IEEE Trans Neural Netw Learn Syst. 2016 Jan;27(1):151-64. doi: 10.1109/TNNLS.2015.2472290. Epub 2015 Oct 26.
This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain nonlinear discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.
本文提出了一种新的自适应神经网络（NN）控制方案，用于在事件采样 NN 输入下的单输入单输出不确定非线性离散时间系统。在这种控制方案中，反馈信号以非周期性方式在事件采样时刻传输，并调整 NN 权重。在回顾了具有事件采样输入的 NN 逼近特性之后，利用由线性参数化神经网络组成的自适应状态估计器（SE）在事件采样环境中近似未知系统动态。SE 被视为模型，并且其在任何两个事件期间的近似动态和状态向量被用于事件触发控制器设计。通过使用估计的 NN 权重和死区运算符来导出自适应事件触发条件，以确定事件采样时刻。该条件既有利于 NN 逼近，又减少了反馈信号的传输。通过 Lyapunov 方法证明了 NN 权重估计误差和系统状态向量的最终有界性。如预期的那样，在初始在线学习阶段，事件观察得更频繁。随着 NN 权重的收敛，事件之间的时间增加，从而减少了触发事件的数量。这些主张通过仿真结果得到了说明。
