Open AccessAdaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations
Author(s) -
Jian Liu,
Kexin Liu,
Shutang Liu
Publication year - 2017
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0175730
Subject(s) - control theory (sociology) , complex system , adaptive control , nonlinear system , complex dynamics , scalar (mathematics) , class (philosophy) , lyapunov function , chaotic , stability theory , controller (irrigation) , computer science , complex space , mathematics , dynamical systems theory , control (management) , artificial intelligence , physics , mathematical analysis , pure mathematics , biology , geometry , quantum mechanics , affine transformation , agronomy
In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n -dimensional time-dependent strict-feedback complex-variable chaotic (hyperchaotic) systems (CVCSs) in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. In detail, we have developed a unified framework for designing the adaptive complex scalar controller to ensure this type of CVCSs asymptotically stable and for selecting complex update laws to estimate unknown complex parameters. In particular, combining Lyapunov functions dependent on complex-valued vectors and back-stepping technique, sufficient criteria on stabilization of CVCSs are derived in the sense of Wirtinger calculus in complex space. Finally, numerical simulation is presented to validate our theoretical results.