14,117 research outputs found
Towards a General Theory of Stochastic Hybrid Systems
In this paper we set up a mathematical structure,
called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a
mixing mechanism of stochastic processes, introduced
by Meyer. We prove that Markov strings are strong Markov processes with the cadlag property. We then show how a very general class of stochastic hybrid processes can be embedded
in the framework of Markov strings. This class, which
is referred to as the General Stochastic Hybrid Systems (GSHS), includes as special cases all the classes of stochastic hybrid processes, proposed in the literature
Stability analysis of event-triggered anytime control with multiple control laws
To deal with time-varying processor availability and lossy communication
channels in embedded and networked control systems, one can employ an
event-triggered sequence-based anytime control (E-SAC) algorithm. The main idea
of E-SAC is, when computing resources and measurements are available, to
compute a sequence of tentative control inputs and store them in a buffer for
potential future use. State-dependent Random-time Drift (SRD) approach is often
used to analyse and establish stability properties of such E-SAC algorithms.
However, using SRD, the analysis quickly becomes combinatoric and hence
difficult to extend to more sophisticated E-SAC. In this technical note, we
develop a general model and a new stability analysis for E-SAC based on Markov
jump systems. Using the new stability analysis, stochastic stability conditions
of existing E-SAC are also recovered. In addition, the proposed technique
systematically extends to a more sophisticated E-SAC scheme for which, until
now, no analytical expression had been obtained.Comment: Accepted for publication in IEEE Transactions on Automatic Contro
Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays
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By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this technical note, the globally exponential stabilization problem is investigated for a general class of stochastic systems with both Markovian jumping parameters and mixed time-delays. The mixed mode-dependent time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. First, by introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem. Then, a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality (LMI) approach. Finally, it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of LMIs. Numerical simulation is carried out to demonstrate the effectiveness of the proposed methods.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany. Recommended by Associate Editor G. Chesi
A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
We propose a new sensitivity analysis methodology for complex stochastic
dynamics based on the Relative Entropy Rate. The method becomes computationally
feasible at the stationary regime of the process and involves the calculation
of suitable observables in path space for the Relative Entropy Rate and the
corresponding Fisher Information Matrix. The stationary regime is crucial for
stochastic dynamics and here allows us to address the sensitivity analysis of
complex systems, including examples of processes with complex landscapes that
exhibit metastability, non-reversible systems from a statistical mechanics
perspective, and high-dimensional, spatially distributed models. All these
systems exhibit, typically non-gaussian stationary probability distributions,
while in the case of high-dimensionality, histograms are impossible to
construct directly. Our proposed methods bypass these challenges relying on the
direct Monte Carlo simulation of rigorously derived observables for the
Relative Entropy Rate and Fisher Information in path space rather than on the
stationary probability distribution itself. We demonstrate the capabilities of
the proposed methodology by focusing here on two classes of problems: (a)
Langevin particle systems with either reversible (gradient) or non-reversible
(non-gradient) forcing, highlighting the ability of the method to carry out
sensitivity analysis in non-equilibrium systems; and, (b) spatially extended
Kinetic Monte Carlo models, showing that the method can handle high-dimensional
problems
Hybrid Behaviour of Markov Population Models
We investigate the behaviour of population models written in Stochastic
Concurrent Constraint Programming (sCCP), a stochastic extension of Concurrent
Constraint Programming. In particular, we focus on models from which we can
define a semantics of sCCP both in terms of Continuous Time Markov Chains
(CTMC) and in terms of Stochastic Hybrid Systems, in which some populations are
approximated continuously, while others are kept discrete. We will prove the
correctness of the hybrid semantics from the point of view of the limiting
behaviour of a sequence of models for increasing population size. More
specifically, we prove that, under suitable regularity conditions, the sequence
of CTMC constructed from sCCP programs for increasing population size converges
to the hybrid system constructed by means of the hybrid semantics. We
investigate in particular what happens for sCCP models in which some
transitions are guarded by boolean predicates or in the presence of
instantaneous transitions
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