General stochastic hybrid systems: modelling and optimal control

Bujorianu, Manuela L.; Lygeros, John

doi:10.1109/cdc.2004.1430320

Cited by 74 publications

(67 citation statements)

References 2 publications

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“…The RTS has also 6 transitions, indexed by e 1 ,...,e 6 . Consider the κ vector equal to (1,0,0,1,1,1): edges e 1 ,e 4 ,e 5 ,e 6 will be approximated as continuous, while the other two remain discrete. The relation ∼ κ has a quotient state space containing two classes: S 1 ={gene 0 } and S 2 ={gene 1 ,gene 2 }.…”

Section: Definition 62mentioning

confidence: 99%

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(Hybrid) automata and (stochastic) programs * The hybrid automata lattice of a stochastic program

Bortolussi¹,

Policriti²

2011

Journal of Logic and Computation

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We define a semantics for stochastic Concurrent Constraint Programming (sCCP), a stochastic process algebra, in terms of stochastic hybrid automata with piecewise deterministic continuous dynamics. To each program we associate a lattice of hybrid models, parameterized with respect to the degree of discreteness left. We study some properties of this lattice, presenting also an alternative semantics in which the degree of discreteness can be dynamically changed.

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Section: Definition 62mentioning

confidence: 99%

“…What we are proposing here is a technique to associate programs as network of interacting agents and simulation tools with specific characteristics. The special feature of the simulation tools is that they are hybrid, in the sense that both discrete and continuous descriptions of the dynamics of a given system co-exist [5,27,36].…”

Section: Introductionmentioning

confidence: 99%

(Hybrid) automata and (stochastic) programs * The hybrid automata lattice of a stochastic program

Bortolussi¹,

Policriti²

2011

Journal of Logic and Computation

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“…We adopt the general stochastic hybrid system model presented in Bujorianu et al [2004] and Bujorianu et al [2006]. In this subsection the model is described and the notation is established.…”

Section: The Computational Modelmentioning

confidence: 99%

State constrained reachability for stochastic hybrid systems

Bujorianu

2011

Nonlinear Analysis: Hybrid Systems

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The stochastic hybrid systems constitute well established classes of realistic models of hybrid discrete/continuous dynamics subject to random perturbations, autonomous uncontrollable transitions, nondeterminism or uncertainty. Stochastic reachability analysis is a key factor in the verification and deployment of stochastic hybrid systems. The encouraging recent progress prompts us to refine the problem to cover more realistic situations. We extend the so called constrained reachability problem from the probabilistic discrete case to stochastic hybrid systems. Then we define mathematically this problem, and we obtain the reach probabilities as solutions of a boundary value problem. The last problem is well studied and numerical, even symbolic solutions exist. This characterization is useful in stochastic control, in probabilistic path planning and for nano-systems.

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“…Continuous-time stochastic hybrid systems (ct-SHS) are a natural model for cyber-physical systems operating under uncertainty [6,8]. A ct-SHS has a hybrid state space consisting of discrete modes and, for each mode, a set of continuous states (called the invariant).…”

Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Method for Statistical Model Checking of Hybrid Systems

Soudjani

Majumdar

Nagapetyan

2017

Quantitative Evaluation of Systems

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Abstract. We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo method (MLMC) and work on a sequence of discrete-time stochastic processes whose executions approximate and converge weakly to that of the original continuous-time stochastic hybrid system with respect to satisfaction of the property of interest. With focus on bounded-horizon reachability, we recast the model checking problem as the computation of the distribution of the exit time, which is in turn formulated as the expectation of an indicator function. This latter computation involves estimating discontinuous functionals, which reduces the bound on the convergence rate of the Monte Carlo algorithm. We propose a smoothing step with tunable precision and formally quantify the error of the MLMC approach in the mean-square sense, which is composed of smoothing error, bias, and variance. We formulate a general adaptive algorithm which balances these error terms. Finally, we describe an application of our technique to verify a model of thermostatically controlled loads.

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General stochastic hybrid systems: modelling and optimal control

Cited by 74 publications

References 2 publications

(Hybrid) automata and (stochastic) programs * The hybrid automata lattice of a stochastic program

(Hybrid) automata and (stochastic) programs * The hybrid automata lattice of a stochastic program

State constrained reachability for stochastic hybrid systems

Multilevel Monte Carlo Method for Statistical Model Checking of Hybrid Systems

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