Complete controllability of impulsive stochastic integro-differential systems

This paper is concerned with the controllability of impulsive stochastic integro-differential systems. Sufficient conditions of complete controllability for impulsive stochastic integro-differential systems are obtained by using Schaefer’s fixed point theorem. A numerical example is provided to show the effectiveness of the proposed results.     

On the Controllability of Nonlocal Second‐Order Impulsive Neutral Stochastic Integro‐Differential Equations with Infinite Delay

In this paper, we investigate the controllability for a class of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay in Hilbert spaces. More precisely, a set of sufficient conditions for the controllability results of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay are derived by means of the Banach fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. As an application, an example is provided to illustrate the obtained theory.     

Sample controllability of impulsive differential systems with random coefficients

In this paper, we investigate the controllability of impulsive differential systems with random coefficients. Impulsive differential systems with random coefficients are a different stochastic model from stochastic differential equations. Sufficient conditions of sample controllability for impulsive differential systems with random coefficients are obtained by using random Sadovskii's fixed-point theorem. Finally, an example is given to illustrate our results.     

Controllability of non-linear impulsive stochastic systems

In this article, we consider the finite-dimensional dynamical control systems described by non-linear impulsive stochastic differential equations. Sufficient conditions for the complete and approximate controllability of non-linear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable.     

Approximate controllability of abstract stochastic impulsive systems with multiple time‐varying delays

This paper investigates the approximate controllability of abstract stochastic impulsive systems with multiple time‐varying delays. The class of stochastic impulsive systems consists of ordinary differential equations effected by impulse and noise environment. We focus first on constructing the control function. With this control function, we present sufficient conditions for approximate controllability problems in Hilbert space. The results are then extended to more easily verified conditions. The methods we choose are mainly Nussbaum fixed point theorem and stochastic analysis techniques combined with a strongly continuous semigroup. Finally, an example is given to illustrate the effectiveness of the results. Copyright © 2012 John Wiley & Sons, Ltd.     

Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces

Many practical systems in physical and technical sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, we prove the approximate controllability of control systems governed by a class of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established under the natural assumption that the corresponding linear system is approximately controllable. The results are obtained by using semigroup theory, stochastic analysis techniques, fixed point approach and abstract phase space axioms. An example is provided to illustrate the application of the obtained results.     

Controllability of impulsive second order semilinear fuzzy integrodifferential control systems with nonlocal initial conditions

In this paper, the controllability for a class of impulsive second order semilinear fuzzy integrodifferential control systems with nonlocal initial conditions has been considered. The sufficient conditions for the controllability are established by using the Banach fixed point theorem and the fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E_N. An example is given to illustrate the results.     

Controllability results for damped second-order impulsive neutral integrodifferential systems with nonlocal conditions

In this paper, we establish a set of sufficient conditions for the controllability of damped second-order impulsive neutral integrodifferential systems with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed point theorem combined with a noncompact condition on the cosine family of operators. An example is presented to illustrate the result.     

Controllability and observability for time‐varying switched impulsive controlled systems

This paper is concerned with the controllability and observability for linear time‐varying switched impulsive systems. First, some new results about the variation of parameters for time‐varying switched impulsive systems are derived. Then less conservative sufficient conditions and necessary conditions for state controllability and observability of such systems are established. And for such system without impulsive control input, sufficient and necessary conditions for controllability and observability are derived. Furthermore, corresponding criteria applied to time‐varying impulsive systems are also discussed and examples are presented to show the effectiveness of the proposed results. Copyright © 2009 John Wiley & Sons, Ltd.     

Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions

In this paper,we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces.We derive the c...     

Controllability of linear stochastic systems

We discuss several concepts of controllability for partially observable stochastic systems: complete controllability, approximate controllability, and stochastic controllability. We show that complete and approximate controllability notions are equivalent, and in turn they are equivalent to the stochastic controllability for linear stochastic systems controlled with Gaussian processes. We derive necessary and sufficient conditions for these concepts of controllability. These criteria reduce to the well-known rank condition     

On controllability of linear stochastic systems

We discuss several concepts of controllability for partially observable stochastic systems: complete controllability, approximate controllability, controllability and S-controllability, and show that complete and approximate controllability notions are equivalent, and in turn are equivalent to the controllability for linear stochastic systems controlled by gaussian processes. We derive necessary and sufficient conditions for these concepts of controllability. These criteria reduce to the well-known rank condition.     

Existence and Controllability Results for a New Class of Impulsive Stochastic Partial Integro‐Differential Inclusions with State‐Dependent Delay

In this paper, we study a new class of impulsive stochastic partial integro‐differential inclusions with state‐dependent delay in separable Hilbert spaces. Firstly, by using stochastic analysis theory, analytic resolvent operators, fractional powers of closed operators and suitable fixed point theorems, we prove the existence of mild and extremal mild solutions for these systems in the α‐norm. Secondly, we establish the controllability of the controlled stochastic partial integro‐differential inclusions with not instantaneous impulses. The results are obtained under the mixed Lipschitz and Carathéodory conditions. Finally, an example is provided to show the application of our results.     

Existence of Optimal Mild Solutions and Controllability of Fractional Impulsive Stochastic Partial Integro‐Differential Equations with Infinite Delay

In this paper, we investigate a new class of fractional impulsive stochastic partial integro‐differential equations with infinite delay in Hilbert spaces. By using the stochastic analysis theory, fractional calculus, analytic α‐resolvent operator and the fixed point technique combined with fractional powers of closed operators, we firstly give the existence of of mild solutions and optimal mild solutions for the these equations. Next, the controllability of the controlled fractional impulsive stochastic partial integro‐differential systems with not instantaneous impulses is presented. Finally, examples are also given to illustrate our results.     

On controllability and observability for a class of impulsive systems

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes. These complex dynamic behaviors can be modeled by impulsive differential systems. This paper studies the controllability and observability for a class of time-varying impulsive control systems. Several sufficient and necessary conditions for state controllability and state observability of such systems are established and the corresponding criteria for time-invariant impulsive control systems are also obtained. Meanwhile, several new results associated with variation of parameters for time-varying impulsive control systems are derived.     

Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems

In this work, the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems in a Banach space has been established by using the theory of fractional calculus, fixed point technique and also we introduced a new concept called (α,u)-resolvent family. As an application that illustrates the abstract results, an example is given.     

Controllability of Stochastic Delay Systems with Impulse in a Separable Hilbert Space

In this paper, we study the controllability of a kind of nonlinear stochastic impulsive system with infinite delay in abstract space. Sufficient conditions for the controllability are obtained via the generalization of the contraction mapping principle and with none of the compactness condition restriction on the evolution family of operators for the system. Finally, a numerical example is given to illustrate the effectiveness of our results.     

Approximate controllability results for impulsive neutral differential inclusions of Sobolev-type with infinite delay

The paper is mainly concerned with the approximate controllability results for a class of impulsive neutral differential control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of impulsive differential inclusions of Sobolev-type with infinite delay. With the help of semigroup theory and Bohnenblust-Karlin's fixed point theorem, we prove our main results. Then, we extend the result to study the approximate controllability for a class of impulsive neutral differential inclusions of Sobolev-type with infinite delay. Finally, an example is also presented to illustrate our theoretical results.     

On stochastic controllability for nonlinear systems

Both the stochastic ε-controllability and the stochastic controllability with probability one are first defined. Second, by using a stochastic Lyapunov-like approach, several theorems are developed which give sufficient conditions for the stochastic controllability defined for an important class of nonlinear stochastic systems. A theorem of stochastic uncontrollability is also presented, giving sufficient conditions for stochastic uncontrollability for a class of nonlinear systems. Finally, the relation between the deterministic controllability and the stochastic one is comparatively discussed.     

Approximate controllability of nonlinear stochastic impulsive systems with control acting on the nonlinear terms

This paper is concerned with the approximate controllability of the stochastic impulsive system with control acting on the nonlinear terms. In the case that the nonlinear terms are dependent on the control, the control cannot be expressed explicitly and analysed. In this situation, we generate the control sequence by the approximate equations and give the properties of the control sequence and the driven solution sets. Some discussions on the assumptions are given to impose on the system. The Hausdorff measure is adopted to relax the requirement of the compactness condition. It is also shown that under some sufficient conditions the stochastic impulsive system is approximately controllable without the requirement of the controllability of the associated linear system. The results of this paper can be degraded into special cases and coincide with some existing ones.