2017
DOI: 10.1016/j.automatica.2017.08.007
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Stochastic stability of Markov jump hyperbolic systems with application to traffic flow control

Abstract: International audienceIn this paper, we investigate the stochastic stability of linear hyperbolic conservation laws governed by a finite-state Markov chain. Both system matrices and boundary conditions are subject to the Markov switching. The existence and uniqueness of weak solutions are developed for the stochastic hyperbolic initial boundary value problem. By means of Lyapunov techniques some sufficient conditions are obtained by seeking the balance between the boundary condition and the transition probabil… Show more

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Cited by 62 publications
(18 citation statements)
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“…where the sign of the velocity (1 + γ)z − γw (positive or negative), indicates the freeway traffic lies in the free-flow or in the congested mode, as in [22]. We assume that the system (25) is strictly hyperbolic.…”
Section: Arz Model and Linearizationmentioning
confidence: 99%
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“…where the sign of the velocity (1 + γ)z − γw (positive or negative), indicates the freeway traffic lies in the free-flow or in the congested mode, as in [22]. We assume that the system (25) is strictly hyperbolic.…”
Section: Arz Model and Linearizationmentioning
confidence: 99%
“…We assume that the system (25) is strictly hyperbolic. Denote (w * , z * ) being the steady state of the system (25), the corresponding (ρ * , v * ) of the system (22), satisfying w * = v f or function v * = V(ρ * ). The deviations from the nominal states (w * , z * ) are defined as…”
Section: Arz Model and Linearizationmentioning
confidence: 99%
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“…Since second-order, PDE traffic flow models (i.e., systems that incorporate two PDE states, one for traffic density and one for traffic speed) constitute realistic descriptions of the traffic dynamics, capturing important phenomena, such as, for example, stop-and-go traffic, capacity drop, etc. [15], [28], [33], boundary control designs are recently developed for such systems [6], [26], [28], [49], [50], [53], [54] some of which are based on techniques originally developed for control of systems of hyperbolic PDEs, such as, for example, [12], [18], [25], [29], [31], [36], [46]. Even though simpler, first-order traffic flow models, in conservation law or Hamilton-Jacobi PDE formulation, are also important for modeling purposes.…”
Section: Introductionmentioning
confidence: 99%