Null controllability of neutral system with infinite delays

<p style='text-indent:20px;'>This work devotes to the study on problems of optimal control and time optimal control for a neutral integro-differential evolution system with infinite delay. The main technique is the theory of resolvent operators for linear neutral integro-differential evolution systems constructed recently in literature. We first establish the existence and uniqueness of mild solutions and discuss the compactness of the solution operator for the considered control system. Then, we investigate the existence of optimal controls for the both cases of bounded and unbounded admissible control sets under some assumptions. Meanwhile, the existence of time optimal control to a target set is also considered and obtained by limit arguments. An example is given at last to illustrate the applications of the obtained results.</p>

In this article, we investigate the existence and uniqueness of solution of controlled hybrid neutral stochastic differential equations with infinite delay (HNSFDEswID). It is known that the time lag generated by the controller in each discrete observation must be different. The controlled HNSFDEswID are affected by the variable delay induced by the control function, the infinite time delay, and the highly nonlinear coefficients of the systems itself, which makes our problem more sophisticated. Different from the classical Khasminskii‐type conditions in the literature, we provide some sufficient conditions for the mean square and almost sure exponential stability for controlled HNSFDEswID by using the ‐matrix technique and a suitable Lyapunov functional. In this sense, the main contributions of our results, compared with those in the literature, are the infinite time delay, the neutral term, and the new Lyapunov functions. Finally, we illustrate our results by a numerical example.

We examine the controllability problem for a class of neutral fractional integrodifferential equations with impulses and infinite delay. More precisely, a set of sufficient conditions are derived for the exact controllability of nonlinear neutral impulsive fractional functional equation with infinite delay. Further, as a corollary, approximate controllability result is discussed by assuming compactness conditions on solution operator. The results are established by using solution operator, fractional calculations, and fixed point techniques. In particular, the controllability of nonlinear fractional control systems is established under the assumption that the corresponding linear control system is controllable. Finally, an example is given to illustrate the obtained theory.

This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.

Sufficient conditions are derived for the controllability of nonlinear neutral evolution integrodifferential systems with infinite delay in a Banach space. The results are obtained by using the resolvent operators and the Schaefer fixed-point theorem. An example is given to illustrate the results.

In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

New criteria on exponential stability of impulsive stochastic delayed differential systems with infinite delays

In this paper, finite element simulations are used to estimate the fatigue life of big turbo-generator shaft in uncontrolled and controlled system. The torque generated by the synchronous generator under loaded condition is analyzed for various types of electrical faults. The dq0 approach is used to model synchronous generator connected to an infinite bus. The torque outcome of loaded synchronous generator under various electrical faults is numerically simulated using MATLAB. The turbo-generator shaft is modeled using finite element formulation using different elements, i.e., solid cylindrical element, hollow cylindrical element and tapered element. The coupled dynamic MDOF equations are solved numerically to estimate the torque variation in shaft. The numbers of stress cycles are calculated using Rain Flow Counting method using stress at critical nodes of turbo-generator shaft. Further using piezoelectric sensor and actuator an active control system is achieved to reduce the vibrations produced in the shaft due to various faults. A closed-loop system is analyzed numerically using proportional and velocity feedback. The results of uncontrolled and controlled system are compared and vibrations in the controlled system found are to be reduced significantly using PD control law. Comparison of fatigue life generated shown that critical stress of the shaft can be reduced effectively in controlled system.

Stability analysis for stochastic neural network with infinite delay

Note on the permanence of a competitive system with infinite delay and feedback controls

We study the existence and asymptotic stability inpth moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite delays in Hilbert spaces. A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point technique for achieving the required result. The uniqueness of the solution of the considered problem is also studied under suitable conditions. Finally, an example is given to illustrate the obtained theory.

A discrete allelopathic phytoplankton model with infinite delays and feedback controls is studied in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantees the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the extinction of the system are obtained. Our results extend and supplement some known results and show that the feedback controls and toxic substances play a crucial role on the permanence and extinction of the system.

Asymptotic stability of impulsive stochastic partial differential equations with infinite delays

In this paper, by using fractional power of operators and Sadovskii fixed point theorem, we study the controllability of abstract neutral functional integrodifferential systems with infinite delay. As application, an example is provided to illustrate the obtained results.

The null controllability of thermoelastic plates and singularity of the associated minimal energy function