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

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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.

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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

Auxin elicits diverse cell behaviors through a simple nuclear signaling pathway initiated by degradation of Aux/IAA co-repressors. Our previous work revealed that members of the large Arabidopsis Aux/IAA family exhibit a range of degradation rates in synthetic contexts. However, it remained an unresolved issue whether differences in Aux/IAA turnover rates played a significant role in plant responses to auxin. Here, we use the well-established model of lateral root development to directly test the hypothesis that the rate of auxin-induced Aux/IAA turnover sets the pace for auxin-regulated developmental events. We did this by generating transgenic plants expressing degradation rate variants of IAA14, a crucial determinant of lateral root initiation. Progression through the well-established stages of lateral root development was strongly correlated with the engineered rates of IAA14 turnover, leading to the conclusion that Aux/IAAs are auxin-initiated timers that synchronize developmental transitions.

Auxin-induced degradation dynamics set the pace for lateral root development

We consider a network of mobile agents in an initially unknown acyclic network configuration and the problem of reconfiguring them into a desired network topology and formation geometry while maintaining connectivity in an asynchronous network. We model the system and solution as an embedded graph grammar and use a method of lexicographically ordered Lyapunov functions to show the system converges non-deterministically regardless of the initial network structure and the order of the communication events.

Non-deterministic reconfiguration of tree formations

Mobile robots are complex systems that combine mechanical elements such as wheels and gears, electromechanical devices such as motors, clutches and brakes, digital circuits such as processors and smart sensors, and software programs such as embedded controllers. They have mechanical constraints (e.g., a carlike robot cannot move sideways), limited energy resources, and computation, sensing, and communication capabilities. They operate in environments cluttered with possibly moving and shape changing obstacles, and their objectives can change over time, such as in the case of appearing and disappearing targets. Robot motion planning and control is the problem of automatic construction of robot control strategies from task specifications given in high-level, human-like language. The challenge in this area is the development of computationally efficient frameworks allowing for systematic, provably correct, control design accommodating both the robot constraints and the complexity of the environment, while at the same time allowing for expressive task specifications. Comments Copyright 2007 IEEE. Reprinted from IEEE Robotics and Automation, Volume 14, Issue 1, March 2007, pages 51-70. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. Author(s) Calin Belta, Antonio Bicci, Magnus Egerstedt, Emilio Frazzoli, Eric Klavins, and George J. Pappas This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/232

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Symbolic Control and Planning of Robotic Motion (Grand Challenges of Robotics)

A true engineering framework for synthetic multicellular systems requires a programmable means of cell-cell communication. Such a communication system would enable complex behaviors, such as pattern formation, division of labor in synthetic microbial communities, and improved modularity in synthetic circuits. However, it remains challenging to build synthetic cellular communication systems in eukaryotes due to a lack of molecular modules that are orthogonal to the host machinery, easy to reconfigure, and scalable. Here, we present a novel cell-to-cell communication system in Saccharomyces cerevisiae (yeast) based on CRISPR transcription factors and the plant hormone auxin that exhibits several of these features. Specifically, we engineered a sender strain of yeast that converts indole-3-acetamide (IAM) into auxin via the enzyme iaaH from Agrobacterium tumefaciens. To sense auxin and regulate transcription in a receiver strain, we engineered a reconfigurable library of auxin degradable CRISPR transcription factors (ADCTFs). Auxin-induced degradation is achieved through fusion of an auxin sensitive degron (from IAA co-repressors) to the CRISPR TF and co-expression with an auxin F-box protein. Mirroring the tunability of auxin perception in plants, our family of ADCTFs exhibits a broad range of auxin sensitivities. We characterized the kinetics and steady state behavior of the sender and receiver independently, and in co-cultures where both cell types were exposed to IAM. In the presence of IAM, auxin is produced by the sender cell and triggers de-activation of reporter expression in the receiver cell. The result is an orthogonal, rewireable, tunable, and arguably scalable cell-cell communication system for yeast and other eukaryotic cells.

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Cell-cell communication in yeast using auxin biosynthesis and auxin responsive CRISPR transcription factors

Control algorithms are difficult to scale up to large decentralized systems because of potentially complex couplings between components. As a result, many such systems function conservatively—damping out most of their energy and moving slowly or in a start-stop fashion. Synthesis tools for dynamical behaviors that admit a modular, bottom-up approach attempt to address this problem. Without such tools, the full potential of modern actuators, sensors and computing power likely cannot be realized, dooming robots (and more generally, physically situated computing systems) to a clumsy and inefficient future. 
This dissertation describes efforts to provide a formal basis for designing and verifying decentralized control algorithms for robotic systems such as factories, dynamic manipulators, hoppers and walkers. The methods are based on synthesis and, particularly, composition. The idea behind the compositional approach is simple. A designer should not have to start from scratch when building complicated systems. Instead knowledge of how to make a machine do two tasks separately should be leveraged to make the machine do the two tasks in some combination. 
To avoid the complexity of arbitrary couplings, we consider systems that may be decomposed in very regular ways. In particular, we focus on methods for coordinating multiple cyclic behaviors, based on defining ideal, model dynamical systems called reference fields. In using reference fields to control coupled cyclic systems, it is assumed that each cyclic system can be continuously actuated. However, many tasks in robotics, such as “juggling” and hopping, allow only intermittent control. Thus, we also show that reference fields can be used as the basis for controlling these more complicated tasks. Finally, reference fields are applied to the control of a six-legged, scampering robot and the performance of the approach is examined with respect to the speed and power consumption of the robot.

Eric Klavins

Papers

Auxin-induced degradation dynamics set the pace for lateral root development

Non-deterministic reconfiguration of tree formations

Symbolic Control and Planning of Robotic Motion (Grand Challenges of Robotics)

Cell-cell communication in yeast using auxin biosynthesis and auxin responsive CRISPR transcription factors

Decentralized phase regulation of cyclic robotic systems