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147
Stochastic Hybrid Systems: Application to Communication Networks
 in Hybrid Systems: Computation and Control, ser. Lect. Notes in Comput. Science
, 2004
"... Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continu ..."
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Cited by 68 (14 self)
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Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for PiecewiseDeterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for onoff TCP flows that considers both the congestionavoidance and slowstart modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finitedimensional model. This model shows that, for transfersize distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms. 1
Eventtriggered Control for MultiAgent Systems
, 2009
"... Eventdriven strategies for multiagent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The control actuation updates considered in this paper are eventdriven, depending on ..."
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Cited by 60 (18 self)
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Eventdriven strategies for multiagent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The control actuation updates considered in this paper are eventdriven, depending on the ratio of a certain measurement error with respect to the norm of a function of the state, and are applied to a first order agreement problem. A centralized formulation of the problem is considered first and then the results are extended to the decentralized counterpart, in which agents require knowledge only of the states of their neighbors for the controller implementation.
Towards a geometric theory of hybrid systems
 In HSCC’00, number 1790 in LNCS
, 2000
"... Abstract. We propose a framework for a geometric theory of hybrid systems. Given a deterministic, nonblocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non ..."
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Cited by 55 (18 self)
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Abstract. We propose a framework for a geometric theory of hybrid systems. Given a deterministic, nonblocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally nonsmooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.
Temporal logic motion planning for dynamic robots,”
 Automatica,
, 2009
"... Abstract In this paper, we address the temporal logic motion planning problem for mobile robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like seque ..."
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Cited by 51 (13 self)
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Abstract In this paper, we address the temporal logic motion planning problem for mobile robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like sequencing and obstacle avoidance. Our approach consists of three basic steps. First, we design a control law that enables the dynamic model to track a simpler kinematic model with a globally bounded error. Second, we built a robust temporal logic specification that takes into account the tracking errors of the first step. Finally, we solve the new robust temporal logic path planning problem for the kinematic model using automata theory and simple local vector fields. The resulting continuous time trajectory is provably guaranteed to satisfy the initial user specification.
Hybrid systems: Generalized solutions and robust stability
 In IFAC Symposium on Nonliear Control Systems
, 2004
"... Abstract: Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used ..."
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Cited by 46 (13 self)
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Abstract: Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used. Then a generalized solution definition is given that leads to continuity with respect to initial conditions and perturbations of the system data. This property enables new results on necessary conditions for asymptotic stability in hybrid systems.
Distributed control of robotic networks: a mathematical approach to motion coordination algorithms
, 2009
"... (i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 ..."
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Cited by 41 (1 self)
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(i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 “Distributed Control of Robotic Networks ” by F. Bullo, J. Cortés and S. Martínez
On synchronous robotic networks Part I: models, tasks, and complexity notions
 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference (CDCECC ’05
, 2005
"... This paper proposes a formal model for a network of robotic agents that move and communicate. Building on concepts from distributed computation, robotics and control theory, we define notions of robotic network, control and communication law, coordination task, and time and communication complexity. ..."
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Cited by 41 (18 self)
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This paper proposes a formal model for a network of robotic agents that move and communicate. Building on concepts from distributed computation, robotics and control theory, we define notions of robotic network, control and communication law, coordination task, and time and communication complexity. We illustrate our model and compute the proposed complexity measures in the example of a network of locally connected agents on a circle that agree upon a direction of motion and pursue their immediate neighbors. I.
A model for stochastic hybrid systems with application to communication networks
 Nonlinear Analysis Special Issue on Hybrid Systems
, 2004
"... Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuo ..."
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Cited by 36 (10 self)
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Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for PiecewiseDeterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for onoff TCP flows that considers both the congestionavoidance and slowstart modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finitedimensional model. This model shows that, for transfersize distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms.
Decentralized, adaptive control for coverage with networked robots
 In Robotics and Automation, 2007 IEEE International Conference on
, 2007
"... AbstractA decentralized, adaptive control law is presented to drive a network of mobile robots to a nearoptimal sensing configuration. The control law is adaptive in that it integrates sensor measurements to provide a converging estimate of the distribution of sensory information in the environme ..."
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Cited by 31 (10 self)
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AbstractA decentralized, adaptive control law is presented to drive a network of mobile robots to a nearoptimal sensing configuration. The control law is adaptive in that it integrates sensor measurements to provide a converging estimate of the distribution of sensory information in the environment. It is decentralized in that it requires only information local to each robot. A Lyapunovtype proof is used to show that the control law causes the network to converge to a nearoptimal sensing configuration, and the controller is demonstrated in numerical simulations. This technique suggests a broader application of adaptive control methodologies to decentralized control problems in unknown dynamical environments.
Connectedness Preserving Distributed Swarm Aggregation for Multiple Kinematic Robots
 IEEE TRANSACTIONS ON ROBOTICS
"... A distributed swarm aggregation algorithm is developed for a team of multiple kinematic agents. Specifically, each agent is assigned with a control law which is the sum of two elements: a repulsive potential field, which is responsible for the collision avoidance objective, and an attractive poten ..."
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Cited by 30 (4 self)
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A distributed swarm aggregation algorithm is developed for a team of multiple kinematic agents. Specifically, each agent is assigned with a control law which is the sum of two elements: a repulsive potential field, which is responsible for the collision avoidance objective, and an attractive potential field, that forces the agents to converge to a configuration where they are close to each other. Furthermore, the attractive potential field forces the agents that are initially located within the sensing radius of an agent to remain within this area for all time. In this way, the connectivity properties of the initially formed communication graph are rendered invariant for the trajectories of the closedloop system. It is shown that under the proposed control law agents converge to a configuration where each agent is located at a bounded distance from each of its neighbors. The results are also extended to the case of nonholonomic kinematic unicycletype agents and to the case of dynamic edge addition. In the latter case, we derive a smaller bound in the swarm size than in the static case.