This paper is concerned with the protocol-based finite-horizon $H_{\infty }$ estimation problem for discrete-time memristive neural networks (MNNs) subject to time-delays and energy-bounded disturbances. With the purpose of effectively alleviating data collisions and saving energy, the stochastic communication protocol (SCP) is adopted to regulate the data transmission procedure in the sensor-to-estimator communication channel, thereby avoiding unnecessary network congestion. It is our objective to construct an $H_{\infty }$ estimator ensuring a prescribed disturbance attenuation level over a finite time-horizon for the delayed MNNs under the SCP. By virtue of the Lyapunov-Krasovskii functional in combination with stochastic analysis methods, the delay-dependent criteria are established that guarantee the existence of the desired $H_{\infty }$ estimator. Subsequently, the estimator gains are computed by resorting to solve a bank of convex optimization problems. Finally, the validity of the designed $H_{\infty }$ estimator is demonstrated via a numerical example.

本文涉及基于协议的有限水平 $H_{\infty }$时滞和能量受限扰动的离散时间忆阻神经网络（MNN）的估计问题。为了有效减轻数据冲突并节约能源，采用随机通信协议（SCP）来规范传感器到估计器通信信道中的数据传输过程，从而避免了不必要的网络拥塞。我们的目标是构建一个$H_{\infty }$估计器可确保在SCP之下的延迟MNN在有限的时间范围内达到规定的干扰衰减水平。借助Lyapunov-Krasovskii函数与随机分析方法的组合，建立了依赖于延迟的标准，以保证所需目标的存在$H_{\infty }$估算器。随后，通过求助于解决一组凸优化问题来计算估计器增益。最后，设计的有效性$H_{\infty }$ 通过一个数值示例来说明估计量。