一类具有非光滑周期扰动Duffing系统的混沌预测

研究了一类具有非光滑周期扰动Duffing系统的动力学行为,尝试采用Fourier级数展开的方法来处理系统的非光滑特性,并在此基础上利用Melnikov方法给出了该系统出现混沌的解析条件.最后,数值模拟的结果显示了该方法的有效性.     

一类非光滑对称三次系统的全局分支

该文对一类对称三次Hamilton系统在非光滑对称摄动下产生的极限环数目进行研究.通过多参数摄动理论和定性分析方法,得到这类在非光滑摄动下的三次系统可以存在至少19个极限环.     

一类非完整系统的Lagrange定理及其应用

本文研究一类非完整系统平衡位置流形的稳定性问题·利用Ляпунов直接法和稳定性定义将完整系统的Ｌａｇｒａｎｇｅ定理推广到一类非完整保守系统与耗散系统，并对该类非完整系统平衡位置流形的渐近稳定性与耗散力间的关系作了新的表述，最后举例说明定理的应用·     

关于非完整力学系统相对部分变量的稳定性*

本文给出研究非完整系统相对部分变量稳定性的一种方法,并得到非完整系统相对部分变量的一些稳定性定理:同时,本文还得到一类非完整系统相对全部变量稳定性与相对部分变量稳定性的关系。     

一类无限维非光滑发展系统的时间最优控制

本文讨论了一类Banach空间上的非光滑半线性发展系统的时间最优控制问题,在适当的条件下证明了相应的Pontryagin型最大值原理.     

一类无限维非光滑发展系统的时间最优控制

本文讨论了一类Banach空间上的非光滑半线性发展系统的时间最优控制问题,在适当的条件下证明了相应的Pontryagin型最大值原理.     

一类非自治系统的稳定性

通过构造 Liapunov函数给出了一类非自治系统的稳定性的判定准则 .并给出了其有关的应用实例     

一类非自治系统的周期解

本文运用重合度理论研究一类非自治非线性系统的周期解问题，得到一些有关存在性，唯一性和稳定性的新结果。     

用两个V函数判别非自治系统的完全渐近稳定性

本文用两个Ｖ函数对一般非自治系统建立了完全渐进稳定性的一类判别条件．     

自治非光滑时滞系统的有限时间稳定

主要讨论右端非光滑的自治时滞系统在Filippov解意义下的有限时间稳定问题.基于Filippov微分包含和非光滑的Lyapunov-Krasovskii泛函,提出自治非光滑时滞系统有限时间稳定的定义和比较原理,并给出有限时间稳定的Lyapunov定理.     

一类不连续系统的推广Matrosov稳定性定理

在一般Filippov解意义下给出利用一族满足一定条件的Lyapunov函数的更一般的Matrosov定理.     

Existence and multiplicity of solutions for second order periodic systems with the <Emphasis Type="Italic">p</Emphasis>-Laplacian and a nonsmooth potential

In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem.     

Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation

In this paper we present an extension of Moreau’s sweeping process for higher order systems. The dynamical framework is carefully introduced, qualitative, dissipativity, stability, existence, regularity and uniqueness results are given. The time-discretization of these nonsmooth systems with a time-stepping algorithm is also presented. This differential inclusion can be seen as a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary-slackness variables. Applications of such high-order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes.     

Asymptotic stability and bifurcations of 3D piecewise smooth vector fields

The paper deals with the analysis of the behavior of a nonsmooth three-dimensional vector field around a typal singularity. We focus on a class of generic one-parameter families \({Z_{\lambda}}\) of Filippov systems and address the persistence problem for the asymptotic stability when the parameter varies near the bifurcation value \({\lambda = 0}\).     

An existence result for gradient-type systems with a nondifferentiable term on unbounded strips

In this paper we study the existence of nontrivial solutions for a class of gradient-type systems on strip-like domains where the nonlinear term is not necessarily continuously differentiable. The proof of the main result is based on a nonsmooth version of the Mountain Pass Theorem which involves the Cerami compactness condition and on the Principle of Symmetric Criticality for locally Lipschitz functions.     

Convex Difference Criteria for the Quantitative Stability of Parametric Quasidifferentiable Systems

In this paper solvability and Lipschitzian stability properties for a special class of nonsmooth parametric generalized systems defined in Banach are studied via a variational analysis approach. Verifiable sufficient conditions for such properties to hold under scalar quasidifferentiability assumptions are formulated by combining *-difference and Demyanov difference of convex compact subsets of the dual space with classic quasidifferential calculus constructions. Applications to the formulation of sufficient conditions for metric regularity/open covering of nonsmooth maps, along with their employment in deriving optimality conditions for quasidifferentiable extremum problems, as well as an application to the study of semicontinuity of the optimal value function in parametric optimization are discussed. In memory of Aleksandr Moiseevich Rubinov (1940–2006).     

复杂非线性系统的控制综合与动态分析

随着当代科学和技术的发展,复杂非线性系统和控制理论研究不断深入,应用领域不断扩大,已影响了科技和社会领域的许多方面.针对当今该领域的研究难点和重点,本文集中讨论了复杂非线性系统控制研究中的3个关键问题,包括非光滑系统控制、网络化系统控制、临界态分析与控制.一方面是对在相关研究领域中的部分科研成果做一个简要的总结;另一方面,想借此机会在自动化学会控制理论专业委员会成立50周年之际向专业委员会表示感谢和祝贺.     

Nonsmooth Mapping of Linear Control Systems

This paper deals with linear control systems of a special form. The main goal of the paper is to find the exact analytic solution of the time-optimal control problem for an arbitrary linear control system with constant coefficients using the analytic solution of this problem for the canonical system. For this aim, we construct a certain nonsmooth mapping between the 0-controllability sets of the given systems. In other words, by means of this mapping, we investigate the equivalence of the systems with the same qualitative behavior in a neighborhood of the stationary point.     

Decentralized Stabilizing State Feedback Controllers for a Class of Large-Scale Systems Including State Delays in the Interconnections

The problem of the decentralized stabilization of a class of large-scale nonlinear and linear systems including time-varying delays in the interconnections is considered. By combining the Razumikhin-type theorem with the Lyapunov stability theory, we propose a class of decentralized state feedback controllers which can guarantee always some type of stability of large-scale time-delay systems. In this paper, we assume that the time-varying delays are continuous and bounded nonnegative functions. Furthermore, since the proposed decentralized state feedback controllers are independent of the delays, the results obtained in this paper are applicable to systems without exact knowledge of the delays, i.e., systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Necessary and Sufficient Condition for Robust Stability and Stabilizability of Continuous-Time Linear Systems with Markovian Jumps

In this paper, we investigate the quadratic stability and quadratic stabilizability of the class of continuous-time linear systems with Markovian jumps and norm-bound uncertainties in the parameters. Under some appropriate assumptions, a necessary and sufficient condition is established for mean-square quadratic stability and mean-square quadratic stabilizability of this class of systems. The quadratic guaranteed cost control problem is also addressed via a LMI optimization problem.