Decentralised network prediction and reconstruction algorithms

This study concerns the decentralised prediction and reconstruction problems in a network. First of all, we propose a decentralised prediction algorithm in the framework of network consensus problem. It allows any individual to compute the consensus value of the whole network in finite time using only the minimal number of successive values of its own history. We further prove that the minimal number of steps can be characterised using other algebraic and graph theoretical notions: minimal external equitable partition (mEEP) that can be directly computed from the Laplacian matrix of the graph and from the underlying network structure. Later, we consider a number of possible theoretical extensions of the proposed algorithm to issues arising from practical applications, e.g., time-delays, noise, external inputs, nonlinearities in the network, and analyse how the proposed algorithm should be changed to incorporate such constraints. For the decentralised reconstruction problem, we firstly define a new presentation: dynamical structure functions encoding structural information and explore the properties of such a representation for the purpose of solving the reconstruction problem. We have studied a number of theoretical problems: identification, realisation, reduction, etc. for dynamical structure functions and showed that how these theoretical can be used in solving decentralised network reconstruction problems. We later illustrate the results on a number of in-silico examples. We conclude the thesis with some ideas and future perspectives to continue based on the research of decentralised prediction and reconstruction problems

Decentralised minimal-time dynamic consensus

Abstract-This paper considers a group of agents that aim to reach an agreement on individually measured time-varying signals by local communication. In contrast to static network averaging problem, the consensus we mean in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises minimal number of local observations of randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically using local information as suggested by Olshevsky and Tsitsiklis

A Privacy-Preserving Finite-Time Push-Sum based Gradient Method for Distributed Optimization over Digraphs

This paper addresses the problem of distributed optimization, where a network of agents represented as a directed graph (digraph) aims to collaboratively minimize the sum of their individual cost functions. Existing approaches for distributed optimization over digraphs, such as Push-Pull, require agents to exchange explicit state values with their neighbors in order to reach an optimal solution. However, this can result in the disclosure of sensitive and private information. To overcome this issue, we propose a state-decomposition-based privacy-preserving finite-time push-sum (PrFTPS) algorithm without any global information such as network size or graph diameter. Then, based on PrFTPS, we design a gradient descent algorithm (PrFTPS-GD) to solve the distributed optimization problem. It is proved that under PrFTPS-GD, the privacy of each agent is preserved and the linear convergence rate related to the optimization iteration number is achieved. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed approach

Distributed estimation techniques forcyber-physical systems

Nowadays, with the increasing use of wireless networks, embedded devices and agents with processing and sensing capabilities, the development of distributed estimation techniques has become vital to monitor important variables of the system that are not directly available. Numerous distributed estimation techniques have been proposed in the literature according to the model of the system, noises and disturbances. One of the main objectives of this thesis is to search all those works that deal with distributed estimation techniques applied to cyber-physical systems, system of systems and heterogeneous systems, through using systematic review methodology. Even though systematic reviews are not the common way to survey a topic in the control community, they provide a rigorous, robust and objective formula that should not be ignored. The presented systematic review incorporates and adapts the guidelines recommended in other disciplines to the field of automation and control and presents a brief description of the different phases that constitute a systematic review. Undertaking the systematic review many gaps were discovered: it deserves to be remarked that some estimators are not applied to cyber-physical systems, such as sliding mode observers or set-membership observers. Subsequently, one of these particular techniques was chosen, set-membership estimator, to develop new applications for cyber-physical systems. This introduces the other objectives of the thesis, i.e. to present two novel formulations of distributed set-membership estimators. Both estimators use a multi-hop decomposition, so the dynamics of the system is rewritten to present a cascaded implementation of the distributed set-membership observer, decoupling the influence of the non-observable modes to the observable ones. So each agent must find a different set for each sub-space, instead of a unique set for all the states. Two different approaches have been used to address the same problem, that is, to design a guaranteed distributed estimation method for linear full-coupled systems affected by bounded disturbances, to be implemented in a set of distributed agents that need to communicate and collaborate to achieve this goal

Distributed Function Calculation over Noisy Networks

Considering any connected network with unknown initial states for all nodes, the nearest-neighbor rule is utilized for each node to update its own state at every discrete-time step. Distributed function calculation problem is defined for one node to compute some function of the initial values of all the nodes based on its own observations. In this paper, taking into account uncertainties in the network and observations, an algorithm is proposed to compute and explicitly characterize the value of the function in question when the number of successive observations is large enough. While the number of successive observations is not large enough, we provide an approach to obtain the tightest possible bounds on such function by using linear programing optimization techniques. Simulations are provided to demonstrate the theoretical results

Multi-agent MPC protocols for microgrid energy management and optimization

Navržení efektivního a spolehlivého řízení mikrosítí s vysokým podílem energie z obnovitelných zdrojů, je jednou z výzev při jejich nasazení. Prediktivní řízení (MPC) systému je slibný přístup, jak vyřešit tento problém v určitém časovém horizontu. Tento přístup umožňuje integraci řízení na základě minimalizace funkce, která dává do souvislosti různé druhy nákladů a omezení systému, ve vazbě na výrobu a spotřebu energie. Navržené multiagentní MPC řízení bylo vyvinuto jako dvoustupňová architektura, založená na konsensuálním algoritmu více agentů, který zajišťuje výkonovou rovnováhu v mikrosíti a centralizovaném MPC, který zefektivňuje řízené procesy tak, aby dosáhly vytyčených cílů. Při zkoumání navržených simulací byla ověřena předpokládaná korelace získaných výsledků a řídicích parametrů. Dále byla identifikována a analyzována situace s nejvyšším zlepšením ve srovnání s výsledky referenční řídící architektury. Na základě výsledků testů řídicího protokolu na testovaných datech, které byly měřeny v reálné mikrosíti, je vidět možnost významného snížení nákladů na provoz mikrosítě. Navrhované řešení tedy ukazuje vhodnost jeho implementace a přínos, jak pro provozovatele mikrosítí, tak pro zákazníky distribuční soustavy.One of the challenges of microgrids under the influence of high shares of intermittent renewable energy sources (RES) is an effective and reliable control. Model predictive control (MPC) is a promising approach to solve this problem for a specified time horizon since it allows integrating of a cost-minimizing objective function and system boundaries while taking power demand and supply into account. An agent-based MPC scheme was developed as a two-level architecture based on multi-agent control system (MAS) consensus algorithm providing power balance in the microgrid and centralized MPC that is aspiring to streamline the control processes to reach the targeted objectives. During the examination of the simulated results, the expected correlation of the result properties and control parameters was found. Additionally, the situations with the highest improvement ratio in comparison with the results of the reference control architecture were discovered and analysed. Based on the results, a significant cost reduction can be seen in most of the tested datasets that were measured on a real-life microgrid solution. Therefore, the implementation of the suggested control can prove to be appropriate and beneficial for microgrid operators and grid customers