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<p>In this paper, for time-delayed reaction–diffusion neural networks (TDRDNNs) with matched and unmatched disturbances, we propose a backstepping-based mixed boundary control strategy integrating higher-order sliding mode control (HOSMC) and an observer via spatiotemporal sampled data (STSD). First, in the sensor network, the STSD strategy is employed to obtain the information of neurons, which facilitates our design of observer errors. Matched and unmatched disturbances consistently affect the observer’s fit to the original TDRDNNs, at which point we devise HOSMC algorithm to counteract the effects of disturbances. Subsequently, it is shown that the estimation error is input-to-state stable (ISS), which means that the observer effectively predicts the state of the neurons in spacetime even though there are ineradicable perturbations in the original TDRDNNs. Secondly, we construct an explicit expression for the boundary controller using the backstepping in conjunction with the STSD and HOSMC algorithm after mapping the observer to the target systems. In this process, our designed control scheme effectively attenuates the disturbances of the TDRDNNs. Further, using this controller and some inequality tools, the ISS of the closed-loop TDRDNNs is demonstrated. Finally, the effectiveness of the control strategy is verified by numerical simulation, and it can be seen from the comparison experiments that TDRDNNs produce less jitter under our controller.</p>

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Observer-based input-to-state stabilization for coupled reaction–diffusion neural networks with disturbances via spatiotemporal sampled measurements and sliding mode control

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Juan Chen,
  • Yuwei Xue,
  • Chenlong Zhang,
  • Yingying Jiao

摘要

In this paper, for time-delayed reaction–diffusion neural networks (TDRDNNs) with matched and unmatched disturbances, we propose a backstepping-based mixed boundary control strategy integrating higher-order sliding mode control (HOSMC) and an observer via spatiotemporal sampled data (STSD). First, in the sensor network, the STSD strategy is employed to obtain the information of neurons, which facilitates our design of observer errors. Matched and unmatched disturbances consistently affect the observer’s fit to the original TDRDNNs, at which point we devise HOSMC algorithm to counteract the effects of disturbances. Subsequently, it is shown that the estimation error is input-to-state stable (ISS), which means that the observer effectively predicts the state of the neurons in spacetime even though there are ineradicable perturbations in the original TDRDNNs. Secondly, we construct an explicit expression for the boundary controller using the backstepping in conjunction with the STSD and HOSMC algorithm after mapping the observer to the target systems. In this process, our designed control scheme effectively attenuates the disturbances of the TDRDNNs. Further, using this controller and some inequality tools, the ISS of the closed-loop TDRDNNs is demonstrated. Finally, the effectiveness of the control strategy is verified by numerical simulation, and it can be seen from the comparison experiments that TDRDNNs produce less jitter under our controller.