共查询到20条相似文献,搜索用时 15 毫秒
1.
K. Balachandran V. Govindaraj L. Rodríguez-Germa J. J. Trujillo 《Journal of Optimization Theory and Applications》2013,156(1):33-44
This paper establishes a set of sufficient conditions for the controllability of nonlinear fractional dynamical system of order 1<α<2 in finite dimensional spaces. The main tools are the Mittag–Leffler matrix function and the Schaefer’s fixed-point theorem. An example is provided to illustrate the theory. 相似文献
2.
Anatoli Torokhti Phil Howlett Charles Pearce 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(3):327-343
We propose a new method for the optimal causal representation of nonlinear systems. The proposed approach is based on the best constrained approximation of mappings in probability spaces by operators constructed from matrices of special form so that the approximant preserves the causality property. It is supposed that the observable input is contaminated with noise. The approximant minimises the mean-square difference between a desired output signal and the output signal of the approximating model. The method provides a numerically realisable mathematical model of the system. An analysis is given of the error associated with this representation. 相似文献
3.
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied
in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping
rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest
in many applications.
相似文献
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5.
The nonlinear variation-of-constants formula is generalizedto the case where the unperturbed operator has nonelliptic Fréchetderivation. 相似文献
6.
Strongly negatively invariant compact sets of set-valued autonomous and nonautonomous dynamical systems on a complete metric
space, the latter formulated in terms of processes, are shown to contain a weakly positively invariant family and hence entire
solutions. For completeness the strongly positively invariant case is also considered, where the obtained invariant family
is strongly invariant. Both discrete and continuous time systems are treated. In the nonautonomous case, the various types
of invariant families are in fact composed of subsets of the state space that are mapped onto each other by the set-valued
process. A simple example shows the usefulness of the result for showing the occurrence of a bifurcation in a set-valued dynamical
system. 相似文献
7.
基于最近发展的矩阵李群上非线性微分方程的显式Magnus展式,给出了非线性动力系统的有效的数值算法,并且在数值求解过程中具有自适应的步长控制特点,可以显著地提高计算效率.最后,通过非线性动力系统典型问题Duffing方程和强刚性的Van derPol方程以及非线性振子的Hamilton方程的数值实验来说明方法的有效性. 相似文献
8.
We establish convergence of the nonlinear filter of the
state of a randomly perturbed dynamical system in which
the perturbation is a rapidly fluctuating ergodic Markov
process, and the observation process conditions the
state of the system.
The limiting nonlinear filter is completely characterized. 相似文献
9.
L. F. Petrov 《Computational Mathematics and Mathematical Physics》2018,58(3):384-393
Numerical-analytical methods for finding periodic solutions of highly nonlinear autonomous and nonautonomous systems of ordinary differential equations are considered. Algorithms for finding initial conditions corresponding to a periodic solution are proposed. The stability of the found periodic solutions is analyzed using corresponding variational systems. The possibility of studying the evolution of periodic solutions in a strange attractor zone and on its boundaries is discussed, and interactive software implementations of the proposed algorithms are described. Numerical examples are given. 相似文献
10.
Samin T. Malik 《Numerical Functional Analysis & Optimization》2013,34(15):1669-1689
AbstractIn this article, an optimal control problem with a delay in control is considered. The second-order necessary condition is obtained for the optimality of singular (in the sense of the maximum principle) control. Also, the notion of degenerate singular control of order k (k?≥?1) is introduced and for optimality of this, the high-order necessary condition is obtained. Moreover, while studying the problem, one of the strengthened version of an analog of the maximum principle is shown. Finally, the rich content of the obtained results is illustrated by specific examples. 相似文献
11.
We consider dynamical systems generated by continuous maps of an interval into itself. We investigate the asymptotic behavior of the trajectories of subsets of the interval. In particular, we prove that if the -limit set of an arbitrary trajectory is a fixed point, then the topological limit of the trajectory of any subinterval exists. 相似文献
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Panos M. Pardalos J. Chris Sackellares Vitaliy A. Yatsenko Sergiy I. Butenko 《Annals of Operations Research》2003,119(1-4):119-142
In this paper we present the application of a method of adaptive estimation using an algebra–geometric approach, to the study of dynamic processes in the brain. It is assumed that the brain dynamic processes can be described by nonlinear or bilinear lattice models. Our research focuses on the development of an estimation algorithm for a signal process in the lattice models with background additive white noise, and with different assumptions regarding the characteristics of the signal process. We analyze the estimation algorithm and implement it as a stochastic differential equation under the assumption that the Lie algebra, associated with the signal process, can be reduced to a finite dimensional nilpotent algebra. A generalization is given for the case of lattice models, which belong to a class of causal lattices with certain restrictions on input and output signals. The application of adaptive filters for state estimation of the CA3 region of the hippocampus (a common location of the epileptic focus) is discussed. Our areas of application involve two problems: (1) an adaptive estimation of state variables of the hippocampal network, and (2) space identification of the coupled ordinary equation lattice model for the CA3 region. 相似文献
14.
一类广义Lipschitz非线性算子的带误差的Ishikawa迭代程序 总被引:33,自引:0,他引:33
借助于周海云和陈东青[4]新近引入的广义Lipschitz概念,研究了实Banach空间中广义Lipschitz -强伪压缩算子的不动点和广义Lipschitz -强增算子方程解的迭代逼近问题,所得结果改进和扩展了近期许多相关的结果,并部分地回答了周海云[3]提出的一个问题. 相似文献
15.
Combined use of the method of sum of squares (SOS) and quantifier elimination (QE) is discussed with regard to the problem of nonlinear gain analysis for a class of dynamical systems. SOS, a numerical method, is used to search for the structure of a gain function quickly, and QE, a symbolic method, determines all gain functions in the structure to find the minimum gain function. QE can also be used for the infeasibility check of gain structures. A proposed analysis procedure for polynomial dynamical systems prevents unnecessary searching for a gain structure. Two illustrative examples show the effectiveness of the proposed gain analysis procedure. 相似文献
16.
The nonlinear variation-of-constants formula is generalizedto infinite-dimensional systems and applied to the stabilityproblem and used to obtain bounds on the states of a nonlinearcontrol system when the controls are bounded. The theory isillustrated by a simple model from nuclear reactor dynamics. 相似文献
17.
A pseudospectral method for generating optimal trajectories of linear and nonlinear constrained dynamic systems is proposed. The method consists of representing the solution of the optimal control problem by an mth degree interpolating polynomial, using Chebyshev nodes, and then discretizing the problem using a cell-averaging technique. The optimal control problem is thereby transformed into an algebraic nonlinear programming problem. Due to its dynamic nature, the proposed method avoids many of the numerical difficulties typically encountered in solving standard optimal control problems. Furthermore, for discontinuous optimal control problems, we develop and implement a Chebyshev smoothing procedure which extracts the piecewise smooth solution from the oscillatory solution near the points of discontinuities. Numerical examples are provided, which confirm the convergence of the proposed method. Moreover, a comparison is made with optimal solutions obtained by closed-form analysis and/or other numerical methods in the literature. 相似文献
18.
In certain physical systems measuring one variable of the system modifies the values of any number of other variables unpredictably. We show in this paper that under these conditions a parallel approach succeeds in carrying out the required measurement while a sequential approach fails. Specifically, we show that for a nonlinear dynamical system, namely, the Belousov–Zhabotinskii chemical reaction, measurement disturbs the equilibrium of the system and causes it to enter into an undesired state. If, however, several measurements are performed in parallel, the effect of perturbations seems to cancel out and the system remains in a stable state.Mathematics Subject Classifications (2000) 37-XX, 37C75, 68Q10, 68Q25, 68W10.This research was supported by the Natural Sciences and Engineering Research Council of Canada. 相似文献
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M. Ben Slimane 《Constructive Approximation》1999,15(2):209-240
We study functions which are self-similar under the action of some nonlinear dynamical systems. We compute the exact pointwise
H{?}lder regularity, then we determine the spectrum of singularities and the Besov ``smoothness' index, and finally we prove
the multifractal formalism. The main tool in our computation is the wavelet analysis.
October 1, 1996. Date revised: May 13, 1997. Date re-revised: January 10, 1998. Date accepted: February 27, 1998. 相似文献