A Sample-Path Condition for the Asymptotic Uniform Distribution of Clearing Processes

In this note we show that the asymptotic time-average distribution of a functional of cumulative input process associated with an imbedded point process follows as asymptotic uniform distribution almost surely under a mild regulatory sample-path condition. Examples from stochastic clearing processes, inventory systems and renewal theory are provided.     

Cascade Observer Design Method for Systems with Uncertainty

The asymptotic observer design problem is considered for a system with uncertainty (i.e., with an unknown bounded input) and with arbitrary relative order. If the zero dynamics is stable, then part of the state vector can be reconstructed asymptotically exactly, but so far there has not been an exhausting asymptotic observer design method for the part of the state vector formed by the derivatives of the measured output. We propose such a method for a system of second relative order and generalize the result to systems of arbitrary relative order.     

动态投入产出系统的稳定性分析

The dynamic input-output model is well known in economic theory and practice. In this paper, the asymptotic stability and balanced growth solutions of the dynamic input-output system are considered. Under some natural assumptions which do not require the technical coefficient matrix to be indecomposable,it has been proved that the dynamic input-output system is not asymptotically stable and the closed dynamic input-output model has a balanced growth solution.     

Quantitative analysis of continuous weighted marked graphs

This paper deals with the computation of the asymptotic firing rate vector and the stationary marking of continuous weighted marked graphs under infinite servers semantics. The continuous weighted marked graphs are a particular class of continuous Petri net where each place has exactly one input and one output transition. First, we give an explicit formula to compute the asymptotic firing rate vector of transitions using the structure of the given net. Then, under the assumption that there exists only one critical circuit in the strongly connected continuous neutral weighted marked graphs, an original approach to compute the vector of stationary marking is presented. Finally, an application to a flexible manufacturing system is given.     

Studying the dynamics of open cyclic replication systems

An open replication model with a matrix circulator is considered. The stability and asymptotic behavior of the system depending on the input parameters is studied.     

Adaptive stabilization of uncertain unified chaotic systems with nonlinear input

This paper addresses the problem of adaptive stabilization of uncertain unified chaotic systems with nonlinear input in the sector form. A novel representation of nonlinear input function, that is, a linear input with bounded time-varying coefficient, is firstly established. Then, an adaptive control scheme is proposed based on the new nonlinear input model. By using Barbalat’s lemma, the asymptotic stability of the closed-loop system is proved in spite of system uncertainties, external disturbance and input nonlinearity. One of the advantages of the proposed design method is that the prior knowledge on the plant parameter, the bound parameters of the uncertainties and the slope parameters inside the sector nonlinearity is not required. Finally, numerical simulations are performed to verify the analytical results.     

An adaptive sliding mode control scheme for a class of chaotic systems with mismatched perturbations and input nonlinearities

This paper is concerned with the stabilization problem for a class of chaotic systems with mismatched perturbations and input nonlinearities. A novel sliding surface is specially designed so that when the system enters the sliding mode, the mismatched perturbations can be effectively overcome and achieve asymptotic stability. Then, an adaptive sliding mode controller (ASMC) is proposed to drive the controlled state trajectories into the designated sliding surface in finite time even subjected to input nonlinearities. Finally, the corresponding numerical simulations are demonstrated to verify the effectiveness of proposed method.     

Asymptotic normality of the continuous-time stochastic approximation algorithm

In this paper the continuous-time stochastic approximation algorithm seeking for the zero of a regression function is considered when the measurement error is a stochastic process generated by an Ito integral as the input of a linear system. The conditions are given to guarantee the asymptotic normality of the algorithm which is modified from the Robbins-Monro procedure proposed for the case where the measurement error is a process of independent increment.     

非对称成长的三角洲

推导了岸线变化的非线性偏微分方程,把解展成某一小参数的渐近级数.然后使用Fourier变换求得Green函数,解就用Green函数来表示.所得的结果表明由于来自河流和沿岸流的输沙,三角洲的成长是非对称的,并对长江三角洲的非对称成长试作解释.     

Asymptotic evaluation of effective complex moduli of fibre‐reinforced viscoelastic composite materials

We propose an asymptotic approach for the evaluation of effective complex moduli of viscoelastic fibre‐reinforced composite materials. Our method is based on the homogenization technique. We start with a non‐trivial expansion of the input plane‐strain boundary value problem by ratios of visco‐elastic constants. This allows to simplify the governing equations to forms analogous to the complex transport problem. Then we apply the asymptotic homogenization method, coming from the original problem on multi‐connected domain to the cell problem, defined on a unit cell of the periodic structure. For the analytical solution of the cell problem we apply the boundary perturbation technique, the asymptotic expansion by a distance between two neighbouring fibres and the method of two‐point Padé approximants. As results we derive uniform analytical representations for effective complex moduli, valid for all values of the components volume fractions and properties.     

Guaranteed asymptotic stability for a class of uncertain linear dynamical systems

We consider a class of linear dynamical systems with bounded, Lebesgue-measurable uncertainties in the system and input matrices as well as in the input itself. A state feedback control is derived, which guarantees global, uniform asymptotic stability of the zero state; this control is continuous, except at the zero state.This paper is based in part on research supported by the National Science Foundation.     

Stabilization of infinite-dimensional undamped second order systems by using a parallel compensator

In this paper stabilization of infinite-dimensional undamped second-order systems is considered in the case where the input and output operators are collocated. The systems have an infinitenumber of poles and zeros on the imaginary axis. In the casewhere only position feedback is available, a parallel compensatoris effective. The stabilizer is constructed by a P-controllerfor the augmented system which consists of the controlled systemand a parallel compensator. The asymptotic stability of theaugmented system is proved by LaSalle's invariance principleunder compactness of the resolvent.     

Robust control for Takagi–Sugeno fuzzy systems with time-varying state and input delays

The paper investigates the robust control for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-varying state and input delays. Delay-dependent stabilization criterion is proposed to guarantee the asymptotic stabilization of fuzzy systems with parametric uncertainties. The result of [Lee HJ, Park JB, Joo YH. Robust control for uncertain Takagi–Sugeno fuzzy systems with time-varying input delay. ASME J Dyn Syst Meas Control 2005;127:302–6] is extended to uncertain fuzzy systems with time-varying state and input delays. Simulations show that significant improvement over the previous results can be obtained.     

A system-theoretic framework for a wide class of systems II: Input-to-output stability

In this work characterizations of the notion of Weighted Input-to-Output Stability (WIOS) for a wide class of systems with disturbances are given. Particularly, for systems with continuous dependence of the solution on the initial state and the input, the WIOS property is shown to be equivalent to robust forward completeness from the input and robust global asymptotic output stability for the corresponding input-free system.     

A Generalization of the Regularization Method to the Singularly Perturbed Integro-Differential Equations With Partial Derivatives

We generalize the Lomov’s regularization method to partial integro-differential equations. It turns out that the procedure for regularization and the construction of a regularized asymptotic solution essentially depend on the type of the integral operator. The most difficult is the case, when the upper limit of the integral is not a variable of differentiation. In this paper, we consider its scalar option. For the integral operator with the upper limit coinciding with the variable of differentiation, we investigate the vector case. In both cases, we develop an algorithm for constructing a regularized asymptotic solution and carry out its full substantiation. Based on the analysis of the principal term of the asymptotic solution, we study the limit in solution of the original problem (with the small parameter tending to zero) and solve the so-called initialization problem about allocation of a class of input data, in which the passage to the limit takes place on the whole considered period of time, including the area of boundary layer.     

Tail asymptotics for a Lévy-driven tandem queue with an intermediate input

We consider a Lévy-driven tandem queue with an intermediate input assuming that its buffer content process obtained by a reflection mapping has the stationary distribution. For this queue, no closed form formula is known, not only for its distribution but also for the corresponding transform. In this paper, we consider only light-tailed inputs. For the Brownian input case, we derive exact tail asymptotics for the marginal stationary distribution of the second buffer content, while weaker asymptotic results are obtained for the general Lévy input case. The results generalize those of Lieshout and Mandjes from the recent papers (Lieshout and Mandjes in Math. Methods Oper. Res. 66:275–298, 2007 and Queueing Syst. 60:203–226, 2008) for the corresponding tandem queue without an intermediate input.     

Stability and positivity of equilibria for subhomogeneous cooperative systems

Building on recent work on homogeneous cooperative systems, we extend results concerning stability of such systems to subhomogeneous systems. We also consider subhomogeneous cooperative systems with constant input, and relate the global asymptotic stability of the unforced system to the existence and stability of positive equilibria for the system with input.     

When are NP-hard location problems easy?

We discuss in this paper several location problems for which it is an NP-hard problem to find an approximate solution. Given certain assumptions on the input distributions, we present polynomial algorithms that deliver a solution asymptotically close to the optimum with probability that is asymptotically one (the exact nature of this asymptotic convergence is described in the paper). In that sense the subproblems defined on the specified family of inputs are in fact easy.This research was supported in part by the National Science Foundation under grant ECS-8204695.     

An accurate formula for the reconstruction of conductivity inhomogeneities

We carefully derive accurate asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. We then apply these accurate asymptotic formulae for the purpose of identifying the location and certain properties of the shape of the conductivity anomaly. Our designed real-time algorithm makes use of constant current sources. It is based on the observation in both the near and far field of the pattern of a simple weighted combination of the input currents and the output voltages. The mathematical analysis provided in this paper indicates that our algorithm is with a very high resolution and accuracy.     

Synchronization and anti-synchronization of chaotic oscillators under input saturation

This paper addresses the design of simple state feedback controllers for synchronization and anti-synchronization of chaotic oscillators under input saturation and disturbance. By employing sector condition, linear matrix inequality (LMI)-based sufficient conditions are derived to design (global or local) controllers for chaos synchronization. The proposed local synchronization strategy guarantees a region of stability in terms of difference between states of the master–slave systems. This region of stability can be enlarged by means of an LMI-based optimization algorithm, through which asymptotic synchronization of chaotic oscillators can be ensured for a large difference in their initial conditions. Further, a novel LMI-based robust control strategy is developed, for local synchronization of input-constrained chaotic oscillators, by providing an upper bound on synchronization error in terms of disturbance and initial conditions of chaotic systems. Moreover, the proposed robust state feedback control methodology is modified to provide an inaugural treatment for robust anti-synchronization of chaotic systems under input saturation and disturbance. The results of the proposed methodologies are verified through numerical simulations for synchronization and anti-synchronization of the master–slave chaotic Chua’s circuits under input saturation.