Secure State Estimation for Artificial Neural Networks With Unknown-But-Bounded Noises: A Homomorphic Encryption Scheme.

This article is concerned with the secure state estimation problem for artificial neural networks (ANNs) subject to unknown-but-bounded noises, where sensors and the remote estimator are connected via open and bandwidth-limited communication networks. Using the encoding-decoding mechanism (EDM) and the Paillier encryption technique, a novel homomorphic encryption scheme (HES) is introduced, which aims to ensure the secure transmission of measurement information within communication networks that are constrained by bandwidth. Under this encoding-decoding-based HES, the data being transmitted can be encrypted into ciphertexts comprising finite bits. The emphasis of this research is placed on the development of a secure set-membership state estimation algorithm, which allows for the computation of estimates using encrypted data without the need for decryption, thereby ensuring data security throughout the entire estimation process. Taking into account the unknown-but-bounded noises, the underlying ANN, and the adopted HES, sufficient conditions are determined for the existence of the desired ellipsoidal set. The related secure state estimator gains are then derived by addressing optimization problems using the Lagrange multiplier method. Lastly, an example is presented to verify the effectiveness of the proposed secure state estimation approach.

Neural-Network-Based Set-Membership Fault Estimation for 2-D Systems Under Encoding-Decoding Mechanism.

In this article, the simultaneous state and fault estimation problem is investigated for a class of nonlinear 2-D shift-varying systems, where the sensors and the estimator are connected via a communication network of limited bandwidth. With the purpose of relieving the communication burden and enhancing the transmission security, a new encoding-decoding mechanism is put forward so as to encode the transmitted data with a finite number of bits. The aim of the addressed problem is to develop a neural-network (NN)-based set-membership estimator for jointly estimating the system states and the faults, where the estimation errors are guaranteed to reside within an optimized ellipsoidal set. With the aid of the mathematical induction technique and certain convex optimization approaches, sufficient conditions are derived for the existence of the desired set-membership estimator, and the estimator gains and the NN tuning scalars are then presented in terms of the solutions to a set of optimization problems subject to ellipsoidal constraints. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed estimator design method.

Distributed Set-Membership Fusion Filtering for Nonlinear 2-D Systems Over Sensor Networks: An Encoding-Decoding Scheme.

In this article, the distributed set-membership fusion filtering problem is investigated for a class of nonlinear 2-D shift-varying systems subject to unknown-but-bounded noises over sensor networks. The sensors are communicated with their neighbors according to a given topology through wireless networks of limited bandwidth. With the purpose of relieving the communication burden as well as enhancing the transmission security, a logarithmic-type encoding-decoding mechanism is introduced for each sensor node so as to encode the transmitted data with a finite number of bits. A distributed set-membership filter is designed to determine the local ellipsoidal set that contains the system state by only utilizing the data from the local sensor node and its neighbors, where the proposed filter scheme is truly distributed with desirable scalability. Then, a new ellipsoid-based fusion rule is developed for the designed set-membership filters in order to form the fused ellipsoidal set that has a globally smaller volume than all local ellipsoidal sets. With the aid of the mathematical induction technique, the set theory, and the convex optimization approach, sufficient conditions are derived for the existence of the desired distributed set-membership filters and the fusion weights. Then, the filter parameters and the fusion weights are acquired by solving a set of constrained optimization problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed fusion filtering algorithm.

Adaptive Set-Membership State Estimation for Nonlinear Systems Under Bit Rate Allocation Mechanism: A Neural-Network-Based Approach.

In this article, the adaptive neural-network-based (NN-based) set-membership state estimation problem is studied for a class of nonlinear systems subject to bit rate constraints and unknown-but-bounded noises. The measurement output signals are transmitted from sensors to a remote estimator via a bit rate constrained communication channel. To relieve the communication burden and ameliorate the state estimation accuracy, a bit rate allocation mechanism is put forward for the sensor nodes by solving a constrained optimization problem. Subsequently, through the NN learning method, an NN-based set-membership estimator is designed to determine an ellipsoidal set that contains the system state, where the proposed estimator relies upon a prediction-correction structure. With the help of the mathematical induction technique and the set theory, sufficient conditions are obtained to ensure the existence of both the adaptive tuning parameters and the set-membership estimators, and then, the corresponding parameters and estimator gains are calculated by solving a set of optimization problems. In addition, the monotonicity of the upper bound on the squared estimation error with respect to the bit rate and the convergence of the NN weight are analyzed, respectively. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed state estimation algorithm.