OPTIMAL SEARCH FOR NONLINEAR DISCRETE SYSTEMS CYCLES

Abstract

We consider a classical problem of stabilization of a priori unknown unstable periodic orbits in nonlinear autonomous discrete dynamical systems. A new approach was suggested in [11], where a nonlinear delay feedback control (DFC) scheme with apparently optimal gain was introduced. The optimality criteria in [11] were stated in terms of the size of the convergence region for the system multipliers. In numerical simulations it turns out that the optimal coefficients (in the above sense) produce slowly convergent recurrences. In this paper we suggest a generalization of the formulas from [11] to improve the rate of convergence while preserving stability. The subtlety of the problem is illustrated in numerous numerical simulations examples. AMS Subject Classification: 93C10, 93C55 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 14, 2018. doi: 10.12732/caa.v22i4.11 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa 664 D. DMITRISHIN, E. FRANZHEVA, I.E. IACOB, AND A. STOKOLOS