Unstable periodic orbits occur naturally in many nonlinear dynamical systems. They can generally not be be observed directly, but a number of control schemes have been suggested to stabilize them. One such scheme is that by Pyragas [35,36,40], which uses time-delayed feedback to target a specific unstable periodic orbit of a given period and stabilize it. This paper considers the global effect ...

Periodic sampling and control has been the dominating paradigm in computer-controlled systems since the 1950s. The periodic approach is very convenient, since it enables the system developer to base the analysis and design on standard sampled-data control theory real-time systems theory. While convenient, periodic control does not utilize the system resources in an optimum way. Sensor values an...

In this article, a finite horizon, multi product and multi period economic order quantity like seasonal items is considered where demand rate is deterministic and known but variable in each period. The order quantities of items come in batch sizes and the end of the period order quantity and, consequently, demand of customers are zero. In addition, storage space is constrained and the problem...

in the present paper the linear oscillator in r3 with z =constanthas been considered. the aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. a newapproach based on a computational method has been used. at the end weapply our method on an example.

Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we...

The history of the linear time-delayed and time-periodic oscillator demonstrates how stability theory has developed from the damped oscillator to the delayed Mathieu equation. Based on these results, it is a natural idea to apply time-periodic control gains when large time delay in the feedback loop tends to destabilize the system. By formulating the act-and-wait control concept as a special ca...

This paper presents a simple feed forward adaptive multi-periodic repetitive control scheme for the ASPR(Almost Strictly Positive Real) or ASNR(Almost Strictly Negative Real, See Appendix for definition) plant to asymptotically track/reject multi-periodic reference/disturbance signals. The lyapunov stability analysis is given. This is an extension work of the lyapunov stability analysis for mul...