[PDF]    http://dx.doi.org/10.3952/lithjphys.50301

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 50, 305–316 (2010)


MODIFICATION OF DELAYED FEEDBACK CONTROL USING ERGODICITY OF CHAOTIC SYSTEMS
V. Pyragas and K. Pyragas
Semiconductor Physics Institute, Center for Physical Sciences and Technology, A. Goštauto 11, LT-01108 Vilnius, Lithuania
E-mail: viktpy@pfi.lt, pyragas@kes0.pfi.lt

Received 17 March 2010; revised 8 June 2010; accepted 16 September 2010

We devise a modified delayed feedback control algorithm that allows one to stabilize unstable target states of chaotic systems for any initial conditions placed on a strange attractor. The algorithm is based on ergodicity of chaotic systems. We first let the chaotic system to evolve unperturbed until it approaches the neighbourhood of the target state. Then we activate the controller that stabilizes that target state. We propose a special algorithm that evaluates the closeness of the current state of the system to the target state. For continuous-time systems, this algorithm can be implemented by simple low-pass filters. We demonstrate the efficacy of our algorithm with numerical computations of statistics of successful stabilizations.
Keywords: chaos, dynamical systems, delayed feedback control, ergodicity
PACS: 05.45.Gg, 02.30.Yy, 02.30.Ks


UŽDELSTO GRĮŽTAMOJO RYŠIO VALDYMO MODIFIKACIJA PANAUDOJANT CHAOTINIŲ SISTEMŲ ERGODIŠKUMĄ
V. Pyragas, K. Pyragas
Fizinių ir technologijos mokslų centro Puslaidininkių fizikos institutas, Vilnius, Lietuva

Pasiūlėme modifikuotą uždelsto grįžtamojo ryšio valdymo algoritmą, kuris stabilizuoja nestabilias periodines orbitas bei rimties taškus, kai sprendinys startuoja iš bet kurių chaotinio atraktoriaus pradinių sąlygų. Algoritmas yra grindžiamas chaotinių sistemų ergodiškumu. Pirma leidžiame chaotinei sistemai evoliucionuoti laisvai tol, kol ji priartės prie norimos orbitos. Tuomet įjungiame valdiklį, kuris stabilizuoja norimą orbitą. Pasiūlėme algoritmą, kuris įvertina esamo sprendinio artumą norimai būsenai. Tolydžiosioms sistemoms šį algoritmą galima įdiegti paprastais žemų dažnių filtrais. Algoritmo veiksmingumą pademonstravome sėkmių statistikos skaitiniais skaičiavimais.

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