Browsing by Subject "Delayed feedback system"

Now showing 1 - 6 of 6

Open Access
A new delayed feedback control scheme for discrete time chaotic systems
(IFAC, 2009) Morgül, Ömer
In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. We consider both one dimensional and higher dimensional cases. We propose a novel generalization of the classical delayed feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized with the proposed method. Although for higher order periods the proposed scheme may possess some limitations, some improvement over the classical delayed feedback scheme still can be achieved with the proposed scheme. The stability proofs also give the possible feedback gains which achieve stabilization. We will also present some simulation results.
Open Access
A new periodic controller for discrete time chaotic systems
(IFAC, 2010) Morgül, Ömer
In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. For simplicity we consider only one dimensional case. We propose a novel periodic feedback controller law and present some stability results. This scheme may be considered as a novel generalization of the classical delayed feedback scheme, which is also known as Pyragas scheme. The stability results show that all hyperbolic periodic orbits can be stabilized with the proposed method. The stability proofs also give the possible feedback gains which achieve stabilization. We will also present some simulation results.
Open Access
A nonlinear control scheme for discrete time chaotic systems
(The International Federation of Automatic Control, 2012-06) Morgül, Ömer
In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. We consider both one dimensional and higher dimensional cases. We propose a nonlinear feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized with the proposed method. By restricting the gain matrix to a special form we obtain some novel stability results. The stability proofs also give the possible feedback gains which achieve stabilization. We also present some simulation results.
Open Access
Stability of delayed feedback controllers for discrete time systems
(IEEE, 2003) Morgül, Ömer
We consider the delayed feedback control (DFC) scheme for one dimensional discrete time systems. To analyze the stability, we construct a map whose fixed points correspond to the periodic orbits of the system to be controlled. Then the stability of the DFC is equivalent to the stability of the corresponding equilibrium point of the constructed map.
Open Access
A stability result for delayed feedback controllers
(IEEE, 2003) Morgül, Ömer
We consider the delayed feedback control (DFC) scheme for one dimensional discrete time systems. To analyze the stability, we construct a map whose fixed points correspond to the periodic orbits of the system to be controlled. Then the stability of the DFC is equivalent to the stability of the corresponding equilibrium point of the constructed map. We obtain a formula for the characteristic polynomial of the Jacobian of this map. Then the Schur stability of this polynomial could be used to analyze the stability of DFC. We also present some simulation results.
Open Access
Stability results for some periodic feedback controllers
(IFAC, 2005) Morgül, Ömer
We propose two periodic feedback schemes for the stabilization of periodic orbits for one dimensional discrete time chaotic systems. These schemes can be generalized to higher dimensional systems in a straightforward way. We show that the proposed schemes achieve stabilization of a wide range of periodic orbits. The proposed schemes are quite simple and we show that any hyperbolic periodic orbit can be stabilized with these schemes. We also present some simulation results.