Controllability of delay systems with restrained controls

Using a geometric growth condition, we characterize both the function space and Euclidean controllability of a nonlinear delay system which has a compact and convex control set. This extends analogous results for ordinary differential systems, and it yields conditions under which perturbed nonlinear delay controllable systems are controllable.This research was supported by the National Aeronautics and Space Administration under Contract No. NSG 1445Now on leave of absence as Professor, Department of Mathematics, University of Jos, Jos, Nigeria.     

Controllability of nonlinear delay systems

A necessary and sufficient condition for complete controllability of differential systems with delay is proved, which extends analogous results for usual differential systems.     

Controllability of stochastic Volterra integrodifferential systems

In this paper, sufficient conditions for the controllability of stochastic integrodifferential systems in Banach spaces are established. The results are obtained by using a fixed point theorem. An example is provided to illustrate the theory.     

Controllability of impulsive neutral stochastic functional differential inclusions with infinite delay

This paper deals with the controllability of a class of impulsive neutral stochastic functional differential inclusions with infinite delay in an abstract space. Sufficient conditions for the controllability are derived with the help of the fixed point theorem for discontinuous multi-valued operators due to Dhage. An example is provided to illustrate the obtained theory.     

Controllability of perturbed nonlinear stochastic integrodifferential systems

The purpose of this paper is to establish the sufficient conditions concerning the complete controllability of stochastic integrodifferential systems in finite dimensional spaces by using the Banach fixed point theorem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Controllability of neutral functional evolution integrodifferential systems with infinite delay

In this paper we establish sufficient conditions for the controllability of neutral functional evolution integrodifferential systems. The results are obtained by using analytic semigroup theory and the Nussbaum fixed point theorem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Controllability of fractional neutral stochastic functional differential systems

In this paper, we study a class of fractional neutral stochastic functional differential systems. We obtain the controllability of the stochastic functional differential systems by the Sadovskii’s fixed point theorem under some suitable assumptions. An example is given to illustrate the theory.     

Controllability of semilinear stochastic systems in Hilbert spaces

We study the weak approximate and complete controllability properties of semilinear stochastic systems assuming controllability of the associated linear systems. The results are obtained by using the Banach fixed point theorem. Applications to stochastic heat equation are given.     

Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay

In this paper we establish sufficient conditions for the approximate controllability of impulsive neutral functional evolution integrodifferential systems in Hilbert spaces. Also we study the exact controllability of the same system. The conditions are obtained by using Schauder’s fixed point theorem when the operator is compact and the Banach fixed point theorem when the operator is not compact. The results are obtained by using the evolution operators.     

Controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space

In this paper, sufficient conditions are given for the controllability of a class of partial stochastic functional differential inclusions with infinite delay in an abstract space with the help of the Leray-Schauder nonlinear alternative. An example is provided to illustrate the theory.     

Stability of interconnected stochastic delay systems

A decomposition of a large-scale stochastic functional differential system into a family of isolated subsystems is made. A set of criteria is obtained under which the uniform asymptotic stability with probability one of the trivial solution process of the large-scale system is preserved. These criteria are expressed in terms of the stability of isolated subsystems and bounds on interconnection components. As a tool of our analysis, Razumikhin-type stability conditions for stochastic functional differential systems are also obtained. Several examples are given to show the applicability of our results.     

Controllability of impulsive functional differential systems with infinite delay in Banach spaces

The paper establishes a sufficient condition for the controllability of the first-order impulsive functional differential systems with infinite delay in Banach spaces. We use Schauder’s fixed point theorem combined with a strongly continuous operator semigroup. An example is given to illustrate our results.     

Controllability of impulsive neutral integrodifferential systems with infinite delay in Banach spaces

In this paper sufficient conditions for the controllability of impulsive neutral integrodifferential systems with infinite delay are established. The results are obtained by using the Schauder fixed point theorem.     

Dynamic programming in stochastic control of systems with delay

We consider optimal control problems for systems described by stochastic differential equations with delay (SDDE). We prove a version of Bellman's principle of optimality (the dynamic programming principle) for a general class of such problems. That the class in general means that both the dynamics and the cost depends on the past in a general way. As an application, we study systems where the value function depends on the past only through some weighted average. For such systems we obtain a Hamilton-Jacobi-Bellman partial differential equation that the value function must solve if it is smooth enough. The weak uniqueness of the SDDEs we consider is our main tool in proving the result. Notions of strong and weak uniqueness for SDDEs are introduced, and we prove that strong uniqueness implies weak uniqueness, just as for ordinary stochastic differential equations.     

Stability analysis for stochastic jump systems with time-varying delay

This paper deals with the mean-square asymptotic stability of stochastic Markovian jump systems with time-varying delay. Based on a new stochastic inequality and convex analysis property, some novel stability conditions are presented. In the derivation, the information of the time-varying delay is retained and the estimation of it by the worst-case enlargement is not involved. Some special cases of the systems under consideration are also investigated. Illustrative examples are given to show the effectiveness of the proposed approach.     

Transient behaviour of semilinear stochastic systems with random parameters

The transient solution of a class of nonautonomous, stochastic differential equations with given random initial conditions is studied. The considered evolution equation is characterized by the presence of a deterministic linear term and of a random nonlinear term whose parameters can be modeled by random processes of Rice noise type. Analytical approximated expressions for the first- and second-order moments and for the probability density of the solution process are derived and are applied to determine the statistical properties of a class of stochastic nonlinear oscillators.     

Controllability of semilinear stochastic functional integrodifferential systems in Hilbert spaces

In this paper approximate and exact controllability for semilinear stochastic functional integrodifferential systems are established. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the theory.