基于事件触发和量化的非线性系统稳定性研究

Research on Stability of Nonlinear Systems Based on Event Triggering and Quantization

针对非线性系统的数据采样稳定性问题,文中设计了基于事件触发机制和数据量化机制的神经网络控制器。采样器时刻监测非线性系统,采样信号经事件触发机制检测,满足阈值后由量化器量化传入控制器,经所设计的控制器输出反馈给非线性系统。为降低系统保守性,选取了新颖的分段Lyapunov-Krasovskii泛函,针对系统中所包含的传输时滞,采用时滞分析法将同步控制器求解问题转化为所对应时滞系统的稳定性问题,并结合Jensen不等式,给出了非线性系统稳定性条件。最后通过数值仿真验证了所提出方法的有效性。

In this paper,based on the data sampling stability problem of nonlinear systems,a neural network controller based on event triggering mechanism and data quantization mechanism was designed.The sampler monitored the nonlinear system at any time,and the sampled signal was detected by the event trigger mechanism.After the threshold was satisfied,the quantizer was used to quantize the incoming controller,and the designed controller output the feedback and the nonlinear system.In order to reduce the conservativeness of the system,a novel piecewise Lyapunov-Krasovskii functional was selected.For the transmission time delay contained in the system,the time delay analysis method was used to transform the solving problem of the synchronous controller into the stability problem of the corresponding time-delay system.Combined with Jensen's inequality,the stability conditions of nonlinear systems were given.Finally,the effectiveness of the proposed method was verified by numerical simulation.