Quantum process in probability representation of quantum mechanics

In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposition for the projection to a certain basis state and a Gaussian-type projection is demonstrated as well as qubit flipping and amplitude damping processes.

Application of Deep Neural Networks to Distribution System State Estimation and Forecasting

Classical neural networks such as feedforward multi-layer perceptron models (MLPs) are well established as universal approximators and as such, show promise in applications such as static state estimation in power transmission systems. The dynamic nature of distributed generation (i.e. solar and wind), vehicle to grid technology (V2G) and false data injection attacks (FDIAs), may pose significant challenges to the application of classical MLPs to state estimation (SE) and state forecasting (SF) in power distribution systems. This paper investigates the application of conventional neural networks (MLPs) and deep learning based models such as convolutional neural networks (CNNs) and long-short term networks (LSTMs) to mitigate the aforementioned challenges in power distribution systems. The ability of MLPs to perform regression to perform power system state estimation will be investigated. MLPs are considered based upon their promise to learn complex functional mapping between datasets with many features. CNNs and LSTMs are considered based upon their promise to perform time-series forecasting by learning the correlation of the dataset being predicted. The performance of MLPS, CNNs, and LSTMs to perform state estimation and state forecasting will be presented in terms of average root-mean square error (RMSE) and training execution time. An IEEE standard 34-bus test system is used to illustrate the proposed conventional neural network and deep learning methods and their effectiveness to perform power system state estimation and power system state forecasting.

Adaptive event-triggered state estimation for complex networks with nonlinearities against hybrid attacks

<abstract><p>This paper investigates the event-triggered state estimation problem for a class of complex networks (CNs) suffered by hybrid cyber-attacks. It is assumed that a wireless network exists between sensors and remote estimators, and that data packets may be modified or blocked by malicious attackers. Adaptive event-triggered scheme (AETS) is introduced to alleviate the network congestion problem. With the help of two sets of Bernoulli distribution variables (BDVs) and an arbitrary function related to the system state, a mathematical model of the hybrid cyber-attacks is developed to portray randomly occurring denial-of-service (DoS) attacks and deception attacks. CNs, AETS, hybrid cyber-attacks, and state estimators are then incorporated into a unified architecture. The system state is cascaded with state errors as an augmented system. Furthermore, based on Lyapunov stability theory and linear matrix inequalities (LMIs), sufficient conditions to ensure the asymptotic stability of the augmented system are derived, and the corresponding state estimator is designed. Finally, the effectiveness of the theoretical method is demonstrated by numerical examples and simulations.</p></abstract>

An Extended Kalman Filtering Technique for Geodetic First Order Data Assimilation

Data assimilation allows merging of different sources of data to estimate possible states of a system as it evolves in time. This therefore supports the idea of combining classical observations with Global Positioning System (GPS) observations to improve the integrity of first order geodetic controls in Nigeria. Given that these geodetic controls, which were established using traditional techniques and whose algorithms are still in use, the task of optimizing the coordinate values of these monuments to improve efficiency and accuracy in conventional geodetic operations around Nigeria is still a challenge. This study introduces the Extended Kalman Filter (EKF) technique for the modeling of these observations and their uncertainties in addition to exogenous noise, which is handled by an approximate set-valued state estimator. The proposed EKF provides a feasible linearization process in merging classical and GPS data collection modes as shown in our study. For each discrete time in the analysis step, it employs the Kalman gain computation, which attempts to weigh and balance uncertainties between the estimate and observation before proceeding to the analysis step. In this setup, the EKF constrains the system state in order to balance and strengthen the integrity of these first order monuments. The relationship of the derived system state with GPS coordinates (R2 = 0.85) and classical observations (R2 = 0.92) over Nigeria using a multi linear regression analysis is considerably strong. This outcome provides insight to the performance of the test algorithm and builds on the usefulness of data assimilation techniques in geodetic operations.