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Phasor Measurement Units (PMUs) have enabled real-time power grid monitoring and control applications realizing an integrated power grid and communication system. The communication network formed by PMUs has strict latency requirements. If PMU measurements cannot reach the control centre within the latency bound, they will be invalid for calculation and may compromise the observability of the whole power grid as well as related applications. To address this issue, this study proposes a model to account for the power grid observability under communication constraints, where effective capacity is adopted to perform a cross-layer statistical analysis in the communication system. Based on this model, three algorithms are proposed for improving power grid observability, which are an observability redundancy algorithm, an observability sensitivity algorithm and an observability probability algorithm. These three algorithms aim at enhancing the power system observability via the optimal communication resource allocation for a given grid infrastructure. Case studies show that the proposed algorithms can improve the power system performance under constrained wireless communication resources.

This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: University of Stuttgart, GermanyRoyal Institute of Technology, SwedenJohannes Kepler University, AustriaGeorgia Tech, USAUniversity of Washington, USAOhio University, USA

The solution of the distribution system state estimation (DSSE) relies on the presence of physical measurements in real time. Sometimes, these measurements may not reach the control center due to the defects in meter functionality, the large communication time delays, and denial-of-service (DoS) attacks on communication channels. Addressing this issue, a novel deep learning (DL) approach is proposed by using a transformer model with the integration of bi-directional long short-term memory (Bi-LSTM) layer. The proposed model can be leveraged to forecast the unavailable measurement data, which maintains the observability of the system to obtain an accurate solution from DSSE. The superiority of the proposed model is probed by comparing it with other forecasting-based DL models at various percentages of missing measurement data. Further, the effectiveness of the proposed model is evaluated for forecasting the power injections of residential, commercial, and industrial loads as well as renewable energy sources. Finally, the solution of the DSSE is tested with forecasted data and compared with the results of the DSSE for the original measurement data. The simulations are performed on modified IEEE 13-node and IEEE 37-node test systems, and their corresponding results highlighted the superiority of the proposed model in the forecasting of the incomplete data.

We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large dimension of the dynamical system state poses a computational obstacle to computing the exact posterior distribution. Model reduction offers a variety of computational tools that seek to reduce this computational burden. In particular, balanced truncation is a system-theoretic approach to model reduction which obtains an efficient reduced-dimension dynamical system by projecting the system operators onto state directions which trade off the reachability and observability of state directions as expressed through the associated Gramians. We introduce Gramian definitions relevant to the inference setting and propose a balanced truncation approach based on these inference Gramians that yield a reduced dynamical system that can be used to cheaply approximate the posterior mean and covariance. Our definitions exploit natural connections between (i) the reachability Gramian and the prior covariance and (ii) the observability Gramian and the Fisher information. The resulting reduced model then inherits stability properties and error bounds from system theoretic considerations, and in some settings yields an optimal posterior covariance approximation. Numerical demonstrations on two benchmark problems in model reduction show that our method can yield near-optimal posterior covariance approximations with order-of-magnitude state dimension reduction.

A wide variety of approaches for set-valued simulation, parameter identification, state estimation as well as reachability, observability and stability analysis for nonlinear discrete-time systems involve the propagation of ellipsoids via nonlinear functions. It is well known that the corresponding image sets usually possess a complex shape and may even be nonconvex despite the convexity of the input data. For that reason, domain splitting procedures are often employed which help to reduce the phenomenon of overestimation that can be traced back to the well-known dependency and wrapping effects of interval analysis. In this paper, we propose a simple, yet efficient scheme for simultaneously determining outer and inner ellipsoidal range enclosures of the solution for the evaluation of multi-dimensional functions if the input domains are themselves described by ellipsoids. The Hausdorff distance between the computed enclosure and the exact solution set reduces at least linearly when decreasing the size of the input domains. In addition to algebraic function evaluations, the proposed technique is—for the first time, to our knowledge—employed for quantifying worst-case errors when extended Kalman filter-like, linearization-based techniques are used for forecasting confidence ellipsoids in a stochastic setting.

Since phasor measurement unit (PMU) was invented, there has been growing interest in developing methodologies for finding the minimum number of PMUs for complete system observability. The methods for the PMU placement must consider the fact that the network topology may change when the power system is affected by a contingency event. Therefore the PMU placement problem can be stated as finding the minimum number of PMUs for complete system observability considering the failure probability of transmission lines. In this study, the authors propose a new reliability- based model for the contingency constrained PMUs placement. Initially, a methodology, that considers the probability of failure of the power system components, is proposed. Next, an algorithm is presented for selecting the minimal number of PMUs and their locations to monitor the system under normal operation and the most credible contingencies. A probabilistic index is introduced to select a desired level of reliability for the wide-area monitoring system. Finally, the availability of PMU measuring channels is incorporated in the model, so more realistic and useful results can be obtained. The problem is formulated and solved as a binary integer linear programming model and tested on the IEEE 9-bus, IEEE 57-bus and RTS96 test systems.

Resilience is a property of major interest for the design and analysis of generic complex systems. A system is resilient if it can adjust in response to disruptive shocks, and still provide the services it was designed for, without interruptions. In this work, we adapt a formal definition of resilience for constraint-based systems to a probabilistic framework derived from hidden Markov models. This allows us to more realistically model the stochastic evolution and partial observability of many complex real-world environments. Within this framework, we propose an efficient and exact algorithm for the inference queries required to construct generic property checking. We show that the time complexity of this algorithm is on par with other state-of-the-art inference queries for similar frameworks (that is, linear with respect to the time horizon). We also provide considerations on the specific complexity of the probabilistic checking of resilience and its connected properties, with particular focus on resistance. To demonstrate the flexibility of our approach and to evaluate its performance, we examine it in four qualitative and quantitative example scenarios: (1) disaster management and damage assessment; (2) macroeconomics; (3) self-aware, reconfigurable computing for aerospace applications; and (4) connectivity maintenance in robotic swarms.

The key findings of this study include a detailed examination of the Lorenz system’s observability, revealing that it maintains high observability compared to other chaotic systems, thus supporting its potential use in cryptographic applications. We also investigated the singularity manifolds, identifying regions where observability might be compromised, but overall demonstrating that the system remains reliable across various states. Additionally, statistical tests confirm that the Lorenz system exhibits strong statistical independence in its outputs, further validating its suitability for encryption purposes. These findings collectively underscore the Lorenz system’s potential to enhance cryptographic security and contribute significantly to the field of secure communications. By providing a thorough analysis of its key properties, this study positions the Lorenz system as a promising candidate for advanced encryption technologies.

In industrial applications, the processes of optimal sequential decision making are naturally formulated and optimized within a standard setting of Markov decision theory. In practice, however, decisions must be made under incomplete and uncertain information about parameters and transition probabilities. This situation occurs when a system may suffer a regime switch changing not only the transition probabilities but also the control costs. After such an event, the effect of the actions may turn to the opposite, meaning that all strategies must be revised. Due to practical importance of this problem, a variety of methods has been suggested, ranging from incorporating regime switches into Markov dynamics to numerous concepts addressing model uncertainty. In this work, we suggest a pragmatic and practical approach using a natural re-formulation of this problem as a so-called convex switching system, we make efficient numerical algorithms applicable.

This paper presents a mathematical linear expansion model for the probabilistic Multistage Phasor Measurement Unit (PMU) Placement (MPP) in which zero-injection buses (ZIBs), as well as communication channel limitations, are taken into consideration. From the linearization perspective, presenting a model formulizing the probabilistic concept of observability while modelling the ZIB is of great significance, and has been done in this paper for the first time. More importantly, the proposed probabilistic MPP utilizes a technique disregarding the prevalent subsidiary optimizations for each planning stage. Although this technique, in turn, increases the problem complexity with manifold variables, it guarantees the global optimal solution in a wider and thorough search space; while in the prevalent methods, some parts of the search space might be missed. Furthermore, the proposed model indicates more realistic aspects of the MPP where system operators are allowed to follow their intention about the importance of buses such as strategic ones based on monitoring the priority principles. In addition, the model is capable of considering the network topology changes due to long-term expansions over the planning horizon. Finally, in order to demonstrate the effectiveness of the proposed formulation, the model is conducted on the IEEE 57-bus standard test system and the large scale 2383-bus Polish power system.