This paper proposes a novel nonlinear adaptive controller for the synchronization of two identical unknown chaotic systems. The proposed controller accomplishes fast convergence of the steady-state error to the origin and reduces the amplitude of the oscillations in the error signals during the transient. The rapid convergence increases the disturbance rejection attributes of the controller. The reduction in the oscillations’ magnitude decreases energy consumption and lowers the actuators’ degradation, reducing the probability of failure. This controller consists of linear adaptive and nonlinear control components, and they jointly synthesize control signals to penalize the synchronization error. The direct linear adaptive term keeps the closed-loop system stable; it ensures that the synchronization error converges to zero. The nonlinear terms heavily penalize the large state error vector in the transient, and its effect becomes minimal in the steady-state. The linear adaptive control is active in the steady-state, which synthesizes a smooth control signal in the vicinity of zero; this behavior causes oscillation free convergence of the error. Analysis based on the Lyapunov direct theorem proves the global asymptotic stabilization of the closed-loop at the origin. The paper also introduces parameters update laws that estimate the controller and unknown parameters of the master system and assure the convergence. This work also presents a comparative study of a numerical example of two identical Lorenz-Like unknown chaotic systems.

本文提出了一种新颖的非线性自适应控制器，用于同步两个相同的未知混沌系统。所提出的控制器实现了稳态误差到原点的快速收敛，并减小了瞬态期间误差信号中的振荡幅度。快速收敛增加了控制器的干扰抑制属性。振荡幅度的减小减少了能耗，并降低了执行器的性能下降，从而降低了故障的可能性。该控制器由线性自适应和非线性控制组件组成，它们共同合成控制信号以补偿同步误差。直接线性自适应项保持闭环系统稳定；它确保同步误差收敛到零。非线性项会严重破坏瞬态中的大状态误差向量，并且在稳态时其影响变得最小。线性自适应控制在稳态下处于活动状态，它在零附近合成一个平滑的控制信号。此行为导致误差的无振荡收敛。基于李雅普诺夫直接定理的分析证明了原点闭环的全局渐近稳定。本文还介绍了参数更新定律，以估计主系统的控制器和未知参数并确保收敛。这项工作还提出了对两个相同的Lorenz-Like未知混沌系统的数值示例的比较研究。线性自适应控制在稳态下处于活动状态，它在零附近合成一个平滑的控制信号。此行为导致误差的无振荡收敛。基于李雅普诺夫直接定理的分析证明了原点闭环的全局渐近稳定。本文还介绍了参数更新定律，以估计主系统的控制器和未知参数并确保收敛。这项工作还提出了对两个相同的Lorenz-Like未知混沌系统的数值示例的比较研究。线性自适应控制在稳态下处于活动状态，它在零附近合成一个平滑的控制信号。此行为导致误差的无振荡收敛。基于李雅普诺夫直接定理的分析证明了原点闭环的全局渐近稳定。本文还介绍了参数更新定律，这些定律估计了主系统的控制器和未知参数，并确保了收敛性。这项工作还提出了对两个相同的Lorenz-Like未知混沌系统的数值示例的比较研究。基于李雅普诺夫直接定理的分析证明了原点闭环的全局渐近稳定。本文还介绍了参数更新定律，以估计主系统的控制器和未知参数并确保收敛。这项工作还提出了对两个相同的Lorenz-Like未知混沌系统的数值示例的比较研究。基于李雅普诺夫直接定理的分析证明了原点闭环的全局渐近稳定。本文还介绍了参数更新定律，以估计主系统的控制器和未知参数并确保收敛。这项工作还提出了对两个相同的Lorenz-Like未知混沌系统的数值示例的比较研究。