In this paper,some kinds of linear and nonlinear tracking-differentiators are designed by using suitable exponent functions instead of switch functions,and the stability of these tracking-differentiators is proved.Fro...In this paper,some kinds of linear and nonlinear tracking-differentiators are designed by using suitable exponent functions instead of switch functions,and the stability of these tracking-differentiators is proved.From the result of simulations,it is manifest that the tracking speeds of these kinds of linear and nonlinear tracking-differentiators are very high,and their design procedures are simple.展开更多
A modified tracking differentiator is proposed. Firstly, a nonlinear odd exponent continuous function is adopted which is only stable at one equilibrium point and proved the global asymptotic stability of the modified...A modified tracking differentiator is proposed. Firstly, a nonlinear odd exponent continuous function is adopted which is only stable at one equilibrium point and proved the global asymptotic stability of the modified tracking differentiator by select a Lyapunov function. Through combining of the nonlinear and linear function properly, it can be sure that the state converges to the equilibrium point with high speed automatically no matter that the state was far away from the equilibrium point or near to it, and it can prevent the chattering.?Simulation results show that the modified tracking differentiator tracking results?are?superior to the classical nonlinear tracking differentiator, and the response?of state variables tracking differentiator estimated?is?almost coincide with the real state of the variables of the given system.展开更多
In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable...In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable coefficient nonlinear ordinary differential equation. Consequently the model of the chaotic system is obtained. Then a fuzzy tracking control and a fuzzy synchronization for chaotic systems is proposed as well. First, a known tracking control for the Rossler’s system is used in this paper. We represent the Rossler’s chaotic and control systems into fuzzy inference rules. Then the variable coefficient nonlinear ordinary differential equation is also got. Simulation results show that such an approach is effective and has a high precision.展开更多
The collective formation control problem of a cluster of rotorcraft unmanned aerial vehicles(UAVs)is investigated in this article.The consensus tracking towards formation centroid with following UAVs forming a predefi...The collective formation control problem of a cluster of rotorcraft unmanned aerial vehicles(UAVs)is investigated in this article.The consensus tracking towards formation centroid with following UAVs forming a predefined configuration around the leader is considered as the objective.Unlike prior studies,the information of the central reference trajectory,which is deemed as a virtual leader in the leader-follower topology,is not directly accessible for partial nodes through the communication network.Therefore,a novel distributed formation tracking control scheme is promoted.Besides,a decentralized saturation observer is employed to estimate the reference acceleration signal of the virtual leader.In the absence of linear velocity measurement,two sliding manifolds are proposed by introducing the relative discrepancy terms of position and velocity.Then a smooth saturation operator in the form of a sigmoid function is applied to generate the command force input.Moreover,under the dilemma of constrained capabilities of the airborne sensors equipped on the rotorcrafts,the angular velocity is difficult to acquire.Two cascaded auxiliary attitude error systems are established on each rotorcraft system to synthesize the rotating torque with no need to require the angular velocity measurement.Due to the strong coupling and nonlinearity of the rotorcraft UAV system,the command angular velocity and the derivatives of command input are hard to obtain.Then a continuous nonlinear differentiator is proposed to work with the difficulties in deriving the explicit expression of system derivatives.Thereafter,a detailed stability analysis is conducted progressively on the angular control loop,reference trajectory observer loop,and the position control loop.A simulation scheme for a cluster of four rotorcraft UAVs tracking sinusoidal trajectory are presented and the formation control results are proven advantageous in comparison with the control protocol in previous literature.展开更多
基金Supported by the National Natural Science Foundation of China (6 0 1 740 2 1 ) and Tianjin Key NaturalScience Foundation(0 1 3 80 0 71 1 )
文摘In this paper,some kinds of linear and nonlinear tracking-differentiators are designed by using suitable exponent functions instead of switch functions,and the stability of these tracking-differentiators is proved.From the result of simulations,it is manifest that the tracking speeds of these kinds of linear and nonlinear tracking-differentiators are very high,and their design procedures are simple.
文摘A modified tracking differentiator is proposed. Firstly, a nonlinear odd exponent continuous function is adopted which is only stable at one equilibrium point and proved the global asymptotic stability of the modified tracking differentiator by select a Lyapunov function. Through combining of the nonlinear and linear function properly, it can be sure that the state converges to the equilibrium point with high speed automatically no matter that the state was far away from the equilibrium point or near to it, and it can prevent the chattering.?Simulation results show that the modified tracking differentiator tracking results?are?superior to the classical nonlinear tracking differentiator, and the response?of state variables tracking differentiator estimated?is?almost coincide with the real state of the variables of the given system.
文摘In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable coefficient nonlinear ordinary differential equation. Consequently the model of the chaotic system is obtained. Then a fuzzy tracking control and a fuzzy synchronization for chaotic systems is proposed as well. First, a known tracking control for the Rossler’s system is used in this paper. We represent the Rossler’s chaotic and control systems into fuzzy inference rules. Then the variable coefficient nonlinear ordinary differential equation is also got. Simulation results show that such an approach is effective and has a high precision.
基金supported by the National Natural Science Foundation of China(Grant Nos.62350048 and U20B2071)。
文摘The collective formation control problem of a cluster of rotorcraft unmanned aerial vehicles(UAVs)is investigated in this article.The consensus tracking towards formation centroid with following UAVs forming a predefined configuration around the leader is considered as the objective.Unlike prior studies,the information of the central reference trajectory,which is deemed as a virtual leader in the leader-follower topology,is not directly accessible for partial nodes through the communication network.Therefore,a novel distributed formation tracking control scheme is promoted.Besides,a decentralized saturation observer is employed to estimate the reference acceleration signal of the virtual leader.In the absence of linear velocity measurement,two sliding manifolds are proposed by introducing the relative discrepancy terms of position and velocity.Then a smooth saturation operator in the form of a sigmoid function is applied to generate the command force input.Moreover,under the dilemma of constrained capabilities of the airborne sensors equipped on the rotorcrafts,the angular velocity is difficult to acquire.Two cascaded auxiliary attitude error systems are established on each rotorcraft system to synthesize the rotating torque with no need to require the angular velocity measurement.Due to the strong coupling and nonlinearity of the rotorcraft UAV system,the command angular velocity and the derivatives of command input are hard to obtain.Then a continuous nonlinear differentiator is proposed to work with the difficulties in deriving the explicit expression of system derivatives.Thereafter,a detailed stability analysis is conducted progressively on the angular control loop,reference trajectory observer loop,and the position control loop.A simulation scheme for a cluster of four rotorcraft UAVs tracking sinusoidal trajectory are presented and the formation control results are proven advantageous in comparison with the control protocol in previous literature.
