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100
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 67 (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
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 54 (19 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.
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 52 (17 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.
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 35 (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.
Is there life after zeno? taking executions past the breaking (zeno) point
 in Proceedings of the 25th American Control Conference
, 2006
"... Abstract — Understanding Zeno phenomena plays an important role in understanding hybrid systems. A natural—and intriguing—question to ask is: what happens after a Zeno point? Inspired by the construction of [9], we propose a method for extending Zeno executions past a Zeno point for a class of hybri ..."
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Cited by 28 (15 self)
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Abstract — Understanding Zeno phenomena plays an important role in understanding hybrid systems. A natural—and intriguing—question to ask is: what happens after a Zeno point? Inspired by the construction of [9], we propose a method for extending Zeno executions past a Zeno point for a class of hybrid systems: Lagrangian hybrid systems. We argue that after the Zeno point is reached, the hybrid system should switch to a holonomically constrained dynamical system, where the holonomic constraints are based on the unilateral constraints on the configuration space that originally defined the hybrid system. These principles are substantiated with a series of examples. I.
Sufficient conditions for the existence of zeno behavior
 44th IEEE Conference on Decision and Control and European Control Conference ECC (2005
, 2005
"... Abstract — In this paper, sufficient conditions for the existence of Zeno behavior in a class of hybrid systems are given; these are the first sufficient conditions on Zeno of which the authors are aware for hybrid systems with nontrivial dynamics. This is achieved by considering a class of hybrid s ..."
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Cited by 28 (12 self)
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Abstract — In this paper, sufficient conditions for the existence of Zeno behavior in a class of hybrid systems are given; these are the first sufficient conditions on Zeno of which the authors are aware for hybrid systems with nontrivial dynamics. This is achieved by considering a class of hybrid systems termed diagonal first quadrant (DFQ) hybrid systems. When the underlying graph of a DFQ hybrid system has a cycle, we can construct an infinite execution for this system when the vector fields on each domain satisfy certain assumptions. To this execution, we can associate a single discrete time dynamical system that describes its continuous evolution. Therefore, we reduce the study of executions of DFQ hybrid systems to the study of a single discrete time dynamical system. We obtain sufficient conditions for the existence of Zeno by determining when this discrete time dynamical system is exponentially stable. I.
Dynamical systems revisited: Hybrid systems with zeno executions
 Proc. Third International Workshop on Hybrid Systems: Computation and Control, volume 1790 of Lecture Notes in Computer Science
, 2000
"... Abstract. Results from classical dynamical systems are generalized to hybrid dynamical systems. The concept of ω limit set is introduced for hybrid systems and is used to prove new results on invariant sets and stability, where Zeno and nonZeno hybrid systems can be treated within the same framewor ..."
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Cited by 27 (3 self)
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Abstract. Results from classical dynamical systems are generalized to hybrid dynamical systems. The concept of ω limit set is introduced for hybrid systems and is used to prove new results on invariant sets and stability, where Zeno and nonZeno hybrid systems can be treated within the same framework. As an example, LaSalle’s Invariance Principle is extended to hybrid systems. Zeno hybrid systems are discussed in detail. The ω limit set of a Zeno execution is characterized for classes of hybrid systems. 1
Lecture notes on hybrid systems
, 2004
"... The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be hi ..."
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Cited by 22 (0 self)
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The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be highlighted. We will introduce general methods for investigating properties such as existence of solutions, reachability and decidability of hybrid systems. The methods will be demonstrated on the motivating applications. Students who successfully complete the course should be able to appreciate the diversity of phenomena that arise in hybrid systems and how discrete “discrete ” entities and concepts such as automata, decidability and bisimulation can coexist with continuous entities and
Laplacian sheep: Hybrid, stopgo policy for leaderbased containment control
 in Hybrid Systems: Computation and Control
, 2006
"... Abstract. The problem of driving a collection of mobile robots to a given target location is studied in the context of partial difference equations. In particular, we are interested in achieving this transfer while ensuring that the agents stay in the convex polytope spanned by dedicated leaderag ..."
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Cited by 21 (7 self)
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Abstract. The problem of driving a collection of mobile robots to a given target location is studied in the context of partial difference equations. In particular, we are interested in achieving this transfer while ensuring that the agents stay in the convex polytope spanned by dedicated leaderagents, whose dynamics will be given by a hybrid StopGo policy. The resulting system ensures containment through the enabling result that under a Laplacian, decentralized control strategy for the followers, these followers will converge to a location in the convex leader polytope, as long as the leaders are stationary and the interaction graph is connected. Simulation results testify to the viability of the proposed, hybrid control strategy. 1