Unified Approach to Convex Robust Distributed Control given Arbitrary Information Structures

We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this technical note, we focus on the requirement that the control policy is distributed, in the sense that it can only be based on partial information about the history of the outputs. It is well-known that when a condition denoted as Quadratic Invariance (QI) holds, the optimal distributed control policy can be computed in a tractable way. Our goal is to unify and generalize the class of information structures over which quadratic invariance is equivalent to a test over finitely many binary matrices. The test we propose certifies convexity of the output-feedback distributed control problem in finite-horizon given any arbitrarily defined information structure, including the case of time varying communication networks and forgetting mechanisms. Furthermore, the framework we consider allows for including polytopic constraints on the states and the inputs in a natural way, without affecting convexity

Decentralized Optimal Control With Application In Power System

An output-feedback decentralized optimal controller is proposed for power systems with renewable energy penetration. Renewable energy source is modeled similar to the classical generator model and is equipped with the unified power flow controller (UPFC). The transient performance of power system is considered and stability of the dynamical states are investigated. An offline decentralized optimal controller is designed that utilizes only the local states. The network comprises conventional synchronous generators as well as renewable sources with inverter equipped with UPFC. Subsequently, the optimal decentralized controller is compared to the initial stabilizing controller used to obtain the optimal controller. An online decentralized optimal controller is designed for discrete-time system. Two neuro networks are utilized to estimate value function and optimal control strategy. Furthermore, a novel observer-based decentralized optimal controller is developed on small scale discrete-time power system. The system is trained followed by least square rules and successive approximation. Simulation results on IEEE 14-, 30-, and 118-bus power system benchmarks shows satisfactory performance of the online decentralized controller. And also, simulation results demonstrate great performance of the observer and the optimal controller compare to the centralized optimal controller

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation. The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification. We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H∞ optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H∞ norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.</p

Synchronization and prediction of chaotic dynamics on networks of optoelectronic oscillators

The subject of this thesis is the exploration of chaotic synchronization for novel applications including time-series prediction and sensing. We begin by characterizing the nonlinear dynamics of an optoelectronic time-delayed feedback loop. We show that synchronization of an accurate numerical model to experimental measurements provides a way to assimilate data and forecast the future of deterministic chaotic behavior. Next, we implement an adaptive control method that maintains isochronal synchrony for a network of coupled feedback loops when the interaction strengths are unknown and time-varying. Control signals are used as real-time estimates of the variations present within the coupling paths. We analyze the stability of synchronous solutions for arbitrary coupling topologies via a modified master stability function that incorporates the adaptation response dynamics. Finally, we show that the master stability function, which is derived from a set of linearized equations, can also be experimentally measured using a two-node network, and it can be applied to predict the convergence behavior of large networks

Efficiency and Sustainability of the Distributed Renewable Hybrid Power Systems Based on the Energy Internet, Blockchain Technology and Smart Contracts

The climate changes that are visible today are a challenge for the global research community. In this context, renewable energy sources, fuel cell systems, and other energy generating sources must be optimally combined and connected to the grid system using advanced energy transaction methods. As this book presents the latest solutions in the implementation of fuel cell and renewable energy in mobile and stationary applications such as hybrid and microgrid power systems based on energy internet, blockchain technology, and smart contracts, we hope that they are of interest to readers working in the related fields mentioned above

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com