Controllability of fractional order stochastic differential inclusions with fractional Brownian motion in finite dimensional space

2016 ◽  
Vol 3 (4) ◽  
pp. 400-410 ◽  
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Fractional Order ◽  
Differential Inclusions ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
Stochastic Differential Inclusions

Estimation of the Hankel Singular Values of Fractional-Order Systems

2009 ◽  
Author(s):  
Jay L. Adams ◽  
Robert J. Veillette ◽  
Tom T. Hartley
Keyword(s):  
Fractional Order ◽  
Dimensional Space ◽  
Ritz Method ◽  
Singular Values ◽  
Finite Dimensional Space ◽  
Fractional Order Systems ◽  
Norm Estimates ◽  
Finite Dimensional ◽  
Hankel Singular Values ◽  
Hankel Norm

This paper applies the Rayleigh-Ritz method to approximating the Hankel singular values of fractional-order systems. The algorithm is presented, and estimates of the first ten Hankel singular values of G(s) = 1/(sq+1) for several values of q ∈ (0, 1] are given. The estimates are computed by restricting the operator domain to a finite-dimensional space. The Hankel-norm estimates are found to be within 15% of the actual values for all q ∈ (0, 1].

scholarly journals Set-Valued Functions of Bounded Generalized Variation and Set-Valued Young Integrals

2020 ◽  
Author(s):  
Mariusz Michta ◽  
Jerzy Motyl
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Differential Inclusions ◽  
Stochastic Integrals ◽  
Stochastic Differential Inclusions ◽  
Generalized Variation

AbstractThe paper deals with some properties of set-valued functions having bounded Riesz p-variation. Set-valued integrals of Young type for such multifunctions are introduced. Selection results and properties of such set-valued integrals are discussed. These integrals contain as a particular case set-valued stochastic integrals with respect to a fractional Brownian motion, and therefore, their properties are crucial for the investigation of solutions to stochastic differential inclusions driven by a fractional Brownian motion.

scholarly journals Value Function and Optimal Control of Differential Inclusions

2015 ◽  
Vol 61 (1) ◽  
pp. 181-193 ◽  
Author(s):  
Tzanko Donchev ◽  
Ammara Nosheen
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Unique Solution ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Value Function ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
The Value Function

Abstract Optimal control system described by differential inclusion with continuous and one sided Perron right-hand side in a finite dimensional space is studied in the paper. We prove that the value function is the unique solution of a proximal Hamilton-Jacobi inequalities.

scholarly journals Well-posed control problems related to second-order differential inclusions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Doria Affane ◽  
Mustapha Fateh Yarou
Keyword(s):  
Differential Inclusions ◽  
Optimal Control Problems ◽  
Dimensional Space ◽  
Maximal Monotone ◽  
Second Order ◽  
Control Problems ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
Quadratic Optimal Control ◽  
Well Posed

<p style='text-indent:20px;'>The paper deals with quadratic optimal control problems, we study the equivalence between well-posed problems and affinity on the control for a second-order differential inclusions with two-points conditions, governed by a maximal monotone operator in a finite dimensional space.</p>

scholarly journals Selection Properties and Set-Valued Young Integrals of Set-Valued Functions

2020 ◽  
Vol 75 (4) ◽  
Author(s):  
Mariusz Michta ◽  
Jerzy Motyl
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Differential Inclusions ◽  
Stochastic Integrals ◽  
Hölder Continuous ◽  
Stochastic Differential Inclusions ◽  
Different Types ◽  
Convexity Assumptions

AbstractThe paper deals with some selection properties of set-valued functions and different types of set-valued integrals of a Young type. Such integrals are considered for classes of Hölder continuous or with bounded Young p-variation set-valued functions. Two different cases are considered, namely set-valued functions with convex values and without convexity assumptions. The integrals contain as a particular case set-valued stochastic integrals with respect to a fractional Brownian motion, and therefore, their properties are crucial for the investigation of solutions to stochastic differential inclusions driven by a fractional Brownian motion.

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.

scholarly journals Second-order limit laws for occupation times of fractional Brownian motion

2017 ◽  
Vol 54 (2) ◽  
pp. 444-461 ◽  
Author(s):  
Fangjun Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Method Of Moments ◽  
Second Order ◽  
Hurst Index ◽  
Occupation Times ◽  
Limit Laws ◽  
Additive Functionals ◽  
Finite Dimensional ◽  
Functional Version

Abstract We prove a second-order limit law for additive functionals of a d-dimensional fractional Brownian motion with Hurst index H = 1 / d, using the method of moments and extending the Kallianpur–Robbins law, and then give a functional version of this result. That is, we generalize it to the convergence of the finite-dimensional distributions for corresponding stochastic processes.

Series in a Finite-Dimensional Space

1997 ◽  
pp. 13-27
Author(s):  
Mikhail I. Kadets ◽  
Vladimir M. Kadets
Keyword(s):  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Finite Dimensional
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