Finite-dimensional discrete linear stochastic accelerated-time systems and their application to quadratic stochastic dynamical systems

1996 ◽  
Vol 59 (5) ◽  
pp. 511-517 ◽  
Author(s):  
N. P. Zimakov
Keyword(s):  
Dynamical Systems ◽  
Stochastic Dynamical Systems ◽  
Finite Dimensional ◽  
Time Systems

scholarly journals Global relative controllability of fractional stochastic dynamical systems with distributed delays in control

2014 ◽  
Vol 32 (2) ◽  
pp. 55 ◽  
Author(s):  
Toufik Guendouzi ◽  
Iqbal Hamada
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Banach Fixed Point Theorem ◽  
Stochastic Dynamical Systems ◽  
Relative Controllability ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Controllability Grammian

This paper is concerned with the global relative controllability of linear and nonlinear fractional stochastic dynamical systems with distributed delays in control for finite dimensional spaces. Sufficient conditions for controllability results are obtained using the Banach fixed point theorem and the controllability Grammian matrix which is dened by the Mittag-Leffler matrix function. An example is provided to illustrate the theory.

Coherent phenomena in stochastic dynamical systems

1999 ◽  
Vol 169 (2) ◽  
pp. 171 ◽  
Author(s):  
Valerii I. Klyatskin ◽  
D. Gurarie
Keyword(s):  
Dynamical Systems ◽  
Stochastic Dynamical Systems

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

DUAL FORMULATION OF OPTIMAL PROBLEM FOR CONTINUOUS-TIME SYSTEMS

2005 ◽  
Vol 02 (03) ◽  
pp. 251-258
Author(s):  
HANLIN HE ◽  
QIAN WANG ◽  
XIAOXIN LIAO
Keyword(s):  
Objective Function ◽  
Continuous Time ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Error Response ◽  
Infinite Dimensional ◽  
Dual Formulation ◽  
Finite Dimensional ◽  
Continuous Time Systems ◽  
Time Systems

The dual formulation of the maximal-minimal problem for an objective function of the error response to a fixed input in the continuous-time systems is given by a result of Fenchel dual. This formulation probably changes the original problem in the infinite dimensional space into the maximal problem with some restrained conditions in the finite dimensional space, which can be researched by finite dimensional space theory. When the objective function is given by the norm of the error response, the maximum of the error response or minimum of the error response, the dual formulation for the problems of L1-optimal control, the minimum of maximal error response, and the minimal overshoot etc. can be obtained, which gives a method for studying these problems.

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