On perturbation range in the feedback synthesis problem for a chain of integrators system

The feedback synthesis problem for a chain of integrators system with continuous bounded unknown perturbation is considered. Our approach is based on the controllability function (CF) method proposed by V.I. Korobov. The perturbation range is determined by the negativity condition for the total derivative of the CF with respect to the perturbed system. The control that does not depend on perturbation under some restrictions and steers an arbitrary initial point from a neighborhood of the origin to the origin in a finite time (settling-time function) is constructed. The settling-time function depends on the perturbation, but it remains bounded from below and from above by the same value.

A globally convergent method for finding zeros of integer functions of finite order

Предложен метод отыскания нулей целых функций конечного порядка, который сходится к корню от произвольной начальной точки, т.е. является глобально сходящимся. Метод основан на представлении производных высшего порядка от логарифмической производной в виде суммы простейших дробей и сводит отыскание корня к выбору минимального числа из конечного множества. Даны оценки скорости сходимости. A method for finding zeros of integer functions of finite order is proposed. This method converges to a root starting from an arbitrary initial point and, hence, is globally convergent. The method is based on a representation of higher-order derivatives of the logarithmic derivative as a sum of partial fractions and reduces the finding of a root to the choice of the minimum number from a finite set. The rate of convergence is estimated.

Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

Assume thatFis a nonlinear operator which is Lipschitzian and strongly monotone on a nonempty closed convex subsetCof a real Hilbert spaceH. Assume also thatΩis the intersection of the fixed point sets of a finite number of Lipschitzian pseudocontractive self-mappings onC. By combining hybrid steepest-descent method, Mann’s iteration method and projection method, we devise a hybrid iterative algorithm with perturbationF, which generates two sequences from an arbitrary initial pointx0∈H. These two sequences are shown to converge in norm to the same pointPΩx0under very mild assumptions.

Hybrid Iteration Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings in Banach Spaces

LetEbe a real uniformly convex Banach space, and let{Ti:i∈I}beNnonexpansive mappings fromEinto itself withF={x∈E:Tix=x, i∈I}≠ϕ, whereI={1,2,…,N}. From an arbitrary initial pointx1∈E, hybrid iteration scheme{xn}is defined as follows:xn+1=αnxn+(1−αn)(Tnxn−λn+1μA(Tnxn)),n≥1, whereA:E→Eis anL-Lipschitzian mapping,Tn=Ti,i=n(mod N),1≤i≤N,μ>0,{λn}⊂[0,1), and{αn}⊂[a,b]for somea,b∈(0,1). Under some suitable conditions, the strong and weak convergence theorems of{xn}to a common fixed point of the mappings{Ti:i∈I}are obtained. The results presented in this paper extend and improve the results of Wang (2007) and partially improve the results of Osilike, Isiogugu, and Nwokoro (2007).

Weak and strong convergence of an iterative method for nonexpansive mappings in Hilbert spaces

In a real Hilbert space H, starting from an arbitrary initial point x0 H, an iterative process is defined as follows: xn+1 = anxn +(1-an)T?n+1 f yn, yn = bnxn + (1 - bn)T?n g xn, n ? 0, where T ?n+1 f x = Tx - ?n+1?f f(Tx), T?n g x = Tx - ?n?gg(Tx), (8 x 2 H), T : H ? H a nonexpansive mapping with F(T) 6= ; and f (resp. g) : H ? H an ?f (resp. ?g)-strongly monotone and kf (resp. kg)-Lipschitzian mapping, {an} _ (0, 1), {bn} _ (0, 1) and {?n} _ [0, 1), {?n} _ [0, 1). Under some suitable conditions, several convergence results of the sequence {xn} are shown.

Automatic Operation of a Mobile Robot Using an RCE Network

This article describes an example using a neural net as a method of mobile robot operation. The method eliminates the need for characteristic equations of a mobile robot, but requires an exercise to some extent using adequate ""patterns."" For accumulating experience of this practice, an RCE (restricted coulomb energy) network, or a pattern recognition-use neural network, is used. A simulation is conducted by driving a car into a garage. A man drives a car into a garage to create pattern data, which an RCE net is made to learn. After learning to some extent, it is allowed to put a car into a garage from an arbitrary initial point. The following are the descriptions of the results.

On the construction of convergent iterative sequences of polynomials

We answer two conjectures suggested by Zalman Rubinstein. We prove his Conjecture 1, that is, we construct convergent iterative sequences for with an arbitrary initial point, where with m ≥ 2. We also show by several counterexamples that Rubinstein's Conjecture 2 is generally false.

A variational method for the construction of convergent iterative sequences

Convergent iterative sequences are constructed for the polynomials fm = z + zm, m ≧ 2, with initial point the lemniscate {z: |fm (z)| ≦1}. In the particular case m = 2 convergent iterative sequences are constructed also for f-1m, (z) with an arbitrary initial point. The method is based on a certain variational principle which allows reducing the problem to the well known situation of an analytic function mapping a simply connected domain into a proper subset of itself and possessing a fixed point in the domain.