This study is concerned with robust synchronization for master–slave chaotic systems with matched/mismatched disturbances and uncertainty in the control input. A robust sliding mode control (SMC) is presented to achieve chaos synchronization even under the influence of matched/mismatched disturbances and uncertainty of inputs. A proportional-integral (PI) switching surface is introduced to make the controlled error dynamics in the sliding manifold easy to analyze. Furthermore, by using the proposed SMC scheme even subjected to input uncertainty, we can force the trajectories of the error dynamics to enter the sliding manifold and fully synchronize the master–slave systems in spite of matched uncertainties and input nonlinearity. As for the mismatched disturbances, the bounds of synchronization errors can be well estimated by introducing the limit of the Riemann sum, which is not well addressed in previous works. Simulation experiments including matched and mismatched cases are presented to illustrate the robustness and synchronization performance with the proposed SMC synchronization controller.

中文翻译：

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具有匹配/不匹配干扰和输入不确定度的主从混沌系统之间的同步误差估计

这项研究涉及具有匹配/不匹配干扰和控制输入不确定性的主从混沌系统的鲁棒同步。提出了鲁棒滑模控制（SMC），即使在匹配/不匹配干扰和输入不确定性的影响下也能实现混沌同步。引入比例积分（PI）切换表面以使滑动歧管中的受控误差动态易于分析。此外，即使在输入不确定性和输入非线性都匹配的情况下，通过使用所提出的SMC方案即使在输入不确定的情况下，我们也可以迫使误差动力学的轨迹进入滑动歧管，并使主-从系统完全同步。至于不匹配的干扰 通过引入黎曼和的极限可以很好地估计同步误差的范围，而在先前的工作中并没有很好地解决这个问题。提出了包括匹配和不匹配情况的仿真实验，以说明所提出的SMC同步控制器的鲁棒性和同步性能。