Abstract
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.
Highlights
Chaos is a ubiquitous phenomenon in nonlinear system
We address a unified framework for adaptive control of time-dependent strict-feedback complexvariable chaotic (hyperchaotic) systems (CVCSs) with uncertain complex parameters and perturbations
Consider the Lyapunov function candidate defined on complex space in the form as
Summary
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 complexvariable chaotic (hyperchaotic) systems (CVCSs) in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. 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. 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. Numerical simulation is presented to validate our theoretical results. Data Availability Statement: All relevant data are within the paper.
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