基于矩阵逻辑方程的识别对象状态转化研究

进行错误识别,首先我们需要研究识别的对象.因此,研究首先将错误识别对象分为识别状态、真是状态、应该状态和目标状态等四种状态,并且讨论了几种类型之间的关系.最后运用矩阵逻辑方程求解了识别状态转化为目标状态的转化方式.     

Numerical analysis for the approximation of optimal control problems with pointwise observations

In this paper, we study the numerical methods for optimal control problems governed by elliptic PDEs with pointwise observations of the state. The first order optimality conditions as well as regularities of the solutions are derived. The optimal control and adjoint state have low regularities due to the pointwise observations. For the finite dimensional approximation, we use the standard conforming piecewise linear finite elements to approximate the state and adjoint state variables, whereas variational discretization is applied to the discretization of the control. A priori and a posteriori error estimates for the optimal control, the state and adjoint state are obtained. Numerical experiments are also provided to confirm our theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Traffic Flows and Product Form Solutions in Stochastic Transfer Networks

This paper focuses on product form and related tractable stationary distributions in a general class of stochastic networks with finite numbers of nodes such that their network states are changed through signal transfers as well as internal transitions. Signals may be customers in traditional queueing applications, but we do not make any restriction on their effects at departing as well as arriving nodes. They may also instantaneously move around among different nodes. Furthermore, signal routing may depend on the whole network state. For analytical simplicity, we assume that the state space is countable. For such a network, we propose an abstract model, called a stochastic transfer network, and consider the stationary distribution of the network state. We introduce conditional traffic rates for arrivals and departures. Using them, we consider when the network has product form or some other tractable stationary distributions.     

Convergent expansions in non-relativistic qed: Analyticity of the ground state

We consider the ground state of an atom in the framework of non-relativistic qed. We show that the ground state as well as the ground state energy are analytic functions of the coupling constant which couples to the vector potential, under the assumption that the atomic Hamiltonian has a non-degenerate ground state. Moreover, we show that the corresponding expansion coefficients are precisely the coefficients of the associated Raleigh-Schrödinger series. As a corollary we obtain that in a scaling limit where the ultraviolet cutoff is of the order of the Rydberg energy the ground state and the ground state energy have convergent power series expansions in the fine structure constant α, with α dependent coefficients which are finite for α?0.     

Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation

In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the flux perturbation vanishes,they converge to the delta-shock and vacuum state solutions of the zero-pressure flow,respectively.Secondly,we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure.Furthermore,we rigorously prove that,as the two-parameter flux perturbation vanishes,any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow;any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Finally,numerical results are given to present the formation processes of delta shock waves and vacuum states.     

Turing instability and coexistence in an extended Klausmeier model with nonlocal grazing

In this paper, we study the coexistence of an extended Klausmeier model with cross-diffusion and nonlocal sustained grazing. First, we analyze a saddle–node bifurcation of spatially homogeneous system. Second, we focus on the reaction–diffusion system with nonlocal sustained grazing. Our main result is that nonlocal terms promote linear stability, and the system may produce pattern under the influences of self-diffusion and cross-diffusion. Moreover, both the grazing parameter and rainfall rate can induce transitions among bare soil state, vegetation pattern state and homogeneous vegetation state. Finally, we address the nonlocal reaction–diffusion system as a bifurcation problem, and analyze the existence and stability of bifurcation solutions. Furthermore, numerical simulations have been illustrated to verify our theoretical findings.     

Bounded pseudo-hoops with internal states

State MV-algebras were introduced by Flaminio and Montagna as MV-algebras with internal states. Di Nola and Dvure?enskij presented the notion of state-morphism MV-algebra which is a stronger variation of a state MV-algebra. Rach?nek and ?alounová introduced state GMV-algebras (pseudo-MV algebras) and state-morphism GMV-algebras, while the state BL-algebras and state-morphism BL-algebras were defined by Ciungu, Dvure?enskij and Hy?ko. Recently, Dvure?enskij, Rach?nek and ?alounová presented state R?-monoids and state-morphism R?-monoids. In this paper we study these concepts for more general fuzzy structures, namely pseudo-hoops and we present state pseudo-hoops and state-morphism pseudo-hoops.     

A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers

In this paper we consider an unreliable single server retrial queue accepting two types of customers, with negative arrivals, preemptive resume priorities and vacations. A distinguishing feature of the model is that the rates of the Poisson arrival process depends on the server state. For this model we investigate the stability conditions and the joint queue length distribution in steady state. We also prove that our model satisfies the stochastic decomposition property. Transient, as well as steady state solutions for reliability measures are obtained. Finally, numerical results demonstrate the typical features of the model under consideration.     

Solution to nonlinear MHDS arising from optimal growth problems

In this paper we propose a method for solving in closed form a general class of nonlinear modified Hamiltonian dynamic systems (MHDS). This method is used to analyze the intertemporal optimization problem from endogenous growth theory, especially the cases with two controls and one state variable. We use the exact solutions to study both uniqueness and indeterminacy of the optimal path when the dynamic system has not a well-defined isolated steady state. With this approach we avoid the linearization process, as well as the reduction of dimension technique usually applied when the dynamic system offers a continuum of steady states or no steady state at all.     

Dirichlet Boundary Control of Semilinear Parabolic Equations Part 1: Problems with No State Constraints

This paper is concerned with distributed and Dirichlet boundary controls of semilinear parabolic equations, in the presence of pointwise state constraints. The paper is divided into two parts. In the first part we define solutions of the state equation as the limit of a sequence of solutions for equations with Robin boundary conditions. We establish Taylor expansions for solutions of the state equation with respect to perturbations of boundary control (Theorem 5.2). For problems with no state constraints, we prove three decoupled Pontryagin's principles, one for the distributed control, one for the boundary control, and the last one for the control in the initial condition (Theorem 2.1). Tools and results of Part 1 are used in the second part to derive Pontryagin's principles for problems with pointwise state constraints. Accepted 12 July 2001. Online publication 21 December 2001.     

Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup

This paper is a survey for development of linear distributed parameter system. At first we point out some questions existing in current study of control theory for the L^p linear system with an unbounded control operator and an unbounded observation operator, such as stabilization problem and observer theory that are closely relevant to state feedback operator. After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations. As a principle, we propose a concept of admissible state feedback operator for system (A, B). Finally we give an existence result of admissible state feedback operators, including semigroup generation and the equivalent conditions of admissibility of state feedback operators, for an L^p well-posed system.     

A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM

In this paper, we study numerical methods for an optimal control problem with pointwise state constraints. The traditional approaches often need to deal with the deltasingularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation. In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms （nonconforming finite element approximation） are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.     

Stability of interconnected impulsive switched systems subject to state dimension variation

The contribution of this article is twofold. First we deal with the stability of continuous-time interconnected impulsive switched systems for which the dimension of the system’s state vector may change at different modes. A dwell time condition is derived to ensure the exponential convergence of the state trajectories, and when the system is subject to a non-vanishing perturbation, a superior bound of the state trajectories is provided as well. The main advantage of the solution we propose is its direct application to practical fields such as metallurgy or traffic control through the use of semi-definite programming solvers. Second, we introduce in the framework a platoon of vehicles in automated highway systems where vehicles may join or leave the platoon. Then, we detail the longitudinal stability problem of such a system and illustrate the features of the proposed stability conditions through numerical simulations.     

Asymptotic properties of constrained Markov Decision Processes

We present in this paper several asymptotic properties of constrained Markov Decision Processes (MDPs) with a countable state space. We treat both the discounted and the expected average cost, with unbounded cost. We are interested in (1) the convergence of finite horizon MDPs to the infinite horizon MDP, (2) convergence of MDPs with a truncated state space to the problem with infinite state space, (3) convergence of MDPs as the discount factor goes to a limit. In all these cases we establish the convergence of optimal values and policies. Moreover, based on the optimal policy for the limiting problem, we construct policies which are almost optimal for the other (approximating) problems. Based on the convergence of MDPs with a truncated state space to the problem with infinite state space, we show that an optimal stationary policy exists such that the number of randomisations it uses is less or equal to the number of constraints plus one. We finally apply the results to a dynamic scheduling problem.This work was partially supported by the Chateaubriand fellowship from the French embassy in Israel and by the European Grant BRA-QMIPS of CEC DG XIII     

Quantity of information; Comparison between information systems: 1. Non-fuzzy states

In statistical theory, experiments or probabilistic information systems are supposed to be informative, since they reduce the amount of uncertainty associated with the states of nature. For the case that the available information systems are vague (fuzzy information systems), H. Tanaka, T. Okuda and K. Asai have proven, using the ‘measure of information’ as provided by ‘entropy’, that the fuzzy information systems are informative too.Now, we wish to state and to study a criterion in order to compare fuzzy information systems by the ‘quantity of information of a fuzzy information system’ (defined by Tanaka et al.).In this first paper we consider the situation where we require information about the original state space (non-fuzzy state space).The second paper will deal with the situation where we require only information on certain vague states (fuzzy states).     

Quantity of information; comparison between information systems: 2. Fuzzy states

In statistical theory, experiments or probabilistic information systems are supposed to be informative, since they reduce the amount of uncertainty associated with the states of nature. For the case that the available information systems are vague (fuzzy information systems), H. Tanaka, T. Okuda and K. Asai have proven, using the ‘measure of information’ as provided by ‘entropy’, that the fuzzy information systems are informative too.Now, we wish to state and to study a criterion in order to compare fuzzy information systems by the ‘quantity of information of a fuzzy information system’ (defined by Tanaka et al.).In the first paper we considered the situation where we require information about the original state space (non-fuzzy state space).This second paper deals with the situation where we require only information on certain vague states (fuzzy states).     

A phase field approach to shape optimization in Navier–Stokes flow with integral state constraints

We consider the shape optimization of an object in Navier–Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we extend the results of earlier works concerning the existence of optimal shapes and the derivation of first order optimality conditions. The control variable is a phase field function that prescribes the shape and topology of the object, while the state variables are the velocity and the pressure of the fluid. In our analysis, we cover a multitude of constraints which include constraints on the center of mass, the volume of the fluid region, and the total potential power of the object. Finally, we present numerical results of the optimization problem that is solved using the variable metric projection type (VMPT) method proposed by Blank and Rupprecht, where we consider one example of topology optimization without constraints and one example of maximizing the lift of the object with a state constraint, as well as a comparison with earlier results for the drag minimization.     

Bilinear minimax control problems for a class of parabolic systems with applications to control of nuclear reactors

This paper considers the bilinear minimax control problem of an important class of parabolic systems with Robin boundary conditions. Such systems are linear on state variables when the control and disturbance are fixed, and linear on the control or disturbance when the state variables are fixed. The objective is to maintain target state variables by taking account the influence of noises in data, while a desired power level and adjustment costs are taken into consideration. Firstly we introduce some classes of bilinear systems and obtain the existence and the uniqueness of the solution, as well as stability under mild assumptions. Afterwards the minimax control problem is formulated. We show the existence of an optimal solution, and we also find necessary optimality conditions. Finally, to illustrate the abstract results, we present two examples of neutron fission systems.     

有界域上三维非等熵半导体方程解的渐近性(英文)

本文讨论了一类三维非等熵半导体方程. 利用能量估计法, 证明了热平衡稳态解的存在唯一性.然后, 得到了Cauchy-Neumann问题光滑解的整体存在性以及当t→ +∞这种光滑解以指数速度收敛到稳定解, 改进了文献[12]的结果.     

The impact of finite precision arithmetic and sensitivity on the numerical solution of partial differential equations

In this paper, we address some fundamental issues concerning “time marching” numerical schemes for computing steady state solutions of boundary value problems for nonlinear partial differential equations. Simple examples are used to illustrate that even theoretically convergent schemes can produce numerical steady state solutions that do not correspond to steady state solutions of the boundary value problem. This phenomenon must be considered in any computational study of nonunique solutions to partial differential equations that govern physical systems such as fluid flows. In particular, numerical calculations have been used to “suggest” that certain Euler equations do not have a unique solution. For Burgers' equation on a finite spatial interval with Neumann boundary conditions the only steady state solutions are constant (in space) functions. Moreover, according to recent theoretical results, for any initial condition the corresponding solution to Burgers' equation must converge to a constant as t → ∞. However, we present a convergent finite difference scheme that produces false nonconstant numerical steady state “solutions.” These erroneous solutions arise out of the necessary finite floating point arithmetic inherent in every digital computer. We suggest the resulting numerical steady state solution may be viewed as a solution to a “nearby” boundary value problem with high sensitivity to changes in the boundary conditions. Finally, we close with some comments on the relevance of this paper to some recent “numerical based proofs” of the existence of nonunique solutions to Euler equations and to aerodynamic design.