Passivity-Based Adaptive Hybrid Synchronization of a New Hyperchaotic System with Uncertain Parameters

Abstract

We investigate the adaptive hybrid synchronization problem for a new hyperchaotic system with uncertain parameters. Based on the passivity theory and the adaptive control theory, corresponding controllers and parameter estimation update laws are proposed to achieve hybrid synchronization between two identical uncertain hyperchaotic systems with different initial values, respectively. Numerical simulation indicates that the presented methods work effectively.

Perturbation observer-based adaptive passive control for nonlinear systems with uncertainties and disturbances

“…Remark 4. Compared with the conventional APC (Bobtsov et al, 2014; Mermoud et al, 2001; Zhou et al, 2012), which can only estimate the linearly parametric uncertainties, the POAPC can be regarded as a nonlinearly functional estimation method, as it can estimate the combinatorial effect of unknown parameters, unmodelled dynamics and fast time-varying external disturbances. If there are no uncertainties or fast time-varying external disturbances, and if an accurate system model is available, it can provide the same performance as that of the exact passive controller.…”

“…To handle the parameter uncertainty, an adaptive passive control (APC) was proposed (Bobtsov et al, 2014; Mermoud et al, 2001; Zhou et al, 2012), in which an uncertain nonlinear system was assumed to have explicit linearly parametric uncertainties, and then a linearly parametric estimation-based adaptation law was developed to approximate these unknown parameters. However, these laws might not be trivial and the resulting adaptive system is highly nonlinear, with slow system responses to parameter variations.…”

Theoretical Analysis and Adaptive Synchronization of a 4D Hyperchaotic Oscillator

“…or may be time varying and/or inaccessible to direct measurements. Therefore, the synchronization of two uncertain chaotic systems is essential [37][38][39][40][41][42].…”