Abstract
This article designs and synthesizes a new Lyapunov-based robust direct-adaptive controller (RDAC) and investigates the control and synchronization of chaos in the nuclear spin generator chaotic (NSGC) system. The inevitable time-varying external disturbances and model uncertainties perturb the NSGC system. The nonlinear terms, external disturbances, model uncertainties, and plant's parameters are unknown and bounded. Avoiding the cancelation of the nonlinear terms of the plant by the controller makes the closed-loop robust stable in the presence of unknown parametric uncertainties; this concept blooms base for efficient control law design. The proposed RDAC eradicates the effects of the time-varying unknwon external disturbances and model uncertainties and accomplishes quick and smooth convergence of the state varaible (error vector) trajectories to the origin with reduced oscillations. Based on the Lyapunov function principle, the article describes a detailed analysis of the closed-loop stability. It provides suitable adaptive laws that estimate the upper bound of unknown controller parameters, external disturbances, and model uncertainties. The computer simulation results endorse the theoretical analysis, and the comparative study highlights the benefits.
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