We consider an improved control method based on the Stability Transformation Method. Stability Transformation Method detects unknown and unstable periodic orbits of chaotic dynamical systems. Based on the approach to realize the Stability Transformation Method in real systems, we have proposed a control method which can stabilize unknown and unstable periodic orbits embedded in chaotic attractors. However, setting of the control parameters of the control system has remained as unsolved issue. When the dynamics of a target system are unknown, the control parameters have to be set by trial and error. In this paper, we improve the control method with the automatic adjustment function of the control parameters. We show an example of stabilizing unstable periodic orbits of the 3-dimensional hysteresis chaos generator by using the proposed control method. Some results are confirmed by laboratory measurements. The results imply that any unknown and unstable periodic orbits can be stabilized by using the proposed method, if the target chaos system is reduced to 1-dimensional return map.

A chaotic neural network consisting of chaotic neurons exhibits such rich dynamical behaviors as nonperiodic associative memory. But it is difficult to distinguish the stored patterns from others, since the chaotic neural network shows chaotic wandering around the stored patterns. In order to apply the nonperiodic associative memory to information search or pattern identification, it is necessary to control chaotic dynamics. In this paper, we propose a delay feedback control method for the chaotic neural network. Computer simulation shows that, by means of the control method, the chaotic dynamics in the chaotic neural network are changed. The output sequence of the controlled network wanders around one stored pattern and its reverse pattern.

This letter proposes a pulse width modulated (PWM) control method which can stabilize chaotic orbits onto unstable fixed points and unstable periodic orbits. Some numerical experiments using the Lorenz equation show that chaotic orbits can be stabilized by the PWM control method. Furthermore, we investigate the stability in the neighborhood of an unstable fixed point and discuss the stability condition of the PWM control method.

The pendulum equation with a periodic impulsive force is investigated. This model described by a second order differential equation is also derived from dynamics of the stepping motor. In this paper, firstly, we analyze bifurcation phenomena of periodic solutions observed in a generalized pendulum equation with a periodic impulsive force. There exist two topologically different kinds of solution which can be chaotic by changing system parameters. We try to stabilize an unstable periodic orbit embedded in the chaotic attractor by small perturbations for the parameters. Secondly, we investigate the intermittent drive characteristics of two-phase hybrid stepping motor. We suggest that the unstable operations called pull-out are caused by bifurcations. Finally, we proposed a control method to avoid the pull-out by changing the repetitive frequency and stepping rate.

We propose a stabilization method of unstable periodic orbits embedded in a chaotic attractor of continuous-time system by using discrete state feedback controller. The controller is designed systematically by the Poincar mapping and its derivatives. Although the output of the controller is applied periodically to system parameter as small perturbations discontinuously, the controlled orbit accomplishes C0. As the stability of a specific orbit is completely determined by the design of controller, we can also use the method to destabilize a stable periodic orbit. The destabilization method may be effectively applied to escape from a local minimum in various optimization problems. As an example of the stabilization and destabilization, some numerical results of Duffing's equation are illustrated.

In this letter a new method for controlling chaos is proposed. Although different several methods based on the OGY- and the OPF-method perturb a value of an accessible system parameter, the proposed method perturbs the only timing of switching three values of a parameter. We apply the proposed method to the well-known Chua's circuit on computer simulations. The chaotic orbits in the Rössler type- and the double scroll type-attractor can be stabilized on several unstable periodic orbits embedded within these attractors.

A laser system which has a mirror outside of it to feedback a delayed output has been described by the Maxwell-Bloch equations with time delay. It is shown that a chaotic behavior in the equations can be controlled by using a OPF control algorithm. Our numerical simulation indicates that the chaotic behavior is stabilized on 1, 2 periodic unstable orbits.