This article discusses the state estimation issue for a type of delayed neural networks (NNs). The investigated NN systems are assumed to face adversarial threats which posed on the data propagation process. Also, the information transmission delays between the sensor and estimator are taken into consideration. Moreover, with hope to better characterize the real-world situations, a constraint is posed on the measurement output by using a saturation function. The purpose of this article is to provide a framework for estimation of the state of NNs, ensuring that the estimation error is enforced not to escape a specific range in probability not less than a predetermined value. With the hope to coordinate the information propagation, the so-called Round-Robin protocol is used in the signal transmission channel. The main results are obtained by virtue of convex optimization algorithms, where the requested estimator parameters can be computed by solving the provided inequalities. On basis of the acquired main results, we further proceed to seek the locally optimal parameters according to different engineering demands. At last, the main theoretical results as well as the design method are demonstrated via an example.
- Open Access
- Article
Protocol-Based State Estimation for a Type of Delayed Neural Networks Subject to Probability Constraint
- Juanjuan Yang 1,
- Lifeng Ma 1,*,
- Yonggang Chen 2,
- Xiaojian Yi 3,4
Author Information
Received: 02 Feb 2026 | Revised: 15 Apr 2026 | Accepted: 11 May 2026 | Published: 11 Jun 2026
Abstract
Keywords
delayed neural networks | sensor saturations | probability constraint | deception attacks | Round- Robin protocol
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