Overcoming Communication Delays in Distributed Frequency Regulation

(Georgia Institute of Technology, 2016-07) Ramachandran, Thiagarajan ; Nazari, Masoud H. ; Grijalva, Santiago ; Egerstedt, Magnus B.

This paper proposes a general framework for determining the effect of communication delays on the convergence of certain distributed frequency regulation (DFR) protocols for prosumer-based energy systems, where prosumers are serving as balancing areas. DFR relies on iterative and distributed optimization algorithms to obtain an optimal feedback law for frequency regulation. But, it is, in general, hard to know beforehand how many iterations suffices to ensure stability. This paper develops a framework to determine a lower bound on the number of iterations required for two distributed optimization protocols. This allows prosumers to determine whether they can compute stabilizing control strategies within an acceptable time frame by taking communication delays into account. The efficacy of the method is demonstrated on two realistic power systems
Optimal Control of Autonomous Switched-Mode Systems: Gradient-Descent Algorithms with Armijo Step Sizes

(Georgia Institute of Technology, 2015-12) Wardi, Yorai Y. ; Egerstedt, Magnus B. ; Hale, M.

This paper concerns optimal mode-scheduling in autonomous switched-mode hybrid dynamical systems, where the objective is to minimize a cost-performance functional defined on the state trajectory as a function of the schedule of modes. The controlled variable, namely the modes’ schedule, consists of the sequence of modes and the switchover times between them. We propose a gradient-descent algorithm that adjusts a given mode-schedule by changing multiple modes over time-sets of positive Lebesgue measures, thereby avoiding the inefficiencies inherent in existing techniques that change the modes one at a time. The algorithm is based on steepest descent with Armijo step sizes along Gˆateaux differentials of the performance functional with respect to schedule-variations, which yields effective descent at each iteration. Since the space of mode-schedules is infinite dimensional and incomplete, the algorithm’s convergence is proved in the sense of Polak’s framework of optimality functions and minimizing sequences. Simulation results are presented, and possible extensions to problems with dwelltime lower-bound constraints are discussed.
Spatio-Temporal Multi-Robot Routing

(Georgia Institute of Technology, 2015-10) Chopra, Smriti ; Egerstedt, Magnus B.

In this paper, we consider the problem of routing multiple robots to service spatially distributed requests at specified time instants. We show that such a routing problem can be formulated as a pure assignment problem. Additionally, we incorporate connectivity constraints into the problem by requiring that range-constrained robots ensure a connected information exchange network at all times. We discuss the feasibility aspects of such a spatio-temporal routing problem, and derive the minimum number of robots required to service the requests. Moreover, we explicitly construct the corresponding routes for the robots, with the total length traveled as the cost to be minimized.
Analyzing Human-Swarm Interactions Using Control Lyapunov Functions and Optimal Control.

(Georgia Institute of Technology, 2015-09) de la Croix, Jean-Pierre ; Egerstedt, Magnus B.

A number of different interaction modalities have been proposed for human engagement with networked systems. In this paper, we establish formal guarantees for whether or not a given such human-swarm interaction (HSI) strategy is appropriate for achieving particular multi-robot tasks, such as guiding a swarm of robots into a particular geometric configuration. In doing so, we define what it means to impose an HSI control structure on a multi-robot system. Control Lyapunov functions are used to establish feasibility for a user to achieve a particular geometric configuration with a multi-robot system under some selected HSI control structure. Several examples of multi-robot systems with unique HSI control structures are provided to illustrated the use of CLFs to establish feasibility. Additionally, we also uses these examples to illustrate how to use optimal control tools to compute three metrics for evaluating an HSI control structure: attention, effort, and scalability.
From Global, Finite-Time, Linear Computations to Local, Edge-Based Interaction Rules

(Georgia Institute of Technology, 2015-08) Costello, Zak ; Egerstedt, Magnus B.

A network of locally interacting agents can be thought of as performing a distributed computation. But not all computations can be faithfully distributed. This paper investigates which global, linear transformations can be computed in finite time using local rules with time varying weights, i.e., rules which rely solely on information from adjacent nodes in a network. The main result states that a linear transformation is computable in finite time using local rules if and only if the transformation has positive determinant. An optimal control problem is solved for finding the local interaction rules, and simulations are performed to elucidate how optimal solutions can be obtained.
Multi-Robot Control Using Time-Varying Density Functions

(Georgia Institute of Technology, 2015-04) Lee, Sung G. ; Diaz-Mercad, Yancy ; Egerstedt, Magnus B.

An approach is presented for influencing teams of robots by means of time-varying density functions, representing rough references for where the robots should be located. A continuous-time coverage algorithm is proposed and distributed approximations are given whereby the robots only need to access information from adjacent robots. Robotic experiments show that the proposed algorithms work in practice as well as in theory.
From Algorithms to Architectures in Cyber-Physical Networks

(Georgia Institute of Technology, 2015-02) Egerstedt, Magnus B.
Characterizing Heterogeneity in Cooperative Networks From a Resource Distribution View-Point

(Georgia Institute of Technology, 2014-11) Abbas, Waseem ; Egerstedt, Magnus B.

A network of agents in which agents with a diverse set of resources or capabilities interact and coordinate with each other to accomplish various tasks constitutes a heterogeneous cooperative network. In this paper, we investigate heterogeneity in terms of resources allocated to agents within the network. The objective is to distribute resources in such a way that every agent in the network should be able to utilize all these resources through local interactions. In particular, we formulate a graph coloring problem in which each node is assigned a subset of labels from a labeling set, and a graph is considered to be completely heterogeneous whenever all the labels in the labeling set are available in the closed neighborhood of every node. The total number of different resources that can be accommodated within a system under this setting depends on the underlying graph structure of the network. This paper provides an analysis of the assignment of multiple resources to nodes and the effect of these assignments on the overall heterogeneity of the network.
Continuous-time Proportional-Integral Distributed Optimization for Networked Systems

(Georgia Institute of Technology, 2014-07) Droge, Greg ; Kawashima, Hiroaki ; Egerstedt, Magnus B.

In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship to gradient-based constrained optimization. By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient method for optimization with one using a proportional control term and the other using an integral control term to drive the system to the constraint set. Therefore, a significant contribution of this paper is to combine these methods to develop a continuous-time proportional-integral distributed optimization method. Furthermore, we establish convergence using Lyapunov stability techniques and utilizing properties from the network structure of the multi-agent system.
Space-time Measurements of Oceanic Sea States

(Georgia Institute of Technology, 2013-10) Fedele, Francesco ; Benetazzo, Alvise ; Gallego, Guillermo ; Shih, Ping-Chang ; Yezzi, Anthony ; Barbariol, Francesco ; Ardhuin,Fabrice

Stereo video techniques are effective for estimating the space-time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes.We present an application of the Wave Acquisition Stereo System (WASS) for the analysis of offshore video measurements of gravity waves in the Northern Adriatic Sea and near the southern seashore of the Crimean peninsula, in the Black Sea. We use classical epipolartechniques to reconstruct the sea surface from the stereo pairs sequentially in time, viz. asequence of spatial snapshots. We also present a variational approach that exploits the entire data image set providing a global space-time imaging of the sea surface, viz. simultaneous reconstruction of several spatial snapshots of the surface in order to guarantee continuity of the sea surface both in space and time. Analysis of the WASS measurements show that the sea surface can be accurately estimated in space and time together, yielding associated directionalspectra and wave statistics at a point in time that agrees well with probabilistic models. In particular, WASS stereo imaging is able to capture typical features of the wave surface,especially the crest-to-trough asymmetry due to second order nonlinearities, and the observedshape of large waves are fairly described by theoretical models based on the theory of quasi-determinism (Boccotti, 2000). Further, we investigate the space-time extremes of the observed stationary sea states, viz. the largest surface wave heights expected over a given area during thesea state duration. The WASS analysis provides the first experimental proof that a space-time extreme is generally larger than that observed in time via point measurements, in agreement withthe predictions based on stochastic theories for global maxima of Gaussian fields.