On general systems with network-enhanced complexities

In recent years, the study of networked control systems (NCSs) has gradually become an active research area due to the advantages of using networked media in many aspects such as the ease of maintenance and installation, the large flexibility and the low cost. It is well known that the devices in networks are mutually connected via communication cables that are of limited capacity. Therefore, some network-induced phenomena have inevitably emerged in the areas of signal processing and control engineering. These phenomena include, but are not limited to, network-induced communication delays, missing data, signal quantization, saturations, and channel fading. It is of great importance to understand how these phenomena influence the closed-loop stability and performance properties

Decentralized control for guaranteed individual costs in a linear multi-agent system: A satisfaction equilibrium approach

International audienceThis work focuses on the design of decentralized feedback control gains that aims at optimizing individual costs in a multi-agent synchronization problem. As reported in the literature, the optimal control design for synchronization of agents using local information is NP-hard. Consequently, we relax the problem and use the notion of satisfaction equilibrium from game theory to ensure that each individual cost is guaranteed to be lower than a given threshold. Our main results provide conditions in the form of linear matrix inequalities (LMIs) to check if a given set of control gains are in satisfaction equilibrium i.e. all individual costs are upper-bounded by the imposed threshold. Moreover, we provide an algorithm in order to synthesize gains that are in satisfaction equilibrium. Finally, we illustrate this algorithm with numerical examples

Optimal Control of Transmission Power Management in Wireless Backbone Mesh Networks

International audienceno abstrac

Performance and design of consensus on matrix-weighted and time scaled graphs

In this paper, we consider the $\mathcal{H}_2$-norm of networked systems with multi-time scale consensus dynamics and vector-valued agent states. This allows us to explore how measurement and process noise affect consensus on matrix-weighted graphs by examining edge-state consensus. In particular, we highlight an interesting case where the influences of the weighting and scaling on the $\mathcal{H}_2$ norm can be separated in the design problem. We then consider optimization algorithms for updating the time scale parameters and matrix weights in order to minimize network response to injected noise. Finally, we present an application to formation control for multi-vehicle systems.Comment: 10 pages, 5 figures, accepted to the IEEE Transactions on Control of Network Systems. arXiv admin note: text overlap with arXiv:1909.0786

Coordination and Privacy Preservation in Multi-Agent Systems

This dissertation considers two key problems in multi-agent systems: coordination (including both synchronization and desynchronization) and privacy preservation. For coordination in multi-agent systems, we focus on synchronization/desynchronization of distributed pulse-coupled oscillator (PCO) networks and their applications in collective motion coordination. Pulse-coupled oscillators were originally proposed to model synchronization in biological systems such as flashing fireflies and firing neurons. In recent years, with proven scalability, simplicity, accuracy, and robustness, the PCO based synchronization strategy has become a powerful clock synchronization primitive for wireless sensor networks. Driven by these increased applications in biological networks and wireless sensor networks, synchronization of pulse-coupled oscillators has gained increased popularity. However, most existing results address the local synchronization of PCOs with initial phases constrained in a half cycle, and results on global synchronization from any initial condition are very sparse. In our work, we address global PCO synchronization from an arbitrary phase distribution under chain or directed tree graphs. More importantly, different from existing global synchronization studies on decentralized PCO networks, our work allows heterogeneous coupling functions and perturbations on PCOs\u27 natural frequencies, and our results hold under any coupling strength between zero and one, which is crucial because a large coupling strength has been shown to be detrimental to the robustness of PCO synchronization to disturbances. Compared with synchronization, desynchronization of PCOs is less explored. Desynchronization spreads the phase variables of all PCOs uniformly apart (with equal difference between neighboring phases). It has also been found in many biological phenomena, such as neuron spiking and fish signaling. Recently, phase desynchronization has been employed to achieve round-robin scheduling, which is crucial in applications as diverse as media access control of communication networks, realization of analog-to-digital converters, and scheduling of traffic flows in intersections. In our work, we systematically characterize pulse-coupled oscillators based decentralized phase desynchronization and propose an interaction function that is more general than existing results. Numerical simulations show that the proposed pulse based interaction function also has better robustness to pulse losses, time delays, and frequency errors than existing results. Collective motion coordination is fundamental in systems as diverse as mobile sensor networks, swarm robotics, autonomous vehicles, and animal groups. Inspired by the close relationship between phase synchronization/desynchronization of PCOs and the heading dynamics of connected vehicles/robots, we propose a pulse-based integrated communication and control approach for collective motion coordination. Our approach only employs simple and identical pulses, which significantly reduces processing latency and communication delay compared with conventional packet based communications. Not only can heading control be achieved in the proposed approach to coordinate the headings (orientations) of motions in a network, but also spacing control for circular motion is achievable to design the spacing between neighboring nodes (e.g., vehicles or robots). The second part of this dissertation is privacy preservation in multi-agent systems. More specifically, we focus on privacy-preserving average consensus as it is key for multi-agent systems, with applications ranging from time synchronization, information fusion, load balancing, to decentralized control. Existing average consensus algorithms require individual nodes (agents) to exchange explicit state values with their neighbors, which leads to the undesirable disclosure of sensitive information in the state. In our work, we propose a novel average consensus algorithm for time-varying directed graphs which can protect the privacy of participating nodes\u27 initial states. Leveraging algorithm-level obfuscation, the algorithm does not need the assistance of any trusted third party or data aggregator. By leveraging the inherent robustness of consensus dynamics against random variations in interaction, our proposed algorithm can guarantee privacy of participating nodes without compromising the accuracy of consensus. The algorithm is distinctly different from differential-privacy based average consensus approaches which enable privacy through compromising accuracy in obtained consensus value. The approach is able to protect the privacy of participating nodes even in the presence of multiple honest-but-curious nodes which can collude with each other

Robust Hybrid Systems for Control, Learning, and Optimization in Networked Dynamical Systems

The deployment of advanced real-time control and optimization strategies in socially-integratedengineering systems could significantly improve our quality of life whilecreating jobs and economic opportunity. However, in cyber-physical systems such assmart grids, transportation networks, healthcare, and robotic systems, there still existseveral challenges that prevent the implementation of intelligent control strategies.These challenges include the existence of limited communication networks, dynamicand stochastic environments, multiple decision makers interacting with the system,and complex hybrid dynamics emerging from the feedback interconnection of physicalprocesses and computational devices.In this dissertation, we study the problem of designing robust control and optimizationalgorithms for cyber-physical systems using the framework of hybrid dynamicalsystems. We propose different theoretical frameworks for the design and analysis offeedback mechanisms that optimize the performance of dynamical systems without requiringan explicit characterization of their mathematical model, i.e., in a model-freeway. The closed-loop system that emerges of the interconnection of the plant with thefeedback mechanism describes, in general, a set-valued hybrid dynamical system. Thesetypes of systems combine continuous-time and discrete-time dynamics, and they usuallylack the uniqueness of solutions property. The framework of set-valued hybriddynamical systems allows us to study many complex dynamical systems that emerge indifferent engineering applications, such as networked multi-agent systems with switching graphs, non-smooth mechanical systems, dynamic pricing mechanisms in transportationsystems, autonomous robots with logic-based controllers, etc. We proposea step-by-step approach to the design of different types of discrete-time, continuous-time,hybrid, and stochastic controllers for different types of applications, extendingand generalizing different results in the literature in the area of extremum seeking control,sampled-data extremization, robust synchronization, and stochastic learning innetworked systems. Our theoretical results are illustrated via different simulations andnumerical examples

Tracking-based distributed equilibrium seeking for aggregative games

We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected pseudo-gradient descent and (ii) a tracking mechanism to locally reconstruct the aggregative variable. To handle coupling constraints arising in generalized settings, we propose another distributed algorithm based on (i) a recently emerged augmented primal-dual scheme and (ii) two tracking mechanisms to reconstruct, for each agent, both the aggregative variable and the coupling constraint satisfaction. Leveraging tools from singular perturbations analysis, we prove linear convergence to the Nash equilibrium for both schemes. Finally, we run extensive numerical simulations to confirm the effectiveness of our methods and compare them with state-of-the-art distributed equilibrium-seeking algorithms