The State-of-the-Art Survey on Optimization Methods for Cyber-physical Networks

Cyber-Physical Systems (CPS) are increasingly complex and frequently integrated into modern societies via critical infrastructure systems, products, and services. Consequently, there is a need for reliable functionality of these complex systems under various scenarios, from physical failures due to aging, through to cyber attacks. Indeed, the development of effective strategies to restore disrupted infrastructure systems continues to be a major challenge. Hitherto, there have been an increasing number of papers evaluating cyber-physical infrastructures, yet a comprehensive review focusing on mathematical modeling and different optimization methods is still lacking. Thus, this review paper appraises the literature on optimization techniques for CPS facing disruption, to synthesize key findings on the current methods in this domain. A total of 108 relevant research papers are reviewed following an extensive assessment of all major scientific databases. The main mathematical modeling practices and optimization methods are identified for both deterministic and stochastic formulations, categorizing them based on the solution approach (exact, heuristic, meta-heuristic), objective function, and network size. We also perform keyword clustering and bibliographic coupling analyses to summarize the current research trends. Future research needs in terms of the scalability of optimization algorithms are discussed. Overall, there is a need to shift towards more scalable optimization solution algorithms, empowered by data-driven methods and machine learning, to provide reliable decision-support systems for decision-makers and practitioners

Challenges to the Integration of Renewable Resources at High System Penetration

Successfully integrating renewable resources into the electric grid at penetration levels to meet a 33 percent Renewables Portfolio Standard for California presents diverse technical and organizational challenges. This report characterizes these challenges by coordinating problems in time and space, balancing electric power on a range of scales from microseconds to decades and from individual homes to hundreds of miles. Crucial research needs were identified related to grid operation, standards and procedures, system design and analysis, and incentives, and public engagement in each scale of analysis. Performing this coordination on more refined scales of time and space independent of any particular technology, is defined as a “smart grid.” “Smart” coordination of the grid should mitigate technical difficulties associated with intermittent and distributed generation, support grid stability and reliability, and maximize benefits to California ratepayers by using the most economic technologies, design and operating approaches

Compressed Sensing in Resource-Constrained Environments: From Sensing Mechanism Design to Recovery Algorithms

Compressed Sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. It is promising that CS can be utilized in environments where the signal acquisition process is extremely difficult or costly, e.g., a resource-constrained environment like the smartphone platform, or a band-limited environment like visual sensor network (VSNs). There are several challenges to perform sensing due to the characteristic of these platforms, including, for example, needing active user involvement, computational and storage limitations and lower transmission capabilities. This dissertation focuses on the study of CS in resource-constrained environments. First, we try to solve the problem on how to design sensing mechanisms that could better adapt to the resource-limited smartphone platform. We propose the compressed phone sensing (CPS) framework where two challenging issues are studied, the energy drainage issue due to continuous sensing which may impede the normal functionality of the smartphones and the requirement of active user inputs for data collection that may place a high burden on the user. Second, we propose a CS reconstruction algorithm to be used in VSNs for recovery of frames/images. An efficient algorithm, NonLocal Douglas-Rachford (NLDR), is developed. NLDR takes advantage of self-similarity in images using nonlocal means (NL) filtering. We further formulate the nonlocal estimation as the low-rank matrix approximation problem and solve the constrained optimization problem using Douglas-Rachford splitting method. Third, we extend the NLDR algorithm to surveillance video processing in VSNs and propose recursive Low-rank and Sparse estimation through Douglas-Rachford splitting (rLSDR) method for recovery of the video frame into a low-rank background component and sparse component that corresponds to the moving object. The spatial and temporal low-rank features of the video frame, e.g., the nonlocal similar patches within the single video frame and the low-rank background component residing in multiple frames, are successfully exploited

Neural Networks: Training and Application to Nonlinear System Identification and Control

This dissertation investigates training neural networks for system identification and classification. The research contains two main contributions as follow:1. Reducing number of hidden layer nodes using a feedforward componentThis research reduces the number of hidden layer nodes and training time of neural networks to make them more suited to online identification and control applications by adding a parallel feedforward component. Implementing the feedforward component with a wavelet neural network and an echo state network provides good models for nonlinear systems.The wavelet neural network with feedforward component along with model predictive controller can reliably identify and control a seismically isolated structure during earthquake. The network model provides the predictions for model predictive control. Simulations of a 5-story seismically isolated structure with conventional lead-rubber bearings showed significant reductions of all response amplitudes for both near-field (pulse) and far-field ground motions, including reduced deformations along with corresponding reduction in acceleration response. The controller effectively regulated the apparent stiffness at the isolation level. The approach is also applied to the online identification and control of an unmanned vehicle. Lyapunov theory is used to prove the stability of the wavelet neural network and the model predictive controller. 2. Training neural networks using trajectory based optimization approachesTraining neural networks is a nonlinear non-convex optimization problem to determine the weights of the neural network. Traditional training algorithms can be inefficient and can get trapped in local minima. Two global optimization approaches are adapted to train neural networks and avoid the local minima problem. Lyapunov theory is used to prove the stability of the proposed methodology and its convergence in the presence of measurement errors. The first approach transforms the constraint satisfaction problem into unconstrained optimization. The constraints define a quotient gradient system (QGS) whose stable equilibrium points are local minima of the unconstrained optimization. The QGS is integrated to determine local minima and the local minimum with the best generalization performance is chosen as the optimal solution. The second approach uses the QGS together with a projected gradient system (PGS). The PGS is a nonlinear dynamical system, defined based on the optimization problem that searches the components of the feasible region for solutions. Lyapunov theory is used to prove the stability of PGS and QGS and their stability under presence of measurement noise

Optimizing Nonlinear Dynamics in Energy System Planning and Control

Understanding the physical dynamics underlying energy systems is essential in achieving stable operations, and reasoning about restoration and expansion planning. The mathematics governing energy system dynamics are often described by high-order differential equations. Optimizing over these equations can be a computationally challenging exercise. To overcome these challenges, early studies focused on reduced / linearized models failing to capture system dynamics accurately. This thesis considers generalizing and improving existing optimization methods in energy systems to accurately represent these dynamics. We revisit three applications in power transmission and gas pipeline systems. Our first application focuses on power system restoration planning. We examine transient effects in power restoration and generalize the Restoration Ordering Problem formulation with standing phase angle and voltage difference constraints to enhance transient stability. Our new proposal can reduce rotor swings of synchronous generators by over 50\% and have negligible impacts on the blackout size, which is optimized holistically. Our second application focuses on transmission line switching in power system operations. We propose an automatic routine actively considering transient stability during optimization. Our main contribution is a nonlinear optimization model using trapezoidal discretization over the 2-axis generator model with an automatic voltage regulator (AVR). We show that congestion can lead to rotor instability, and variables controlling set-points of automatic voltage regulators are critical to ensure oscillation stability. Our results were validated against PowerWorld simulations and exhibit an average error in the order of 0.001 degrees for rotor angles. Our third contribution focuses on natural gas compressor optimization in natural gas pipeline systems. We consider the Dynamic Optimal Gas Flow problem, which generalizes the Optimal Gas Flow Problem to capture natural gas dynamics in a pipeline network. Our main contribution is a computationally efficient method to minimize gas compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flows. The scheme yields solutions that are feasible for the continuous problem and practical from an operational standpoint. Scalability of the scheme is demonstrated using realistic benchmark data