existence and global attractivity of positive periodic solutions of functional differential equations with feedback control sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the delay differential system with feedback controldxdt b t x t f t x email protected 1 t x email protected n t u email protected t email protected t u t a t x email protected t the method involves the application of krasnoselskii s fixed point theorem and estimates of uniform upper and lower bounds of solutions when these results are applied to some special delay population models with multiple delays some new results are obtained and some known results are generalized

convergence of controlled models and finite state approximation for discounted continuous time markov decision processes with constraints abstract in this paper we consider the convergence of a sequence m n of the models of discounted continuous time constrained markov decision processes mdp to the limit one denoted by m for the models with denumerable states and unbounded transition rates under reasonably mild conditions we prove that the constrained optimal policies and the optimal values of m n converge to those of m respectively using a technique of occupation measures as an application of the convergence result developed here we show that an optimal policy and the optimal value for countable state continuous time mdp can be approximated by those of finite state continuous time mdp finally we further illustrate such finite state approximation by solving numerically a controlled birth and death system and also give the corresponding error bound of the approximation

parabolic evolution equations and nonlinear boundary conditions on etudie le probleme aux valeurs limites et initiales u 7b a t u f t u 7b b t u g t u 0 t t u 0 u 0 qui peut etre considere comme une contrepartie abstraite a des problemes paraboliques semilineaires

denumerable constrained markov decision processes and finite approximations the purpose of this paper is two fold first to establish the theory of discounted constrained markov decision processes with a countable state and action spaces with general multi chain structure second to introduce finite approximation methods we define the occupation measures and obtain properties of the set of all achievable occupation measures under the different admissible policies we establish the optimality of stationary policies for the constrained control problem and obtain an lp with a countable number of decision variables through which stationary optimal policies are computed since for such an lp one cannot expect to find an optimal solution in a finite number of operations we present two schemes for finite approximations and establish the convergence of optimal values and policies for both the discounted and the expected average cost with unbounded cost sometimes it turns out to be easier to solve the problem with infinite state space than the problem with finite yet large state space based on the optimal policy for the problem with infinite state space we construct policies which are almost optimal for the problem with truncated state space this method is applied to obtain an e optimal policy for a problem of optimal priority assignment under constraints for a system of k finite queues

bias optimality for continuous time controlled markov chains in this paper we give conditions for the existence of bias optimal policies in a class of continuous time controlled markov chains with unbounded reward and transition rates several characterizations of bias optimality are proposed we also introduce new sets of conditions ensuring uniform exponential ergodicity of continuous time controlled markov chains

the vanishing discount approach to constrained continuous time controlled markov chains we consider a denumerable state continuous time controlled markov chain cmc with possibly unbounded transition and reward rates we deal with constrained optimality that is we want to maximize a discounted reward an average reward criterion subject to a constraint on a discounted cost an average cost we give conditions ensuring that the average constrained optimal reward and policies can be obtained as the limit as the discount rate vanishes of the corresponding discounted constrained optimal reward and policies this extends to average constrained cmcs the standard results on the vanishing discount approach for the average unconstrained case we also present an example showing that the vanishing discount results for constrained problems might not hold

almost periodic solutions of n species competitive system with feedback controls abstract in this paper the following almost periodic n species competitive system with feedback controls x i t x i t b i t j 1 n a ij t x j t j 1 j i n c ij t x i t x j t d i t u i t u i t r i t e i t u i t f i t x i t i 1 2 n are studied by using the comparison theorem and constructing suitable lyapunov function where some important factors such as the effect of toxic and the age structure are also considered simultaneously some sufficient conditions are obtained for the existence of a unique almost periodic solution of above model examples show that the obtained criteria are new general and easily verifiable

ergodic control of continuous time markov chains with pathwise constraints this paper deals with unichain ergodic continuous time controlled markov chains cmcs with a denumerable state space and possibly unbounded reward rates as well as unbounded transition rates the problem we are concerned with is to find control policies that maximize a sample path average reward over the family of admissible policies for which a certain pathwise average cost is below a given value with probability one to study this problem first we give conditions for the existence of sample path average optimal policies then we analyze constrained average reward cmcs with expected constraints and finally we apply these results to our original control problem with pathwise constraints examples on the control of a queueing system and an epidemic process illustrate the feasibility of our approach

new results on positive periodic solutions of a periodic integro differential competition system considered is the periodic integro differential competition system with infinite delays recently studied by fan and wang z angew math mech 81 2001 197 using the method of coincidence degree we present another set of sufficient conditions for the existence of positive componentwise periodic solutions of the system our results improve and supplement those obtained by fan and wang z angew math mech 81 2001 197

permanence in nonautonomous multi species predator prey system with feedback controls a nonautonomous multi species predator prey system with feedback controls is proposed in this paper where the competition among the predator species and among the prey species is considered also some important factors such as the effect of toxins and the age structure are also considered average conditions are obtained for permanence and global attractivity in the system the results obtained here generalized the main results of zhao and jiang j d zhao j f jiang permanence in nonautonomous lotka volterra system with predator prey appl math computat 152 2004 99 109

computable approximations for continuous time markov decision processes on borel spaces based on empirical measures in this paper we propose an approach for approximating the value function and an optimal policy of continuous time markov decision processes with borel state and action spaces with possibly unbounded cost and transition rates under the total expected discounted cost optimality criterion under adequate assumptions which in particular include that the transition rate has a density function with respect to a reference measure together with piecewise lipschitz continuity of the elements of the control model we approximate the original controlled process by a model with finite state and action spaces the approximation error is related to the 1 wasserstein distance between suitably defined probability measures and approximating measures with finite support we also study the case when the reference measure is approximated with empirical distributions and we show that convergence of the approximations takes place at an exponential rate in probability

positive almost periodic solutions of a class of lotka volterra type competitive system with delays and feedback controls abstract in this paper we study the positive almost periodic solutions for a class of almost periodic lotka volterra type system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive almost periodic solution of the system is obtained our new criterion which improves and generalizes some well known results can be easily checked

a different consideraton about the globally asymptotically stable solution of the periodic n competing species problem abstract we consider the volterra lotka equations for n competing species n 2 in which the right hand sides are periodic in time we show that conditions given by k gopalsamy j austral math soc ser b 27 1985 66 72 which imply the existence of a periodic solution with positive components also imply the uniqueness and asymptotic stability of the solution

periodic solutions and almost periodic solutions for a delay multispecies logarithmic population model by using the method of fixed point theory and lyapunov functional a set of easily applicable criteria are established for the existence uniqueness and global attractivity of positive periodic almost periodic solution of a delay multispecies logarithmic population model

drift and monotonicity conditions for continuous time controlled markov chains with an average criterion we give conditions for the existence of average optimal policies for continuous time controlled markov chains with a denumerable state space and borel action sets the transition rates are allowed to be unbounded and the reward cost rates may have neither upper nor lower bounds in the spirit of the drift and monotonicity conditions for continuous time markov processes we propose a new set of conditions on the controlled process primitive data under which the existence of optimal deterministic stationary policies in the class of randomized markov policies is proved using the extended generator approach instead of kolmogorov s forward equation used in the previous literature and under which the convergence of a policy iteration method is also shown moreover we use a controlled queueing system to show that all of our conditions are satisfied whereas those in the previous literature fail to hold

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

approximating ergodic average reward continuous time controlled markov chains we study the approximation of an ergodic average reward continuous time denumerable state markov decision process mdp by means of a sequence of mdps our results include the convergence of the corresponding optimal policies and the optimal gains for a controlled upwardly skip free process we show some computational results to illustrate the convergence theorems

exact finite approximations of average cost countable markov decision processes for a countable state markov decision process we introduce an embedding which produces a finite state markov decision process the finite state embedded process has the same optimal cost and moreover it has the same dynamics as the original process when restricting to the approximating set the embedded process can be used as an approximation which being finite is more convenient for computation and implementation