Approximate controllability of semilinear fractional stochastic control system

2018 ◽  
Vol 11 (06) ◽  
pp. 1850088
Author(s):  
Anurag Shukla ◽  
N. Sukavanam ◽  
D. N. Pandey
Keyword(s):  
Control System ◽  
Stochastic Control ◽  
Stochastic System ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Nonlinear Function ◽  
Lipschitz Continuous ◽  
Stochastic Control System ◽  
Fractional System ◽  
The Given

The objective of this paper is to present some sufficient conditions for approximate controllability of semilinear fractional stochastic control system with delay. The results hold when the nonlinear function is Lipschitz continuous. Sufficient conditions are obtained by separating the given fractional semilinear stochastic system into two systems namely a semilinear fractional system and a fractional linear stochastic system. To prove our results, the Schauder fixed point theorem is applied. At the end, one example is given to illustrate the results.

Approximate Controllability of Partial Fractional Neutral Integro-Differential Inclusions With Infinite Delay in Hilbert Spaces

2016 ◽  
Vol 11 (1) ◽  
Author(s):  
Zuomao Yan ◽  
Hongwu Zhang
Keyword(s):  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Multivalued Operators ◽  
Approximately Controllable ◽  
Fractional System ◽  
The Fixed Point Theorem ◽  
Necessary And Sufficient

We study the approximate controllability of a class of fractional partial neutral integro-differential inclusions with infinite delay in Hilbert spaces. By using the analytic α-resolvent operator and the fixed point theorem for discontinuous multivalued operators due to Dhage, a new set of necessary and sufficient conditions are formulated which guarantee the approximate controllability of the nonlinear fractional system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is provided to illustrate the main results.

scholarly journals Approximate Controllability of Semilinear Control System Using Tikhonov Regularization

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Ravinder Katta ◽  
N. Sukavanam
Keyword(s):  
Control System ◽  
Mild Solutions ◽  
Nonlinear Function ◽  
Actual State ◽  
Initial State ◽  
Lipschitz Continuous ◽  
Target State ◽  
Arbitrary Initial State ◽  
Ill Posed ◽  
Approximately Controllable

For an approximately controllable semilinear system, the problem of computing control for a given target state is converted into an equivalent problem of solving operator equation which is ill-posed. We exhibit a sequence of regularized controls which steers the semilinear control system from an arbitrary initial statex0to anϵneighbourhood of the target statexτat timeτ>0under the assumption that the nonlinear functionfis Lipschitz continuous. The convergence of the sequences of regularized controls and the corresponding mild solutions are shown under some assumptions on the system operators. It is also proved that the target state corresponding to the regularized control is close to the actual state to be attained.

scholarly journals Quality estimation of stochastic control system using simulation methods

2021 ◽  
Vol 61 ◽  
pp. 29-37
Author(s):  
Linas Aidokas ◽  
Laimutis Adolfas Telksnys
Keyword(s):  
Control System ◽  
Control Systems ◽  
Stochastic Control ◽  
Human Behavior ◽  
Experimental Research ◽  
Simulation Modeling ◽  
Management Systems ◽  
Simulation Methods ◽  
Quality Estimation ◽  
Stochastic Control System

The stochastic control system is investigated.  The article solves the problem of human-robot humanoid communication.  The problem arises in the development of human behavior formation management systems. They describe human behavior in terms of probabilistic characteristics. Such control systems are stochastic. The management system of human behavior formation and its functioning is described quality assessment. The problem is solved by simulation modeling. The software implementing the method is described. The results of experimental research are presented.

Controllability of nonlinear stochastic fractional higher order dynamical systems

2019 ◽  
Vol 22 (4) ◽  
pp. 1063-1085
Author(s):  
R. Mabel Lizzy ◽  
K. Balachandran ◽  
Yong-Ki Ma
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Necessary And Sufficient Condition ◽  
Bounded Operators ◽  
Semilinear Systems ◽  
Operator Functions ◽  
Fractional System ◽  
Necessary And Sufficient ◽  
The Given

Abstract This paper deals with the study of controllability of stochastic fractional dynamical systems with 1 < α ≤ 2. Necessary and sufficient condition for controllability of linear stochastic fractional system is obtained. Sufficient conditions for controllability of stochastic fractional semilinear systems, integrodifferential systems, systems with neutral term, systems with delays in control and systems with Lévy noise is formulated and established. The solution is obtained in terms of Mittag-Leffler operator functions by considering bounded operators. The Banach fixed point theorem is used to obtain the desired results from an equivalent nonlinear integral equation of the given system.

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