Pinning dynamic systems of networks with Markovian switching couplings and controller-node set

In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller-node set. Here, the coupling matrices and the controller-node sets change with time, induced by a continuous-time Markovian chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponentially stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller-node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, in particular, for the problem of spatial pinning control of network with mobile agents, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable sub-systems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.Comment: 9 pages; 3 figure

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations

Control Theory: Mathematical Perspectives on Complex Networked Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Its range of applicability and its techniques evolve rapidly with new developments in communication systems and electronic data processing. Thus, in recent years networked control systems emerged as a new fundamental topic, which combines complex communication structures with classical control methods and requires new mathematical methods. A substantial number of contributions to this workshop was devoted to the control of networks of systems. This was complemented by a series of lectures on other current topics like fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control

Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach

This paper presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on oscillator phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. Although the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of spacecraft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework

Improved Distributed Estimation Method for Environmental\ud time-variant Physical variables in Static Sensor Networks

In this paper, an improved distributed estimation scheme for static sensor networks is developed. The scheme is developed for environmental time-variant physical variables. The main contribution of this work is that the algorithm in [1]-[3] has been extended, and a filter has been designed with weights, such that the variance of the estimation errors is minimized, thereby improving the filter design considerably\ud and characterizing the performance limit of the filter, and thereby tracking a time-varying signal. Moreover, certain parameter optimization is alleviated with the application of a particular finite impulse response (FIR) filter. Simulation results are showing the effectiveness of the developed estimation algorithm

Computational Methods for Cognitive and Cooperative Robotics

In the last decades design methods in control engineering made substantial progress in the areas of robotics and computer animation. Nowadays these methods incorporate the newest developments in machine learning and artificial intelligence. But the problems of flexible and online-adaptive combinations of motor behaviors remain challenging for human-like animations and for humanoid robotics. In this context, biologically-motivated methods for the analysis and re-synthesis of human motor programs provide new insights in and models for the anticipatory motion synthesis. This thesis presents the author’s achievements in the areas of cognitive and developmental robotics, cooperative and humanoid robotics and intelligent and machine learning methods in computer graphics. The first part of the thesis in the chapter “Goal-directed Imitation for Robots” considers imitation learning in cognitive and developmental robotics. The work presented here details the author’s progress in the development of hierarchical motion recognition and planning inspired by recent discoveries of the functions of mirror-neuron cortical circuits in primates. The overall architecture is capable of ‘learning for imitation’ and ‘learning by imitation’. The complete system includes a low-level real-time capable path planning subsystem for obstacle avoidance during arm reaching. The learning-based path planning subsystem is universal for all types of anthropomorphic robot arms, and is capable of knowledge transfer at the level of individual motor acts. Next, the problems of learning and synthesis of motor synergies, the spatial and spatio-temporal combinations of motor features in sequential multi-action behavior, and the problems of task-related action transitions are considered in the second part of the thesis “Kinematic Motion Synthesis for Computer Graphics and Robotics”. In this part, a new approach of modeling complex full-body human actions by mixtures of time-shift invariant motor primitives in presented. The online-capable full-body motion generation architecture based on dynamic movement primitives driving the time-shift invariant motor synergies was implemented as an online-reactive adaptive motion synthesis for computer graphics and robotics applications. The last chapter of the thesis entitled “Contraction Theory and Self-organized Scenarios in Computer Graphics and Robotics” is dedicated to optimal control strategies in multi-agent scenarios of large crowds of agents expressing highly nonlinear behaviors. This last part presents new mathematical tools for stability analysis and synthesis of multi-agent cooperative scenarios.In den letzten Jahrzehnten hat die Forschung in den Bereichen der Steuerung und Regelung komplexer Systeme erhebliche Fortschritte gemacht, insbesondere in den Bereichen Robotik und Computeranimation. Die Entwicklung solcher Systeme verwendet heutzutage neueste Methoden und Entwicklungen im Bereich des maschinellen Lernens und der künstlichen Intelligenz. Die flexible und echtzeitfähige Kombination von motorischen Verhaltensweisen ist eine wesentliche Herausforderung für die Generierung menschenähnlicher Animationen und in der humanoiden Robotik. In diesem Zusammenhang liefern biologisch motivierte Methoden zur Analyse und Resynthese menschlicher motorischer Programme neue Erkenntnisse und Modelle für die antizipatorische Bewegungssynthese. Diese Dissertation präsentiert die Ergebnisse der Arbeiten des Autors im Gebiet der kognitiven und Entwicklungsrobotik, kooperativer und humanoider Robotersysteme sowie intelligenter und maschineller Lernmethoden in der Computergrafik. Der erste Teil der Dissertation im Kapitel “Zielgerichtete Nachahmung für Roboter” behandelt das Imitationslernen in der kognitiven und Entwicklungsrobotik. Die vorgestellten Arbeiten beschreiben neue Methoden für die hierarchische Bewegungserkennung und -planung, die durch Erkenntnisse zur Funktion der kortikalen Spiegelneuronen-Schaltkreise bei Primaten inspiriert wurden. Die entwickelte Architektur ist in der Lage, ‘durch Imitation zu lernen’ und ‘zu lernen zu imitieren’. Das komplette entwickelte System enthält ein echtzeitfähiges Pfadplanungssubsystem zur Hindernisvermeidung während der Durchführung von Armbewegungen. Das lernbasierte Pfadplanungssubsystem ist universell und für alle Arten von anthropomorphen Roboterarmen in der Lage, Wissen auf der Ebene einzelner motorischer Handlungen zu übertragen. Im zweiten Teil der Arbeit “Kinematische Bewegungssynthese für Computergrafik und Robotik” werden die Probleme des Lernens und der Synthese motorischer Synergien, d.h. von räumlichen und räumlich-zeitlichen Kombinationen motorischer Bewegungselemente bei Bewegungssequenzen und bei aufgabenbezogenen Handlungs übergängen behandelt. Es wird ein neuer Ansatz zur Modellierung komplexer menschlicher Ganzkörperaktionen durch Mischungen von zeitverschiebungsinvarianten Motorprimitiven vorgestellt. Zudem wurde ein online-fähiger Synthesealgorithmus für Ganzköperbewegungen entwickelt, der auf dynamischen Bewegungsprimitiven basiert, die wiederum auf der Basis der gelernten verschiebungsinvarianten Primitive konstruiert werden. Dieser Algorithmus wurde für verschiedene Probleme der Bewegungssynthese für die Computergrafik- und Roboteranwendungen implementiert. Das letzte Kapitel der Dissertation mit dem Titel “Kontraktionstheorie und selbstorganisierte Szenarien in der Computergrafik und Robotik” widmet sich optimalen Kontrollstrategien in Multi-Agenten-Szenarien, wobei die Agenten durch eine hochgradig nichtlineare Kinematik gekennzeichnet sind. Dieser letzte Teil präsentiert neue mathematische Werkzeuge für die Stabilitätsanalyse und Synthese von kooperativen Multi-Agenten-Szenarien

Contraction and partial contraction : a study of synchronization in nonlinear networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (p. 121-128).This thesis focuses on the study of collective dynamic behaviors, especially the spontaneous synchronization behavior, of nonlinear networked systems. We derives a body of new results, based on contraction and partial contraction analysis. Contraction is a property regarding the convergence between two arbitrary system trajectories. A nonlinear dynamic system is called contracting if initial conditions or temporary disturbances are forgotten exponentially fast. Partial contraction, introduced in this thesis, is a straightforward but more general application of contraction. It extends contraction analysis to include convergence to behaviors or to specific properties (such as equality of state components, or convergence to a manifold). Contraction and partial contraction provide powerful analysis tools to investigate the stability of large-scale complex systems. For diffusively coupled nonlinear systems, for instance, a general synchronization condition can be derived which connects synchronization rate to net- work structure explicitly. The results are applied to construct flocking or schooling models by extending to coupled networks with switching topology. We further study the networked systems with different kinds of group leaders, one specifying global orientation (power leader), another holding target dynamics (knowledge leader). In a knowledge-based leader-followers network, the followers obtain dynamics information from the leader through adaptive learning. We also study distributed networks with non-negligible time-delays by using simplified wave variables and other contraction-oriented analysis. Conditions for contraction to be preserved regardless of the explicit values of the time-delays are derived.(cont.) Synchronization behavior is shown to be robust if the protocol is linear. Finally, we study the construction of spike-based neural network models, and the development of simple mechanisms for fast inhibition and de-synchronization.by Wei Wang.Ph.D