Radially Stable Periodic Solutions for Radially Symmetric Keplerian-Like Systems

In this paper, we study the existence of radially stable periodic solutions of radially symmetric Keplerian-like systems. The proof is based on the third-order approximation method combined with the averaging method.     

Approximate Controllability for a Class of Linear Neutral Evolution Systems with Infinite Delay

This paper deals with the approximate controllability problem for a class of linear neutral evolution systems with infinite delay in Banach spaces. Since the concerned system involves additional linear terms, the fundamental solution theory is used to describe the mild solutions. Based on the spectral analysis and the adjoint system, sufficient conditions for the approximate controllability of the concerned system are established. The rank condition is also shown when the control space is finite-dimensional. A practical example is given to show the application of the obtained results.

     

On Properties of Solutions to Nonlinear Parabolic Equations of the Second Order

A quasilinear elliptic problem is considered for which conditions for existence and nonexistence of positive solutions are discussed.     

Normal Form for Second Order Differential Equations

Applying methods of CR-geometry, we give a solution to the local equivalence problem for second order (smooth or analytic) ordinary differential equations. We do so by presenting a complete normal form (which is smooth or analytic respectively) for this class of ordinary differential equations (ODEs). The normal form is optimal in the sense that it is defined up to the automorphism group of the model (flat) ODE y ^″ =?0. For a generic ODE, we also provide a unique (up to a discrete group action) normal form. By doing so, we give a solution to a problem which remained unsolved since the work of Arnold (1988). As another application of the normal form, we obtain distinguished curves associated with a differential equation that we call chains due to their analogy with the chains defined by Chern and Moser (Acta Math. 7;133:219–271).     

On the Existence of Positive Periodic Solutions for N-Species Lotka-Volterra Competitive Systems with Distributed Delays and Impulses

Journal of Dynamical and Control Systems - In the present paper, we investigate the existence of positive periodic solutions for an n-species Lotka-Volterra system with distributed delays and...     

Bounds for the Vanishing Order for Solutions of a Linear Differential System

We provide upper bounds for the order of vanishing of a polynomial restricted to a solution of a linear differential system through a nonsingular point. We deduce an estimate on the maximum order of inflection of the trajectories of a linear nonautonomous vector field.     

Boundary Exponential Stabilization for a Class of Coupled Reaction-Diffusion Equations with State Delay

A class of coupled parabolic PDEs with time delay is considered. We treat the problem of boundary exponential stabilization where the goal is to present a state feedback law with actuation on only one end of the domain which provide the exponential stability of the closed-loop system. We consider both the Dirichlet and Neumann boundary conditions. The corresponding proposed control law is given in explicit form. Numerical simulations are carried out to show the effectiveness of the obtained results.

     

Limit Cycles for a Class of Three-Dimensional Polynomial Differential Systems

Perturbing the system inside the family of polynomial differential systems of degree n in , we obtain at most n ² limit cycles using the first-order averaging theory. Moreover, there exist such perturbed systems having at least n ² limit cycles.      

Second Order Necessary Conditions for Optimal Impulsive Control Problems

First and second order necessary conditions of optimality for an impulsive control problem are presented and derived. One of the main features of these results is that no a priori normality assumptions are required and they are informative for abnormal control processes as well. This feature follows from the fact that the conditions are derived from an extremal principle, which is proved for an abstract minimization problem with equality and inequality type constraints and constraints given by convex cone.Two simple examples illustrate the power of our result.     

Constrained Optimal Control for a Class of Semilinear Infinite Dimensional Systems

The aim of this paper is to investigate a constrained optimal control problem governed by a class of semilinear infinite dimensional systems. For a state-quadratic cost functional and a closed convex set of admissible controls, the existence of an optimal control is proven, then this control is characterized for several cases of constraints. An algorithm is developed in order to compute the optimal control. The results are illustrated through simulations of a transport equation and a wave equation.     

Analytic Solutions of Systems

In this paper, functional series solutions of the nonlinear analytic system for the unknown state variable x(t), and functional series solutions of the analytic infinite-dimension

Remarks on Periodic Solutions of Ordinary Differential Equations

The paper is written in comparison of the power of the Leray–Schauder method and the method of translation along trajectories in the boundary values problems theory for ordinary differential equations. The author suggests a new version of the continuation principle for the method of translation along trajectories. Then he shows how to use the new approach to obtain in a simpler way a reinforced analog of a thaeorem of J. Mawhin.     

Asymptotics of Solutions of Periodic Problem for Generalized Nonlinear Hamiltonian System Singularly Perturbed by a Matrix

The paper deals with the periodic problem for a generalized nonlinear Hamiltonian system, which appears from the control optimality condition for the periodic problem of the minimization of the functional on trajectories of the equation with the operator A + ɛB standing before the derivative, where the operator A is singular and A + ɛB is invertible for sufficiently small ɛ > 0. Under some conditions, the asymptotic solution of such problem has been constructed in the form of the series with respect to nonnegative integer powers of ɛ. The solvability of the considered problem has also been established for sufficiently small ɛ > 0. This work was supported by the Russian Fundamental Research Foundation (project No. 06–01–00296).     

Time-Varying z-Transform for the Analysis of Discrete-Time Linear Time Periodic Systems

This article deals with a new representation of linear discrete-time periodic systems. This representation, based on the time-varying z-transform, turns out to be highly efficient in the field of automatic control, when an appropriate choice of the sampling period is made. This representation permits to extend many well-known theorems, in particular, the initial- and final-value theorems, to the case of these systems and to predict the presence of limit cycles. Finally, this representation can be used to establish an extension of the Nyquist criterion to the feedback discrete-time periodic systems.     

Stochastic Control of a Class of Dynamical Systems via Path Limits

Journal of Dynamical and Control Systems - Some limit theorems are derived for a class of controled Markov systems with small noises. The aim is to understand the effects of strategies of actions...     

Fuzzy Variable Structure Control of a Class of Nonlinear Sampled-Data Systems

A novel approach to the fuzzy variable structure control is presented. The method is applicable to a class of discrete-time multi-input, multi-output systems. The controller for each subsystem is a two-input single-output fuzzy inference system partitioning the input space. The scheme presented analytically demonstrates that an appropriate tuning of the defuzzifier parameters can drive the plant to the desired sliding regime. The analysis begins with the extraction of the equivalent measure of the applied control signal, and continues with the proof of convergence claims for the discrete time sliding mode control. The method discussed has been applied to a double pendulum system, whose dynamics is assumed to be unknown, and the mathematical claims of the paper have been justified through a series of simulations. The results observed strongly recommend the use of the algorithm in the cases where the tracking precision and robustness against disturbances are sought.     

随机时滞电力系统稳定性分析

以励磁系统输入信号延时作为时滞环节,并通过引入负荷扰动项,建立单机无穷大随机时滞系统的数学模型;仿真获得随机时滞电力系统的受扰轨迹,分析不同时滞、不同扰动强度下随机时滞电力系统的稳定性;负荷模型分别采用恒阻抗、恒功率、恒电流模型,分析比较采用不同负荷模型对系统稳定性的影响,分析表明3种负荷模型所能承受的时滞上限能力从大到小依次为:恒阻抗模型、恒电流模型、恒功率模型。     

管道内水流冲击滞留气团的二阶Godunov数学模型

长距离输水、城市供排水等工程管道系统中常存在水流冲击滞留气团的现象,极可能产生异常压力波动,严重时甚至发生爆管事故.对此,提出将一种准确高效的非恒定摩阻模型引入水流冲击滞留气团的计算中,建立了考虑非恒定摩阻的二阶Godunov模型;并采用“虚拟单元”处理上游入口边界及下游水气交界面,实现了边界通量和内部单元通量的统一计...