Chance-Constrained H∞ State Estimation for Recursive Neural Networks Under Deception Attacks and Energy Constraints: The Finite-Horizon Case

In this article, the chance-constrained H_{\infty } state estimation problem is investigated for a class of time-varying neural networks subject to measurements degradation and randomly occurring deception attacks. A novel energy-constrained deception attack model is proposed, in which both the occurrence of the attack and the selection of released faked packet are random and the energy of the deception attack is introduced, calculated, and analyzed quantitatively. The main purpose of the addressed problem is to design an H_{\infty } estimator such that the prefixed probabilistic constraints of the system error dynamics are satisfied and the H_{\infty } performance is also ensured. Subsequently, the explicit expression of the estimator gains is derived by solving a minimization problem subjected to certain recursive inequality constraints. Finally, a numerical example and a practical three-tank system are utilized to demonstrate the correctness and effectiveness of the proposed estimation scheme.