EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

Approximate controllability of infinite dimensional linear systems in nonreflexive state spaces

This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p（[0, T], U）, 1≤p〈∞ is obtained,where L^p（ [0, T], U） is the control function space.

APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS

In this article,we study the approximate controllability results for an integroquasilinear evolution equation with random impulsive moments under sufficient conditions.The results are obtained by the theory of C0 semigroup of bounded linear operators on evolution equations and using trajectory reachable sets.Finally,we generalize the results too with and without fixed type impulsive moments.

The cost of approximate controllability for semilinear heat equations

We consider the semilinear heat equation with globally Lipschitz non-linearity involving gradient terms in a bounded domain of R^n. In this paper, we obtain explicit bounds of the cost of approximate controllability, i.e., of the minimal norm of a control needed to control the system approximately. The methods we used combine global Carleman estimates, the variational approach to approximate controllability and Schauder＇s fixed point theorem.

Approximate Controllability of the System Governed by Double Coupled Semilinear Degenerate Parabolic Equations

This paper concerns the approximate controllability of the initialboundary problem of double coupled semilinear degenerate parabolic equations.The equations are degenerate at the boundary,and the control function acts in the interior of the spacial domain and acts only on one equation.We overcome the difficulty of the degeneracy of the equations to show that the problem is approximately controllable in L2 by means of a fixed point theorem and some compact estimates.That is to say,for any initial and desired data in L2,one can find a control function in L2 such that the weak solution to the problem approximately reaches the desired data in L2 at the terminal time.

APPROXIMATE CONTROLLABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS AND INFINITE DELAY

This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.

Approximate controllability results of semilinear integrodifferential equations with infinite delays

We study the approximate controllability of control systems governed by a class of semilinear integrod- ifferential equations with infinite delays. Sufficient conditions for approximate controllability of semilinear control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using fixed-point theorems and semigroup theory. As an illustration of the application of the approximate controllability results, a simple example is provided.

Approximate Controllability of Neutral Functional Differential Systems with State-Dependent Delay

This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.

Approximate Controllability of Second-order Semilinear Evolution Systems with Finite Delay

In this work,we study the approximate controllability for a class of semilinear second-order control systems with finite delay.Sufficient conditions for approximate controllability are established by constructing fundamental solutions and using the resolvent condition and techniques on cosine family of linear operators.To illustrate the applications of the obtained results,an example is provided in the end.

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.

Approximate Controllability for Degenerate Heat Equation with Bilinear Control

This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control.Both non-controllability and approximate controllability are studied for the system.If the control is restricted to act on a fixed domain,it is not controllable.If the control is allowed to mobile,it is approximately controllable.

Rothe’s Fixed Point Theorem and the Controllability of the Benjamin-Bona-Mahony Equation with Impulses and Delay

For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.

Call for papers Journal of Control Theory and Applications Special issue on Approximate dynamic programming and reinforcement learning

Approximate dynamic programming (ADP) is a general and effective approach for solving optimal control and estimation problems by adapting to uncertain and nonconvex environments over time.

OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES

This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations. The maximum principle and some kind of approximate controllability are studied.

Controllability of Semilinear Integrodifferential Degenerate Sobolev Equations

In this paper,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is investigated in the sense of integral solution in Hilbert spaces.Some sufficient and necessary conditions are obtained.Firstly,the existence and uniqueness of integral solutions of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions are considered by GE-evolution operator theory and Sadovskii’s fixed point theorem,the existence and uniqueness theorem of solutions is given.Secondly,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is studied in the sense of integral solution.The criterion for approximate controllability is provided.The obtained results have important theoretical and practical value for the study of controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions.

A Novel Distributed Optimal Adaptive Control Algorithm for Nonlinear Multi-Agent Differential Graphical Games

In this paper, an online optimal distributed learning algorithm is proposed to solve leader-synchronization problem of nonlinear multi-agent differential graphical games. Each player approximates its optimal control policy using a single-network approximate dynamic programming(ADP) where only one critic neural network(NN) is employed instead of typical actorcritic structure composed of two NNs. The proposed distributed weight tuning laws for critic NNs guarantee stability in the sense of uniform ultimate boundedness(UUB) and convergence of control policies to the Nash equilibrium. In this paper, by introducing novel distributed local operators in weight tuning laws, there is no more requirement for initial stabilizing control policies. Furthermore, the overall closed-loop system stability is guaranteed by Lyapunov stability analysis. Finally, Simulation results show the effectiveness of the proposed algorithm.

Energy Efficiency Optimization for D2D Communications Based on SCA and GP Method

In this paper, we propose an energy-efficient power control scheme for device-to-device(D2D) communications underlaying cellular networks, where multiple D2D pairs reuse the same resource blocks allocated to one cellular user. Taking the maximum allowed transmit power and the minimum data rate requirement into consideration, we formulate the energy efficiency maximization problem as a non-concave fractional programming(FP) problem and then develop a two-loop iterative algorithm to solve it. In the outer loop, we adopt Dinkelbach method to equivalently transform the FP problem into a series of parametric subtractive-form problems, and in the inner loop we solve the parametric subtractive problems based on successive convex approximation and geometric programming method to obtain the solutions satisfying the KarushKuhn-Tucker conditions. Simulation results demonstrate the validity and efficiency of the proposed scheme, and illustrate the impact of different parameters on system performance.

Sufficiency of Kalman's Rank Condition for the Approximate Boundary Controllability on an Annular Domain

In this paper the author establishes the sufficiency of Kalman’s rank condition on the approximate boundary controllability at a finite time for diagonalizable systems on an annular domain in higher dimensional case.

Controllability of Singular Distributed Parameter Systems in the Sense of Mild Solution

Necessary and sufficient conditions for the exact controllability and approximate controllability of a singular distributed parameter system are obtained.These general results are used to examine the exact controllability and approximate controllability of the Dzektser equation in the theory of seepage.