Abstract
This paper mainly investigates the projection synchronization of complex chaotic systems with both uncertainty and disturbance. Using the linear feedback method and the uncertainty and disturbance estimation- (UDE-) based control method, the projection synchronization of such systems is realized by two steps. In the first step, a linear feedback controller is designed to control the nominal complex chaotic systems to achieve projection synchronization. An UDE-based controller is proposed to estimate the whole of uncertainty and disturbance in the second step. Finally, numerical simulations verify the feasibility and effectiveness of the control method.
Highlights
Using the linear feedback method and the uncertainty and disturbance estimation- (UDE-) based control method, the projection synchronization of such systems is realized by two steps
In case of projective synchronization, the master and the slave system can be synchronized up to a scaling factor and the scaling factor is a constant transformation between the driving and the response variables that can further increase the security of secure communication and the transmission speed of communication
The UDE-based linear feedback control method is proposed in two steps
Summary
Where X ∈ Rn is the state, F(X) (F1(X), · · · , Fn(X))T is a continuous Ul∗)T is the vector function, controller to be. Linear Feedback Control-Like Method for Chaos Projection Synchronization. Us, the linear feedback control method is very suitable to be adopted to solve the projective synchronization problem of a given nominal complex chaotic system (i.e., there is no both uncertainty and disturbance). Where Wm, Z, A(Z) are given in equations (4) and (5) and B1 ∈ Rs×r; the linear feedback controller is designed as follows:. Where x ∈ Rn is the state, ud Δf(x) + d(t) is the whole of model uncertainty and external disturbance, b ∈ Rn×k is a constant matrix, k ≥ 1, and u ∈ Rk is the controller to be designed.
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