Topological Fiber Entropy for Linear Flows on Vector Bundles

For linear flows on vector bundles, it is shown that the topological entropy of lower dimensional subspaces in the fibers is determined by the Morse spectrum over chain recurrent components of the induced flows on Grassmann bundles.     

Extended Holonomy and Topological Invariance of Vanishing Holonomy Group

In this work, we introduce the notion of extended holonomy and discuss some of its properties. As an application of it, we consider vanishing projective holonomy groups of germs of vector fields with zero (n − 1)-jet and prove, under some genericity assumptions, that the corresponding vanishing holonomy groups are topologically conjugated for orbitally topologically equivalent germs of vector fields. This work was supported by the grants NCNIL_a 05-01-02801, RFBR 7-01-00017-a, and CONACyT 14300, PAPIIT-UNAM IN114703-3, IN102407.     

On Topological Equivalence of Linear Lows with Applications to Bilinear Control Systems

This paper classifies continuous linear flows using concepts and techniques from topological dynamics. Specifically, the concepts of equivalence and conjugacy are adapted to flows on vector bundles, and the Lyapunov decomposition is characterized using the induced flows on the Grassmann and the flag bundles. These results are then applied to bilinear control systems, for which their behavior in , on the projective space , and on the Grassmannians is characterized. This research was partially supported by Proyecto FONDECYT No. 1060981 and Proyecto FONDECYT de Incentivo a la Cooperación Internacional No. 7020439.     

Topological Entropy of Free Semigroup Actions and Skew-Product Transformations

A definition of topological entropy for a free semigroup action is suggested. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a skew-product transformation whose fiber entropy is taken to be the entropy of the initial action. The main result is Theorem 1, a topological analogue of the Abramov–Rokhlin formula.     

Time-Restricted Sensitivity and Entropy for Random Dynamical Systems

Journal of Dynamical and Control Systems - This paper is devoted to the investigation of fiber measure-theoretical restricted sensitivity and fiber topological restricted sensitivity by restricting...     

Almost Additive Topological Pressure of Proper Systems

We introduce a natural extension of almost additive topological pressure for a proper map of locally compact metric spaces and present a corresponding variational principle. As an application, for a class of almost additive sequence, we describe a multi-fractal analysis of the u-dimension spectra of their generalized Birkhorff averages.     

Robust Constrained Regulator Problem for Linear Uncertain Systems

The robust regulator problem for linear uncertain systems with constrained control is considered. Necessary and su.cient conditions of positive invariance of polyhedral domains with respect to motion of uncertain systems are given. Further, it is shown that in contrast to the case of perfectly known systems, positive invariance with respect to uncertain systems and stability of n - m assigned eigenvalues from the open loop system do not imply asymptotic stability. Furthermore, conditions ensuring this asymptotic stability are derived. This enables us to construct robust constrained regulators, i.e., control laws satisfying control constraints and achieving asymptotic stability in presence of parametric uncertainties.     

Local Controllability for Linear Control Systems on Lie Groups

Abtract  In this work, we study controllability properties of linear control systems on Lie groups. Using Lie theory of semigroups, we obtain local controllability results for this type of systems. In addition, properties for the flow of the drift vector field X and for the reachable set of the system are presented. Finally, an example on the Heisenberg Lie group is considered, and its properties are proved using the theory developed. 2000 Mathematics Subject Classification. Primary 93B05; Secondary 93C25, 93B27. The authors want to thank the Fachbereich Mathematik of the Technische Universit?t Darmstadt for warm hospitality during the production of this work. The first author is pleased to thank Professor Guillermo Ferreyra and the department of mathematics at LSU for their support.     

Uniform Stability and Stabilization of Linear Thermoelastic Systems

The object of this work is the study of uniform stability and stabilization of linear thermoelastic systems. We construct an explicit stabilizer feedback for the thermoelastic system and use a Lyapunov function to prove the exponential stability.     

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.     

基于熵分析法的回热系统通用损分布矩阵

熵分析法的核心就是求取过程的熵产,而熵产的大小体现着过程不可逆程度.在回热系统中,节流、有限温差传热以及摩擦与扰动等过程都是不可逆过程,它们必然会导致做功能力损失即(火用)损,而这损失可以利用Gouy-Stodola关系式由这些过程所造成的熵产转化获得.针对回热系统的(火用)损分布进行讨论,在划分单一回热加热器为独立系统后,对系统采用黑箱分析,对方程进行水侧定流量法处理,通过Gouy-Stodola关系式转化最终获得通用炯损分布矩阵方程.     

Dynamic Improvement for Linear Constrained Control Continuous-Time Systems with a State Observer

The main idea of this paper is to apply a dynamic improvement technique to linear constrained control continuous-time systems with a state observer. Two known cases with the full-order observer and the minimal-order observer are used for reconstructing the inaccessible state. This leads to using a large set of initial states where the control saturation does not occur to the cost of a slow dynamic of the closed-loop. As soon as the state tends to the origin, the dynamics becomes better and better while the constraints on the control vector are respected.     

On the Reachability of Discrete-Time Switched Linear Systems

This paper studies the reachability realization problem of discrete-time switched linear systems. A new constructive approach is developed to design switching sequence such that the reachable subspace is realized. Compared with the existing results, the length of the designed switching sequence is smaller and the proposed algorithm has fewer calculations. One numerical example is presented to illustrate the effectiveness of the obtained results.     

Approximate and Near Weak Invariance for Nonautonomous Differential Inclusions

Let X be a real Banach space and I a nonempty interval. Let \(K:I\rightsquigarrow X\) be a multi-function with the graph \(\mathcal {K} \). We give here a characterization for \(\mathcal {K} \) to be approximate/near weakly invariant with respect to the differential inclusion \(x^{\prime }(t)\in F(t, x(t))\) by means of an appropriate tangency concept and Lipschitz conditions on F. The tangency concept introduced in this paper extends in a natural way the quasi-tangency concept introduced by Cârj? et al. (Trans Amer Math Soc. [2009];361:343–90) (see also Cârj? et al. ([2007])). Viability, invariance and applications. Amsterdam: Elsevier Science B V) in the case when F is independent of t. As an application, we give some results concerning the set of solutions for the differential inclusion \(x^{\prime }(t)\in F(t,x(t))\).     

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.

     

Haar Wavelet-Based Approach for Optimal Control of Second-Order Linear Systems in Time Domain

In this paper, a Haar wavelet-based method for optimal control of the second-order linear systems with respect to a quadratic cost function for any length of time is proposed. A Haar wavelet integral operational matrix and properties of the Kronecker product are used in finding the approximate solutions of optimal trajectories and optimal control by solving only two algebraic equations instead of solving the Riccati differential equation. Numerical results of a typical example are presented to illustrate the advantage of the approach.2000 Mathematics Subject Classification. 53A04, 30C15.This research was partially supported under Research Grant 8101004-1-1 provided by university of Tehran and partially by the German Academic Exchange Service (DAAD).     

Singular Perturbation of Linear Systems with a Regular Singularity

We study singularly perturbed inhomogeneous linear systems which have a regular singularity at the origin. Under some extra assumption, this system has a unique formal solution which is a power series in the variable z and the perturbation parameter . Here we investigate its summability properties. In particular, we show that the series, regarded as a power series in with coefficients depending on z, is 1-summable under some eigenvalue condition. Moreover, we show that this condition in general is sharp.     

Specification Property for Topological Spaces

We introduce and study here the notion of specification property termed as topological specification property for homeomorphisms on non-compact non-metrizable spaces. We prove that if a self homeomorphism on a totally bounded uniform space is mixing, topologically expansive and topologically shadowing then the map has topological specification property.