Semilinear Stochastic Systems Research Articles

Stochastic controllability of semilinear fractional control differential equations

The purpose of our research is to identify some sufficient conditions for the stochastic controllability of fractional-order semilinear stochastic systems. The required outcomes are achieved by dividing the system under consideration into two systems: a linear stochastic system and a semilinear deterministic system. The key outcomes are achieved by employing the Schauder fixed point technique, nonlinear monotonicity, and keeping just fractional-order α∈(1/2,1). One example is presented for demonstrating the outcomes.

Mean Square Finite-Approximate Controllability of Semilinear Stochastic Differential Equations with Non-Lipschitz Coefficients

In this paper, we present a study on mean square approximate controllability and finite-dimensional mean exact controllability for the system governed by linear/semilinear infinite-dimensional stochastic evolution equations. We introduce a stochastic resolvent-like operator and, using this operator, we formulate a criterion for mean square finite-approximate controllability of linear stochastic evolution systems. A control is also found that provides finite-dimensional mean exact controllability in addition to the requirement of approximate mean square controllability. Under the assumption of approximate mean square controllability of the associated linear stochastic system, we obtain sufficient conditions for the mean square finite-approximate controllability of a semilinear stochastic systems with non-Lipschitz drift and diffusion coefficients using the Picard-type iterations. An application to stochastic heat conduction equations is considered.

Partial observability of stochastic semilinear systems

In this article, we consider an Itô stochastic semilinear differential equation with unknown initial state and a linear observation system. It is proved that under a certain condition on the observability Gramian, the initial state of the equation can be recovered. This result is demonstrated by an example.

Approximate Controllability of Semilinear Stochastic Generalized Systems in Hilbert Spaces

Approximate controllability of two types of nonlinear stochastic generalized systems is investigated in the sense of mild solution in Hilbert spaces. Firstly, the approximate controllability of semilinear stochastic generalized systems with control only acting on the drift terms is discussed by GE-evolution operator and Nussbaum fixed-point theorem. Secondly, the approximate controllability of semilinear stochastic systems with control acting on both drift and diffusion terms is handled by using GE-evolution operator and Banach fixed-point theorem. At last, two illustrative examples are given.

Approximate controllability of semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control

The objective of this paper is to interpret the approximate controllability of a semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control in infinite-dimensional spaces. Sufficient conditions for the approximate controllability of semi-linear control system have been established. The results are obtained using the Banach fixed point theorem and the theory of resolvent operator developed in Grimmer [Resolvent operator for integral equations in Banach spaces, Trans. Am. Math. Soc. 273 (1982), pp. 333– 349.]. An example is introduced to show the effectiveness of the result.

Null controllability results for stochastic delay systems with delayed perturbation of matrices

Abstract In this paper, we adopt a notation of delayed perturbation of matrices to study controllability of stochastic delay systems in finite dimensional spaces. By using the delayed perturbation of matrix, we write an explicit formula of solutions to linear stochastic delay systems. We present the necessary and sufficient conditions for null controllability of linear stochastic delay systems by using perturbed controllability matrix and rank correlation method. Thereafter, sufficient conditions are derived for null controllability of semilinear stochastic delay systems under the proved results of corresponding linear stochastic system is null controllable, stochastic linear controllability operator, appropriate hypothesis on semilinear term and stochastic delay analysis techniques. The obtained theoretical results is verified through numerical simulation.

Output Feedback Stabilization for MIMO Semi-linear Stochastic Systems with Transient Optimisation

This paper investigates the stabilisation problem and consider transient optimisation for a class of the multi-input-multi-output (MIMO) semi-linear stochastic systems. A control algorithm is presented via an m-block backstepping controller design where the closed-loop system has been stabilized in a probabilistic sense and the transient performance is optimisable by optimised by searching the design parameters under the given criterion. In particular, the transient randomness and the probabilistic decoupling will be investigated as case studies. Note that the presented control algorithm can be potentially extended as a framework based on the various performance criteria. To evaluate the effectiveness of this proposed control framework, a numerical example is given with simulation results. In summary, the key contributions of this paper are stated as follows: 1) one block backstepping-based output feedback control design is developed to stabilize the dynamic MIMO semi-linear stochastic systems using a linear estimator; 2) the randomness and probabilistic couplings of the system outputs have been minimized based on the optimisation of the design parameters of the controller; 3) a control framework with transient performance enhancement of multi-variable semi-linear stochastic systems has been discussed.

Approximate controllability of semilinear fractional stochastic control system

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 Semilinear Stochastic Integrodifferential System with Nonlocal Conditions

The objective of this paper is to analyze the approximate controllability of a semilinear stochastic integrodifferential system with nonlocal conditions in Hilbert spaces. The nonlocal initial condition is a generalization of the classical initial condition and is motivated by physical phenomena. The results are obtained by using Sadovskii’s fixed point theorem. At the end, an example is given to show the effectiveness of the result.

The Solvability and Fractional Optimal Control for Semilinear Stochastic Systems

The Solvability and Fractional Optimal Control for Semilinear Stochastic Systems

Approximate controllability for a retarded semilinear stochastic evolution system

Approximate controllability for a retarded semilinear stochastic evolution system

Controllability of semilinear stochastic delay systems with distributed delays in control

This paper considers the problem of controllability for a class of semilinear stochastic delay systems with distributed delays in control. With the aid of fixed point arguments, sufficient conditions for the relative controllability of the above system are established. Examples are given to illustrate the procedure of the proposed method.

Approximate Controllability of Fractional Semilinear Stochastic System of Order α∈ (1,2

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in Lp spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory.

Controllability of semilinear stochastic control system with finite delay

Controllability of semilinear stochastic control system with finite delay

S-Controllability of a partially observed semilinear integrodifferential stochastic control system

In this article, some sufficient conditions are given for the S-controllability of a partially observed semilinear integrodifferential stochastic control system. Here, we established the controllability result using the separation principle approach in which the given semilinear stochastic control system is splitted into two control systems, namely one is semilinear deterministic control system and another is linear stochastic control system. An example is given to illustrate the result.

Semilinear stochastic equations with bilinear fractional noise

In the paper, we study existence and uniqueness of solutions to semilinear stochastic evolution systems, driven by a fractional Brownian motion with bilinear noise term, and the long time behavior of solutions to such equations. For this purpose, we study at first the random evolution operator defined by the corresponding bilinear equation which is later used to define the mild solution of the semilinear equation. The mild solution is also shown to be weak in the PDE sense. Furthermore, the asymptotic behavior is investigated by using the Random Dynamical Systems theory. We show that the solution generates a random dynamical system that, under appropriate stability and compactness conditions, possesses a random attractor.

Approximate controllability of semilinear stochastic system with multiple delays in control

The paper deals with the approximate controllability of a semi-linear stochastic system with multiple delays in control in infinite dimensional spaces. Sufficient conditions for the approximate controllability of the semi-linear control system have been established. The results are obtained using the Banach fixed-point theorem. An example is introduced to show the effectiveness of the result.

Approximate controllability of impulsive semilinear stochastic system with delay in state

ABSTRACTMany practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process that can be modeled by impulsive differential equations. This article studies the approximate controllability of impulsive semilinear stochastic system with delay in state in Hilbert spaces. Assuming the conditions for the approximate controllability of the corresponding deterministic linear system, we obtain the sufficient conditions for the approximate controllability of the impulsive semilinear stochastic system with delay in state. The results are obtained by using Banach fixed point theorem. Finally, two examples are given to illustrate the developed theory.

On controllability for a class of second order semilinear stochastic systems

Many dynamical systems are modeled as second order differential systems. In this paper we address the problem of controllability for second order semilinear stochastic systems in finite dimensional spaces. Sufficient criteria for the complete controllability are formulated under some appropriate assumptions. The results are obtained by using the Banach fixed point theorem. Finally an illustrative example is provided.

Approximate controllability of abstract semilinear stochastic control systems with nonlocal conditions

This paper studies the approximate controllability issue of an abstract semilinear stochastic control system with nonlocal conditions. Sufficient conditions are formulated and proved for the approximate controllability of such systems by splitting the given semilinear system into two systems, namely a semilinear deterministic system and a linear stochastic system. To prove the approximate controllability of semilinear deterministic system, Schauder fixed point theorem has been used. At the end, an example has been presented to illustrate the feasibility of the proposed result.