Fixed-Time Asymptotic Stability and Energy Consumption Estimation of Nonlinear Systems
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摘要: 讨论了非线性系统的固定时间渐近稳定性和能量消耗估计问题. 首先, 提出了一种新的具有非线性和时变时滞的动态模型. 其次, 为了有效提高系统的收敛速率, 采用了一种固定时间控制策略. 通过构建Lyapunov泛函, 以及使用不等式分析方法, 获得了误差系统达到固定时间渐近稳定的准则. 同时, 为了预测系统运行过程中的能量消耗, 估计了系统能量消耗的上界, 这有助于评估系统的运行时间. 最后, 通过一个数值例子进行了模拟实验, 验证了所得结果的可行性和有效性.Abstract: The fixed-time asymptotic stability and energy consumption estimation problems of nonlinear systems were discussed. First, a novel dynamic model with nonlinearity and time-varying delays was proposed. Second, to effectively improve the convergence rate of the system, a fixed-time control strategy was adopted. Through construction of the Lyapunov functional and with the inequality analysis method, sufficient conditions for the error system were obtained to achieve the fixed-time asymptotic stability. Moreover, to predict the energy consumption during the operation of the system, the upper bound of the energy consumption for the system was estimated, which is helpful to evaluate the operation time of the system. Finally, a numerical example was given to verify the feasibility and effectiveness of the results.
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