Control by Interconnection and Energy Shaping of the Timoshenko Beam

In this paper, the dynamical control of a mixed finite and infinite dimensional mechanical system is approached within the framework of port Hamiltonian systems. In particular, a flexible beam, modeled according to the Timoshenko theory and in distributed port Hamiltonian form, with a mass under gravity field connected at a free end, is considered. The control problem is approached by generalization of the concept of structural invariant (Casimir function) to the infinite dimensional case and the so-called control by interconnection technique is extended to the infinite dimensional case. In this way, finite dimensional passive controllers can stabilize distributed parameter systems by shaping their total energy, i.e., by assigning a new minimum in the desired equilibrium configuration that can be reached if a dissipation effect is introduced.     

Partial Differential Equations That Are Hard to Classify

Semi-linear n×n systems of the form A∂u/∂x+B∂u/∂y=f can generally be solved, at least locally, provided data are imposed on non-characteristic curves. There are at most n characteristic curves and they are determined by the coefficient matrices on the left-hand sides of the equations. We consider cases where such problems become degenerate as a result of ambiguity associated with the definition of characteristic curves. In such cases, the existence of solutions requires restrictions on the data and solutions might not be unique.     

Model of traffic flow and blocking probability analysis of an m-asymmetrical two stage incomplete link system

In the first part of this study we present and review a simplified model for the traffic flow between the switches of a modular switching system. In the second part, an approximated model for calculating the blocking probability on a system with this type of architecture is presented and then generalized to a structure here defined as an m-asymmetrical incomplete link system. The model is based on the probabilistic hypothesis of Jacobaeus and leads to a system of formulae which may be calculated using a computing language allowing for recursive subprograms.     

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.     

Peakon, pseudo-peakon, loop, and periodic cusp wave solutions of a three-dimensional 3DKP(2, 2) equation with nonlinear dispersion

In this paper, we study the three-dimensional Kadomtsev-Petviashvili equation (3DKP(m, n)) with nonlinear dispersion for m=n=2. By using the bifurcation theory of dynamical systems, we study the dynamical behavior and obtain peakon, pseudo-peakon, loop and periodic cusp wave solutions of the three-dimensional 3DKP(2, 2) equation. The parameter expressions of peakon, pseudo-peakon, loop and periodic cusp wave solutions are obtained and numerical graph are provided for those peakon, pseudo-peakon, loop and periodic cusp wave solutions.     

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.     

Controllability and stabilizability of linear time‐varying distributed hereditary control systems

This paper is concerned with the controllability and stabilizability problem for control systems described by a time‐varying linear abstract differential equation with distributed delay in the state variables. An approximate controllability property is established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operators associated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptotic stability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximate controllability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes the system. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley & Sons, Ltd.     

Approximate controllability of second‐order distributed systems

In this paper, we study the approximate controllability of control systems with state and control in Banach spaces and described by a second‐order semilinear abstract differential equation. We compare the approximate controllability of the system with the approximate controllability of an associated discrete system. Copyright © 2013 John Wiley & Sons, Ltd.     

Boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term

In this paper, we are concerned with the sublinear reversible systems with a nonlinear damping and periodic forcing term

x^″+f(x)g(x^′)+γ|x|^α−1x=p(t),     

Some New Regularity Criteria for the Navier-Stokes Equations Containing Gradient of the Velocity

We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.     

Measure-Valued Solutions to Initial-Boundary Value Problems for Certain Systems of Conservation Laws: Existence and Dynamics

A framework for studying initial-boundary value problems for systems of conservation laws, in what concerns to the existence of measure-valued solutions and their asymptotic behavior, is developed here with the helpful introduction of a class of flux maps which allow a rather complete treatment of these questions including systems of practical importance as those arising in multiphase flow in porous media. The systems of this class may, in general, admit umbilic points, submanifolds where genuine nonlinearity fails, as well as elliptic regions. We prove the existence of measure-valued solutions by using the vanishing viscosity method and, also, finite difference schemes. The main result about the dynamics of the measure-valued solutions is that for certain special boundary values, given by constant states, the time-averages of these m-v solutions converge weakly to the Dirac measure concentrated at those states, for a.e. space variable. The rate of convergence of the time-averages of the expected values can be estimated by properties of the flux maps only.

     

Banach空间中非线性脉冲Volterra型积分方程组的可解性

在较弱的条件下，利用锥理论和单调迭代方法首先建立了Banach空间中一类非线性算子方程组最小最大解的存在性定理；然后作为应用，利用一个新的比较结果，得到了Banach空间中非线性脉冲Volterra型积分方程组的整体解，改进了最近的许多结果．     

On perturbation of roots of homogeneous algebraic systems

A problem concerning the perturbation of roots of a system of homogeneous algebraic equations is investigated. The question of conservation and decomposition of a multiple root into simple roots are discussed. The main theorem on the conservation of the number of roots of a deformed (not necessarily homogeneous) algebraic system is proved by making use of a homotopy connecting initial roots of the given system and roots of a perturbed system. Hereby we give an estimate on the size of perturbation that does not affect the number of roots. Further on we state the existence of a slightly deformed system that has the same number of real zeros as the original system in taking the multiplicities into account. We give also a result about the decomposition of multiple real roots into simple real roots.

     

On the Geometry of Inner Approximations to the Set of Null Controllability for Constrained Linear Systems

The problem of obtaining inner approximations to the set of null controllability for linear systems is considered, and the geometry of certain sets arising in the approximation of using linear feedback is explored. A two-dimensional example is worked in detail in order to delineate the limitations to the use of linear feedback.     

Invariant curves and boundedness of solutions of a class of reversible systems

In this paper, the boundedness of all solutions for the following planar reversible system Ju ′ = ?H (u) + G (u) + h (t) (1) is discussed, where the function H (u) ∈ C²(?², ?⁺) is positive for u ≠ 0 and positively (q, p)‐quasihomogeneous of quasi‐degree pq, G ∈ C⁵ is bounded, h ∈ C⁶ is 2π ‐periodic and J is the standard symplectic matrix. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two results on entire solutions of Ginzburg-Landau system in higher dimensions

In this short article we prove two results on the Ginzburg-Landau system of equations Δu=u(|u|²−1), where . First we prove a Liouville-type theorem which asserts that every solution u, satisfying , is constant (and of unit norm), provided N?4 (here M?1). In our second result, we give an answer to a question raised by Brézis (open problem 3 of (Proceedings of the Symposium on Pure Mathematics, vol. 65, American Mathematical Society, Providence, RI, 1999), about the symmetry for the Ginzburg-Landau system in the case N=M?3. We also formulate three open problems concerning the classification of entire solutions of the Ginzburg-Landau system in any dimension.     

MULTIPLICITY OF SOLUTIONS TO ASYMPTOTICALLY LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL SYSTEM

In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory.     

Computations via Newtonian and relativistic kinematic systems

We are developing a rigorous methodology to analyse experimental computation, by which we mean the idea of computing a set or function by experimenting with some physical equipment. Here we consider experimental computation by kinematic systems under both Newtonian and relativistic kinematics. An experimental procedure, expressed in a language similar to imperative programming languages, is applied to equipment, having the form of a bagatelle, and is interpreted using the two theories. We prove that for any set A of natural numbers there exists a two-dimensional kinematic system B_A with a single particle P whose observable behaviour decides n∈A for all n∈N. The procedure can operate under (a) Newtonian mechanics or (b) relativistic mechanics. The proofs show how any information (coded by some A) can be embedded in the structure of a simple kinematic system and retrieved by simple observations of its behaviour. We reflect on the methodology, which seeks a formal theory for performing abstract experiments with physical restrictions on the construction of systems. We conclude with some open problems.