Towards Stabilization of Distributed Systems under Denial-of-Service

In this paper, we consider networked distributed systems in the presence of Denial-of-Service (DoS) attacks, namely attacks that prevent transmissions over the communication network. First, we consider a simple and typical scenario where communication sequence is purely Round-robin and we explicitly calculate a bound of attack frequency and duration, under which the interconnected large-scale system is asymptotically stable. Second, trading-off system resilience and communication load, we design a hybrid transmission strategy consisting of Zeno-free distributed event-triggered control and Round-robin. We show that with lower communication loads, the hybrid communication strategy enables the systems to have the same resilience as in pure Round-robin

Information Theory and Cooperative Control in Networked Multi-Agent Systems with Applications to Smart Grid

This dissertation focuses on information theoretic aspects of and cooperative control techniques in networked multi-agent systems (NMAS) with communication constraints. In the first part of the dissertation, information theoretic limitations of tracking problems in networked control systems, especially leader-follower systems with communication constraints, are studied. Necessary conditions on the data rate of each communication link for tracking of the leader-follower systems are provided. By considering the forward and feedback channels as one cascade channel, we also provide a lower bound for the data rate of the cascade channel for the system to track a reference signal such that the tracking error has finite second moment. Finally, the aforementioned results are extended to the case in which the leader system and follower system have different system models. In the second part, we propose an easily scalable hierarchical decision-making and control architecture for smart grid with communication constraints in which distributed customers equipped with renewable distributed generation (RDG) interact and trade energy in the grid. We introduce the key components and their interactions in the proposed control architecture and discuss the design of distributed controllers which deal with short-term and long-term grid stability, power load balancing and energy routing. At microgrid level, under the assumption of user cooperation and inter-user communications, we propose a distributed networked control strategy to solve the demand-side management problem in microgrids. Moreover, by considering communication delays between users and microgrid central controller, we propose a distributed networked control strategy with prediction to solve the demand-side management problem with communication delays. In the third part, we consider the disturbance attenuation and stabilization problem in networked control systems. To be specific, we consider the string stability in a large group of interconnected systems over a communication network. Its potential applications could be found in formation tracking control in groups of robots, as well as uncertainty reduction and disturbance attenuation in smart grid. We propose a leader-following consensus protocol for such interconnected systems and derive the sufficient conditions, in terms of communication topology and control parameters, for string stability. Simulation results and performance in terms of disturbance propagation are also given. In the fourth part, we consider distributed tracking and consensus in networked multi-agent systems with noisy time-varying graphs and incomplete data. In particular, a distributed tracking with consensus algorithm is developed for the space-object tracking with a satellite surveillance network. We also intend to investigate the possible application of such methods in smart grid networks. Later, conditions for achieving distributed consensus are discussed and the rate of convergence is quantified for noisy time-varying graphs with incomplete data. We also provide detailed simulation results and performance comparison of the proposed distributed tracking with consensus algorithm in the case of space-object tracking problem and that of distributed local Kalman filtering with centralized fusion and centralized Kalman filter. The information theoretic limitations developed in the first part of this dissertation provide guildlines for design and analysis of tracking problems in networked control systems. The results reveal the mutual interaction and joint application of information theory and control theory in networked control systems. Second, the proposed architectures and approaches enable scalability in smart grid design and allow resource pooling among distributed energy resources (DER) so that the grid stability and optimality is maintained. The proposed distributed networked control strategy with prediction provides an approach for cooperative control at RDG-equipped customers within a self-contained microgrid with different feedback delays. Our string stability analysis in the third part of this dissertation allows a single networked control system to be extended to a large group of interconnected subsystems while system stability is still maintained. It also reveals the disturbance propagation through the network and the effect of disturbance in one subsystem on other subsystems. The proposed leader-following consensus protocol in the constrained communication among users reveals the effect of communication in stabilization of networked control systems and the interaction between communication and control over a network. Finally, the distributed tracking and consensus in networked multi-agent systems problem shows that information sharing among users improves the quality of local estimates and helps avoid conflicting and inefficient distributed decisions. It also reveals the effect of the graph topologies and incomplete node measurements on the speed of achieving distributed decision and final consensus accuracy

Stability of interconnected impulsive systems with and without time-delays using Lyapunov methods

In this paper we consider input-to-state stability (ISS) of impulsive control systems with and without time-delays. We prove that if the time-delay system possesses an exponential Lyapunov-Razumikhin function or an exponential Lyapunov-Krasovskii functional, then the system is uniformly ISS provided that the average dwell-time condition is satisfied. Then, we consider large-scale networks of impulsive systems with and without time-delays and we prove that the whole network is uniformly ISS under a small-gain and a dwell-time condition. Moreover, these theorems provide us with tools to construct a Lyapunov function (for time-delay systems - a Lyapunov-Krasovskii functional or a Lyapunov-Razumikhin function) and the corresponding gains of the whole system, using the Lyapunov functions of the subsystems and the internal gains, which are linear and satisfy the small-gain condition. We illustrate the application of the main results on examples

Feedback stabilization of dynamical systems with switched delays

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with timevarying delays. We consider both cases where delay-dependent and delay independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Distributed Design for Decentralized Control using Chordal Decomposition and ADMM

We propose a distributed design method for decentralized control by exploiting the underlying sparsity properties of the problem. Our method is based on chordal decomposition of sparse block matrices and the alternating direction method of multipliers (ADMM). We first apply a classical parameterization technique to restrict the optimal decentralized control into a convex problem that inherits the sparsity pattern of the original problem. The parameterization relies on a notion of strongly decentralized stabilization, and sufficient conditions are discussed to guarantee this notion. Then, chordal decomposition allows us to decompose the convex restriction into a problem with partially coupled constraints, and the framework of ADMM enables us to solve the decomposed problem in a distributed fashion. Consequently, the subsystems only need to share their model data with their direct neighbours, not needing a central computation. Numerical experiments demonstrate the effectiveness of the proposed method.Comment: 11 pages, 8 figures. Accepted for publication in the IEEE Transactions on Control of Network System

Stabilization over power-constrained parallel Gaussian channels

This technical note is concerned with state-feedback stabilization of multi-input systems over parallel Gaussian channels subject to a total power constraint. Both continuous-time and discrete-time systems are treated under the framework of H2 control, and necessary/sufficient conditions for stabilizability are established in terms of inequalities involving unstable plant poles, transmitted power, and noise variances. These results are further used to clarify the relationship between channel capacity and stabilizability. Compared to single-input systems, a range of technical issues arise. In particular, in the multi-input case, the optimal controller has a separation structure, and the lower bound on channel capacity for some discrete-time systems is unachievable by linear time-invariant (LTI) encoders/decoder