In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.

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Consensus problems in networks of agents with switching topology and time-delays

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations

/pdf/consensus-and-cooperation-in-networked-multi-agent-systems-5ame7z72ny.pdf

Consensus and Cooperation in Networked Multi-Agent Systems

BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

“Bioinformatics” 특집을 내면서

In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called /spl alpha/-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or /spl alpha/-agents, and virtual agents associated with /spl alpha/-agents called /spl beta/- and /spl gamma/-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.

/pdf/flocking-for-multi-agent-dynamic-systems-algorithms-and-5efqu9aidp.pdf

Flocking for multi-agent dynamic systems: algorithms and theory

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

We describe a method for the decentralized phase regulation of two coupled hybrid oscillators. In particular, we prove that the application of this synchronization method to two hopping robots, each of which individually achieves only asymptotically stable hopping, results in an asymptotically stable limit cycle for the coupled system exhibiting the desired phase difference. This extends our previous work wherein the application of the method to two individually deadbeat-stabilized oscillators (paddle juggling mechanisms) was shown to yield the desired result. Central to this method is the idea that cyclic systems may be composed into a larger, aggregate, cyclic system. Its application entails moving from physical coordinates (for example, the position and velocity of each constituent mechanism) to the coordinates of phase and phase velocity. Within this canonical coordinate system we construct a model dynamical system, called a reference field, which encodes the desired behavior of each cyclic system as well as the phase relationships between them. We then force the actual composite system to behave like the model.

/pdf/stability-of-coupled-hybrid-oscillators-pjiz6v523c.pdf

Stability of coupled hybrid oscillators

We address the problem of controlling large distributed robotic systems such as factories. We introduce tools which help us compose local, hybrid control programs for a class of distributed robotic systems, assuming a palette of controller for individual tasks is already constructed. These tools, which combine backchaining behaviors with Petri Nets, expand on successful work in sequential composition of robot behaviors. We apply these ideas to the design of a robotic bucket brigade and simple, distributed assembly tasks.

/pdf/a-formalism-for-the-composition-of-loosely-coupled-robot-53c3c81ina.pdf

A Formalism for the Composition of Loosely Coupled Robot Behaviors

The behavior of systems of stochastically interacting particles, be they molecules comprising a chemical reaction network or multi-robot systems in a stochastic environment, can be described using the Chemical Master Equation (CME). In this paper we extend the applicability of the CME to the case when the underlying system of particles is not well-mixed, by constructing an extended state space. The proposed approach fits into the general framework of approximating stochastic processes by Hidden Markov Models (HMMs). We consider HMMs where the hidden states are equivalence classes of states of some underlying process. The sets of equivalence classes we consider are refinements of macrostates used in the CME. We construct a series of HMMs that use the CME to describe their hidden states. We demonstrate the approach by building a series of increasingly accurate models for a system of robots that interact in a non-well-mixed manner.

/pdf/hidden-markov-models-for-non-well-mixed-reaction-networks-12smac69s7.pdf

Hidden Markov Models for non-well-mixed reaction networks

Stochastic differentiation and programmed cell death are common developmental processes in microbes, driving diverse altruistic behaviors that promote cooperation. Utilizing cell death in developmental programs requires control over the rate of differentiation to balance cell proliferation against the utility of sacrifice. However, the regulatory networks that control these behaviors are often complex and have yet to be successfully harnessed as biotechnology. Here, we engineered a synthetic developmental gene network that couples stochastic differentiation with programmed cell death to implement a two-member division of labor. Progenitor cellobiose consumer cells were engineered to grow on cellobiose and differentiate at a controlled rate into self-destructive altruists that release an otherwise sequestered cellulase enzyme payload through autolysis to form a developmental Escherichia coli consortium that utilizes cellulose for growth. We used an experimentally parameterized model of task switching, payload delivery and cellulose conversion to nutrients to set key parameters to achieve overall population growth supported by cellulase release, liberating 14-23% of the available carbon. An inevitable consequence of engineering altruistic developmental behaviors is the emergence of cheaters that undermine cooperation. We observed cheater phenotypes for consumers and altruists, identified mutational hotspots and constructed a predictive model of circuit longeivity based on mutation rate estimates for each mode of evolutionary escape. This work introduces the altruistic developmental program as a new tool for synthetic biology, demonstrates the utility of population dynamics models to engineer complex phenotypes and provides a testbed for probing the evolutionary biology of self-destructive altruism.

https://www.biorxiv.org/content/biorxiv/early/2016/11/12/086900.full.pdf

Self-destructive altruism in a synthetic developmental program enables complex feedstock utilization

A new biological device known as a 'load driver' improves the performance of synthetic circuits by insulating genetic parts from each other.

Eric Klavins

Papers

Stability of coupled hybrid oscillators

A Formalism for the Composition of Loosely Coupled Robot Behaviors

Hidden Markov Models for non-well-mixed reaction networks

Self-destructive altruism in a synthetic developmental program enables complex feedstock utilization

Lightening the load in synthetic biology