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Abstract The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain. The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions. The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data. 相似文献
143.
This paper focuses on the class of finite-state, discrete-index, reciprocal processes (reciprocal chains). Such a class of processes seems to be a suitable setup in many applications and, in particular, it appears well-suited for image-processing. While addressing this issue, the aim is 2-fold: theoretic and practical. As to the theoretic purpose, some new results are provided: first, a general stochastic realization result is provided for reciprocal chains endowed with a known, arbitrary, distribution. Such a model has the form of a fixed-degree, nearest-neighbour polynomial model. Next, the polynomial model is shown to be exactly linearizable, which means it is equivalent to a nearest-neighbour linear model in a different set of variables. The latter model turns out to be formally identical to the Levi–Frezza–Krener linear model of a Gaussian reciprocal process, although actually non-linear with respect to the chain's values. As far as the practical purpose is concerned, in order to yield an example of application an estimation issue is addressed: a suboptimal (polynomial-optimal) solution is derived for the smoothing problem of a reciprocal chain partially observed under non-Gaussian noise. To this purpose, two kinds of boundary conditions (Dirichlet and Cyclic), specifying the reciprocal chain on a finite interval, are considered, and in both cases the model is shown to be well-posed, in a ‘wide-sense’. Under this view, some well-known representation results about Gaussian reciprocal processes extend, in a sense, to a ‘non-Gaussian’ case. 相似文献
144.
一类非齐次树上的Shannon-McMillan定理 总被引:2,自引:0,他引:2
通过构造适当的辅助鞅差序列,利用鞅差序列的收敛定理给出了一类特殊非齐次树上具有a.e.收敛性质的Shannon-M cM illan定理. 相似文献
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June?DongEmail author Ding?Zhang Hong?Yan Anna?Nagurney 《Annals of Operations Research》2005,135(1):155-178
In this paper, we present a supply chain network model with multiple tiers of decision-makers, consisting, respectively, of
manufacturers, distributors, and retailers, who can compete within a tier but may cooperate between tiers. We consider multicriteria
decision-making for both the manufacturers and the distributors whereas the retailers are subject to decision-making under
uncertainty since the demands associated with the product are random. We derive the optimality conditions for the decision-makers,
establish the equilibrium conditions, and derive the variational inequality formulation. We then utilize the variational inequality
formulation to provide both qualitative properties of the equilibrium product shipment, service level, and price pattern and
to propose a computational procedure, along with convergence results. This is the first supply chain network model to capture
both multicriteria decision-making and decision-making under uncertainty in an integrated equilibrium framework. 相似文献
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Resource availability optimization is studied on a server–client system where different users are partitioned into priority classes. The aim is to provide higher resource availability according to the priority of each class. For this purpose, resource reservation is modeled by a homogeneous continuous time Markov chain (CTMC), but also by a cyclic non-homogeneous Markov chain (CNHMC) as there is a cyclic behavior of the users’ requests for resources. The contribution of the work presented consists in the formulation of a multiobjective optimization problem for both the above cases that aims to determine the optimal resource reservation policy providing higher levels of resource availability for all classes. The optimization problem is solved either with known methods or with a proposed kind of heuristic algorithm. Finally, explicit generalized approximate inverse preconditioning methods are adopted for solving efficiently sparse linear systems that are derived, in order to compute resource availability. 相似文献
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