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Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization. According to the Jacobian matrix of the nonlinear system, the stabilization control region is gotten. The controller is designed to stabilize fast the minimum phase Lorenz-Chen chaotic system after equivalently transforming from chaotic system to passive system. The simulation results show that the system not only can be controlled at the different equilibria, but also can be transformed between the different chaotic attractors. 相似文献
2.
An adaptive passive strategy for controlling uncertain
L\"{u} system is proposed. Since the uncertain L\"{u} system is minimum
phase and the uncertain parameters are from a bounded compact set, the
essential conditions are studied by which uncertain L\"{u} system could be
equivalent to a passive system, and the adaptive control law is given. Using
passive theory, the uncertain L\"{u} system could be globally asymptotically
stabilized at different equilibria by the smooth state feedback. 相似文献
3.
In this paper we present a new simple controller for a chaotic system, that is, the
Newton--Leipnik equation with two strange attractors: the upper attractor (UA) and
the lower attractor (LA). The controller design is based on the passive technique.
The final structure of this controller for original stabilization has a simple
nonlinear feedback form. Using a passive method, we prove the stability of a
closed-loop system. Based on the controller derived from the passive principle, we
investigate three different kinds of chaotic control of the system, separately: the
original control forcing the chaotic motion to settle down to the origin from an
arbitrary position of the phase space; the chaotic intra-attractor control for
stabilizing the equilibrium points only belonging to the upper chaotic attractor or
the lower chaotic one, and the inter-attractor control for compelling the chaotic
oscillation from one basin to another one. Both theoretical analysis and simulation
results verify the validity of the suggested method. 相似文献
4.
The stability control of fractional order unified chaotic system with sliding mode control theory
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This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts: the continuous part and switching part. With Gronwall’s inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method. 相似文献
5.
Comparison between two different sliding mode controllers for a fractional-order unified chaotic system
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Two different sliding mode controllers for a fractional order unified chaotic system are presented. The controller for an integer-order unified chaotic system is substituted directly into the fractional-order counterpart system, and the fractional-order system can be made asymptotically stable by this controller. By proving the existence of a sliding manifold containing fractional integral, the controller for a fractional-order system is obtained, which can stabilize it. A comparison between these different methods shows that the performance of a sliding mode controller with a fractional integral is more robust than the other for controlling a fractional order unified chaotic system. 相似文献
6.
This paper studies the stability of the fractional order
unified chaotic system. On the unstable equilibrium points, the
``equivalent passivity' method is used to design the nonlinear
controller. With the definition of fractional derivatives and
integrals, the Lyapunov function is constructed by which it is
proved that the controlled fractional order system is stable. With
Laplace transform theory, the equivalent integer order state
equation from the fractional order nonlinear system is obtained, and the
system output can be solved. The simulation results validate the
effectiveness of the theory. 相似文献
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