Title: Optimisation of the synchronisation of a class of chaotic systems: combination of sliding mode and feedback control

Authors: Michaux Kountchou; Patrick Louodop; Samuel Bowong; Hilaire Fotsin

Addresses: Department of Physics, Laboratory of Electronics and Signal Processing, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon; Nuclear Technology Section, Institute of Geological and Mining Research, P.O. Box 4110, Yaounde, Cameroon ' Department of Physics, Laboratory of Electronics and Signal Processing, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon ' Department of Mathematics and Computer Science, Laboratory of Applied Mathematics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon ' Department of Physics, Laboratory of Electronics and Signal Processing, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon

Abstract: This paper addresses the problem of optimisation of the synchronisation for a class of uncertain chaotic systems from a control theoretic point of view. A robust adaptive feedback which accomplishes the synchronisation of chaotic systems using an optimal tuning scheme based on Riccatti equations is successfully adapted. The underlying idea is to optimise the synchronisation of chaotic systems by accounting the control effort despite the uncertainties. The approach developed considers incomplete state measurements and no detailed model of the systems to guarantee robust stability. This approach includes a high-order sliding mode estimator and leads to a robust adaptive feedback control scheme. A finite horizon can be arbitrarily established by ensuring that the chaos synchronisation is achieved at established time. An advantage is that the studied scheme accounts the energy wasted by the controller and the closed-loop performance on synchronisation. Both mathematic proof and numerical simulations are presented o show the feasibility of the optimisation strategy for establishing the synchronisation of chaotic systems even if there are some modelling mismatches and parametric variations.

Keywords: chaos synchronisation; optimal feedback control; Ricatti equation.

DOI: 10.1504/IJNDC.2017.083628

International Journal of Nonlinear Dynamics and Control, 2017 Vol.1 No.1, pp.51 - 77

Received: 28 Jan 2015
Accepted: 19 Oct 2015
Published online: 13 Apr 2017 *