Optimal feedback control in the stationary mathematical model of low concentrated aqueous polymer solutions

In this article we will consider the feedback control problem in the stationary model of motion of low concentrated aqueous polymer solutions. We demonstrate the solvability of an approximating problem, using some a priori estimates and the topological degree theory. Then the convergence (in some generalized sense) of solutions of approximating problems to a solution of the given problem is proved. Moreover, we show the existence of a solution minimizing a given convex, lower semicontinuous functional.     

Bifurcation from single periodic orbit in discontinuous autonomous systems

This article is devoted to the study of bifurcations of periodic solutions for discontinuous autonomous systems from single periodic solutions of unperturbed discontinuous equations. In addition, local asymptotic properties of derived perturbed periodic solutions are also investigated. An example of planar discontinuous ordinary differential equations is given to illustrate the theory.     

Algebraic Multiplicities Arising from Static Feedback Control Systems of Parabolic Type

In stabilization studies of linear parabolic control systems, a successful approach is a scheme employing dynamic compensators in the feedback loop. An essential reason is the fact that both sensors and actuators cannot be designed freely, especially in the case of boundary observation/boundary feedback. Most fundamental in this scheme is a simple stabilization result under the static feedback control scheme. In this scheme, little attention has been paid to how to assign new eigenvalues of the feedback system. In this article, we show a new feature of pole assignment that shows some choices of new eigenvalues cause a deterioration of the stability property. An algebraic growth rate is added to the feedback system in such a choice.     

Orbit projections as fibrations

The orbit projection π: M → M/G of a proper G-manifold M is a fibration if and only if all points in M are regular. Under additional assumptions we show that π is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: π is a G-quasifibration if and only if all points are regular.     

On the multi-phase M/G/1 queueing system with random feedback

In this paper we consider an M/G/1 queue with k phases of heterogeneous services and random feedback, where the arrival is Poisson and service times has general distribution. After the completion of the i-th phase, with probability θ _i the (i + 1)-th phase starts, with probability p _i the customer feedback to the tail of the queue and with probability 1 − θ _i − p _i  = q _i departs the system if service be successful, for i = 1, 2 , . . . , k. Finally in kth phase with probability p _k feedback to the tail of the queue and with probability 1 − p _k departs the system. We derive the steady-state equations, and PGF’s of the system is obtained. By using them the mean queue size at departure epoch is obtained.     

关于LF拓扑空间的正则闭分离性

利用正则闭集概念在LF拓扑空间中引入RC-正则(正规)分离性概念,给出了它们的刻画,并利用广义Zadeh型函数证明了它们是LF拓扑性质,在LF拓扑空间的半正则化中RC-正则(正规)分离性与正则(正规)分离性是等价的.     

Asymptotic phase and invariant foliations near periodic orbits

The paper deals with asymptotic phase and invariant foliations near periodic orbits, extending for two-dimensional smooth vector fields results that have been obtained by Chicone and Liu (2004). The problem of the existence of asymptotic phase is completely solved for analytic vector fields and is reduced to a problem of infinite codimension for systems. Moreover it is proven that whenever asymptotic phase occurs, or in other words, when the periodic orbit is isochronous, then there also exists a foliation, with leaves transversally cutting the periodic orbit and invariant under the flow of the vector field. The paper also provides some results in three dimensions.

     

Simultaneous output feedback stabilization of time-delay systems

^** Email: magdi_mahmoud{at}cic-cairo.com^*** Email: hnounou{at}uaeu.ac.ae This paper develops new results to the problem of simultaneousfeedback stabilization using static output feedback (SOF) controlfor a finite collection of linear dynamical systems with unknownstate delay. We establish tractable synthesis conditions fornominal SOF controllers and subsequently extend the resultsto resilient SOF to cope with possible additive controller gainperturbations. In both cases, the design of SOF controllersis based on guaranteed cost and approaches. Previous relatedresults are recovered and all the developed results are convenientlycast in the format of linear matrix inequalities. A numericalexample is presented.     

Stabilization of the wave equation with variable coefficients and a delay in dissipative boundary feedback

We consider the stabilization of the wave equation with variable coefficients and a delay in the dissipative boundary feedback. By virtue of the Riemannian geometry methods, the energy-perturbed approach and the multiplier skills, we establish the uniform stability of the energy of the closed-loop system.     

Hopf-pitchfork bifurcation in van der Pol's oscillator with nonlinear delayed feedback

First, we identify the critical values for Hopf-pitchfork bifurcation. Second, we derive the normal forms up to third order and their unfolding with original parameters in the system near the bifurcation point, by the normal form method and center manifold theory. Then we give a complete bifurcation diagram for original parameters of the system and obtain complete classifications of dynamics for the system. Furthermore, we find some interesting phenomena, such as the coexistence of two asymptotically stable states, two stable periodic orbits, and two attractive quasi-periodic motions, which are verified both theoretically and numerically.