancellation of unknown mismatch between the dynamics of different chaotic systems. The proposed control technique is numerically tested for synchronization of two different chaotic Chua＇s circuits and for obtaining identical behavior between the modified Chua＇s circuit and the R6ssler system.

Robust leaderless time-varying formation control for unmanned aerial vehicle swarm system with Lipschitz nonlinear dynamics and directed switching topologies

This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topologies.In comparison with the previous achievements on formation control problems,the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances.Firstly,by applying the consensus theory,a TVF controller is developed with the local neighborhood status information,the errors of real time status of all UAVs,the expected formation configuration and the pre-given trajectory under directed switching topologies.Secondly,through a certain matrix variable substitution,the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue.Thirdly,by introducing the minimum dwell time,the design steps of formation control algorithm are further acquired.In the meantime,the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities(LMIs)method.Finally,the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.

Event-triggered dynamic output-feedback control for a class of Lipschitz nonlinear systems

This paper investigates the problem of dynamic output-feedback control for a class of Lipschitz nonlinear systems.First,a continuous-time controller is constructed and sufficient conditions for stability of the nonlinear systems are presented.Then,a novel event-triggered mechanism is proposed for the Lipschitz nonlinear systems in which new event-triggered conditions are introduced.Consequently,a closed-loop hybrid system is obtained using the event-triggered control strategy.Sufficient conditions for stability of the closed-loop system are established in the framework of hybrid systems.In addition,an upper bound of a minimum inter-event interval is provided to avoid the Zeno phenomenon.Finally,numerical examples of a neural network system and a genetic regulatory network system are provided to verify the theoretical results and to show the superiority of the proposed method.

Reference tracking and transient response shaping of uncertain quasi one-sided Lipschitz nonlinear systems

This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.

Simultaneous state and actuator fault estimation for satellite attitude control systems

In this paper, a new nonlinear augmented observer is proposed and applied to satellite attitude control systems. The observer can estimate system state and actuator fault simultaneously. It can enhance the performances of rapidly-varying faults estimation. Only original system matrices are adopted in the parameter design. The considered faults can be unbounded, and the proposed augmented observer can estimate a large class of faults. Systems without disturbances and the fault whose finite times derivatives are zero piecewise are initially considered, followed by a discussion of a general situation where the system is subject to disturbances and the finite times derivatives of the faults are not null but bounded. For the considered nonlinear system, convergence conditions of the observer are provided and the stability analysis is performed using Lyapunov direct method. Then a feasible algorithm is explored to compute the observer parameters using linear matrix inequalities （LMIs）. Finally, the effectiveness of the proposed approach is illustrated by considering an example of a closed-loop satellite attitude control system. The mance in estimating states and actuator faults. It also successfully. simulation results show satisfactory perfor- shows that multiple faults can be estimated