A dynamic controller, based on the Stability Transformation Method (STM), has been used to stabilize unknown and unstable periodic orbits (UPOs) in dynamical systems. An advantage of the control method is that it can stabilize unknown UPOs. In this study, we introduce a novel control method, based on STM, to stabilize UPOs in DC-DC switching power converters. The idea of the proposed method is to apply temporal perturbations to the switching time. These perturbations are calculated without information of the locations of the target orbits. The effectiveness of the proposed method is verified by numerical simulations and laboratory measurements.

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.

In this paper, we consider a stabilization problem for the cart-pendulum system based on discrete mechanics, which is known as a good discretizing method for mechanical systems and has not been really applied to control theory. First, the continuous and discrete cart-pendulum systems are explained. We next propose a transformation method that converts a discrete-time input derived from the discrete-time optimal regulator theory into a continuous-time zero-order hold input, and carry out some simulations on stabilization of the cart-pendulum system by the transformation method. Then, we apply not only our proposed method but also existing methods to an experimental laboratory of the cart-pendulum system and perform some experiments in order to verify the availability of the proposed method.