control of singularly perturbed hybrid stochastic systems we study a class of optimal stochastic control problems involving two different time scales the fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process under a fundamental ergodicity property for a class of infinitesimal control systems associated with the fast mode we show that there exists a limit problem which provides a good approximation to the optimal control of the perturbed system both the finite and infinite discounted horizon cases are considered we show how an approximate optimal control law can be constructed from the solution of the limit control problem in the particular case where the infinitesimal control systems possess the so called turnpike property i e characterized by the existence of global attractors the limit control problem can be given an interpretation related to a decomposition approach

perturbation analysis for production control and optimization of manufacturing systems we use stochastic fluid models sfm to capture the operation of threshold based production control policies in manufacturing systems without resorting to detailed discrete event models by applying infinitesimal perturbation analysis ipa to a sfm of a workcenter we derive gradient estimators of throughput and buffer overflow metrics with respect to production control parameters it is shown that these gradient estimators are unbiased and independent of distributional information of supply and service processes involved in addition based on the fact that they can be evaluated using data from the observed actual discrete event system we use them as approximate gradient estimators in simple iterative schemes for adjusting thresholds hedging points on line seeking to optimize an objective function that trades off throughput and buffer overflow costs

global weak solutions in a three dimensional keller segel navier stokes system involving a tensor valued sensitivity with saturation abstract this paper is concerned with the following keller segel navier stokes system n t u n n n s x n c c x t 0 c t u c c c n x t 0 u t u u u p n x t 0 u 0 x t 0 where r 3 is a bounded domain with smooth boundary r and s denotes a given tensor valued function fulfilling s x n c c s 1 n with some c s 0 and 0 as the case 0 has been considered in 25 it is shown in the present paper that the corresponding initial boundary problem with 0 admits at least one global weak solution if 3 7

jump control of probability densities with applications to autonomous vehicle motion we investigate the problem of controlling the probability density of the state of a process that is observed by the controller via a fixed but unknown scalar non negative function of the state the goal is to control the process so that its probability density at a point in the state space becomes proportional to the value of the function observed at that point our solution inspired by bacterial chemotaxis involves a randomized controller that switches among different deterministic modes we show that under appropriate existence conditions this controller guarantees convergence of the probability density to the desired function the results can be applied to the problem of in loco optimization of a measurable signal using a team of autonomous vehicles that measure the signal but do not have access to position measurements alternative applications in the area of mobile robotics include deployment and environmental monitoring

robust control strategies for multi inventory systems with average flow constraints in this paper we consider multi inventory systems in the presence of uncertain demand we assume that i demand is unknown but bounded in an assigned compact set and ii the control inputs controlled flows are subject to assigned constraints given a long term average demand we select a nominal flow that feeds such a demand in this context we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average we provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows such conditions are based on linear programming and thus they are constructive in the special case of a static flow i e a system with 0 capacity buffers we show that the strategy must be affine the dynamic problem can be solved by a linear saturated control strategy inspired by the previous one we provide numerical analysis and illustrative examples

structural properties of optimal production controllers in failure prone manufacturing systems a failure prone manufacturing system with one part type and multiple machine states is considered each machine state has a given production capacity but is associated with several possible failure stages although transition times between failure stages are assumed exponential the existence of multiple stages within each machine state allows failure times to have a distribution more general than the exponential distribution for such a system it is shown that the well known hedging point policy minimizes inventory and backlog costs for a constant demand rate the value of the optimal hedging points is now a function of failure stage as well as machine state by ordering machine states according to increasing distance from the zero capacity state and failure stages according to distance from the capacity reduction transition we show that hedging points increase monotonically when the machine state number decreases or the stage number increases this can be intuitively interpreted as follows the closer to the zero capacity state the system is the larger the hedging point should be this structural property of the optimal control is very useful in searching for the optimal control or designing near optimal controls

overtaking optimal regulation and tracking of piecewise diffusion linear systems the infinite horizon optimal control of linear stochastic systems with quadratic cost integrand is studied and the tracking of a periodic signal on an infinite time interval is considered the system is exposed to three types of noises and is modeled by a nonhomogeneous linear stochastic control plant with modal and diffusion disturbances where the dynamics switch at random times within a finite number of descriptions according to a markov chain the overtaking optimality criterion is employed considering the expected cost the existence of a unique optimal control is established for the above noisy control systems with partial information this is realized as an affine feedback control of the best estimate of the state moreover in the case of partial information this feedback control is proved to be also almost surely overtaking optimal

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

hierarchical production control in a stochastic n machine flowshop with limited buffers abstract this paper is concerned with an asymptotic analysis of hierarchical production planning in a stochastic manufacturing system consisting of machines that are subject to breakdown and repair the system produces a single product whose rate of demand over time is constant the problem is formulated as a continuous time dynamic programming problem in which the objective is to minimize the cost of production inventories and backlogs the size of the buffer between the two adjacent machines is assumed to have lower and upper bound constraints as the rates of change of the machine states approach infinity the analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability the value function for the original problem converges to the value function of the limiting problem a method of shrinking total lifting and modification is introduced in order to construct near optimal controls for the original problem by using near optimal controls of the limiting problem the convergence rate of the value function for the original problem to that of the limiting problem is established this helps in providing an error estimate for the constructed open loop asymptotic optimal control

symmetric solutions for an elliptic partial differential equation that arises in stochastic production planning with production constraints abstract in this article we consider the question of the existence of positive symmetric solutions to the problems of the following type u a x h u b x g u for x r n which are called entire large solutions here n 3 and we assume that a and b are nonnegative continuous spherically symmetric functions on r n we extend results previously obtained for special cases of h and g and we will describe a real world model in which such problems may arise

production control of manufacturing systems with production rate dependent failure rates it is known that for single part type production systems with homogeneous markovian machine failure rates special single threshold feedback policies called hedging point policies are optimal and the stationary probability distribution of the part type surplus for given tentative hedging point values can be obtained analytically this approach is extended to multiple threshold policies with production rate dependent machine failure rates it is shown that the stationary distribution of the part type surplus can be obtained under the extended policy and in the presence of production rate dependent failure rates the advantage of multiple threshold policies is that they can provide a piecewise constant step function approximation of any feedback policy it is observed that hedging point policies are not always optimal and in fact feedback policies are not always optimal either

stability analysis for stochastic hybrid systems this survey addresses stability analysis for stochastic hybrid systems shs which are dynamical systems that combine continuous change and instantaneous change and that also include random effects we re emphasize the common features found in most of the models that have appeared in the literature which include stochastic switched systems markov jump systems impulsive stochastic systems switching diffusions stochastic impulsive systems driven by renewal processes diffusions driven by levy processes piecewise deterministic markov processes general stochastic hybrid systems and stochastic hybrid inclusions then we review many of the stability concepts that have been studied including lyapunov stability lagrange stability asymptotic stability and recurrence next we detail lyapunov based sufficient conditions for these properties and additional relaxations of lyapunov conditions many other aspects of stability theory for shs like converse lyapunov theorems and robustness theory are not fully developed hence we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces

boundedness and finite time collapse in a chemotaxis system with volume filling effect abstract we consider the elliptic parabolic pde system u t u u u v x t 0 0 v m u x t 0 with nonnegative initial data u 0 having mean value m under homogeneous neumann boundary conditions in a smooth bounded domain r n the nonlinearities and are supposed to generalize the prototypes u u 1 p u u u 1 q 1 with p 0 and q r problems of this type arise as simplified models in the theoretical description of chemotaxis phenomena under the influence of the volume filling effect as introduced by painter and hillen k j painter t hillen volume filling and quorum sensing in models for chemosensitive movement can appl math q 10 2002 501 543 it is proved that if p q 2 n then all solutions are global in time and bounded whereas if p q 2 n q 0 and is a ball then there exist solutions that become unbounded in finite time the former result is consistent with the aggregation inhibiting effect of the volume filling mechanism the latter however is shown to imply that if the space dimension is at least three then chemotactic collapse may occur despite the presence of some nonlinearities that supposedly model a volume filling effect in the sense of painter and hillen

optimal feedback production planning in a stochastic two machine flowshop abstract in this paper we consider a production planning problem in a two machine flowshop subject to breakdown and repair of machines and subject to non negativity constraints on work in process the machine capacities and demand processes are assumed to be finite state markov chains the problem is to choose the rate of production over time so as to minimize the expected discounted cost of production and inventory backlog over an infinite horizon the problem is formulatred as a stochastic dynamic programming problem it is shown that the value function of the problem is locally lipschitz and is a viscosity solution to the dynamic programming equation together with certain boundary conditions optimal feedback control policies are obtained in terms of the partial derivatives of the value function it is shown that the derived control policy is feasible on the boundary of the state space the results establish the theoretical framework within which further analyses and or numerical solutions of the problem can be attempted

comments on a generalization of rosenbrock s theorem by m schlegel in the above paper ibid vol ac 32 p 155 feb 1987 the author presents a generalization of the famous rosenbrock theorem concerning the problem of synthesis of linear state feedback control laws for linear controllable systems the commenters point out that this result was published by them earlier in an alternative form here they give again alternative conditions for solvability of the problem since the original papers published in 1979 and 1985 were in russian in contrast to the conditions given in the above paper their conditions are not redundant and are given in terms of order relation on the lattice of integer partitions

stability and optimality of a multi product production and storage system under demand uncertainty this work develops a discrete event model for a multi product multi stage production and storage p s problem subject to random demand the intervention problem consists of three types of possible decisions made at the end of one stage which depend on the observed demand or lack of for each item i to proceed further with the production of the same product ii to proceed with the production of another product or iii to halt the production the intervention problem is formulated in terms of dynamic programming dp operators and each possible solution induces an homogeneous markov chain that characterizes the dynamics however solving directly the dp problem is not a viable task in situations involving a moderately large number of products with many production stages and the idea of the paper is to detach from strict optimality with monitored precision and rely on stability the notion of stochastic stability brought to bear requires a finite set of positive recurrent states and the paper derives necessary and sufficient conditions for a policy to induce such a set in the studied p s problem an approximate value iteration algorithm is proposed which applies to the broader class of control problems described by homogeneous markov chains that satisfy a structural condition pointed out in the paper this procedure iterates in a finite subset of the state space circumventing the computational burden of standard dynamic programming to benchmark the approach the proposed algorithm is applied to a simple two product p s system

on controlability of linear systems with stochastic jump parameters this note studies the notion of stochastic e controllability in probability for linear systems subject to sudden jumps in parameter values by using a lyapunov like approach sufficient conditions are obtained in terms of a set of coupled bernoulli equations the potential use of the results is illustrated by an example

on an infinite dimensional perturbed riccati differential equation arising in stochastic control existence and uniqueness of solutions for a class of infinite dimensional perturbed riccati differential equations in a certain banach space is our main concern in this paper besides the interest in its own right this class arises in control problems involving linear systems with countably infinite markov jump parameters

electric load model synthesis by diffusion approximation of a high order hybrid state stochastic system a statistical approach is used to model the dynamics of the electric demand of large aggregates of electric space heaters or air conditioners the importance of such loads is twofold first they account for a significant portion of power system dynamics following a power outage second because they are associated with energy storage they are often selected for load shedding within a load management program the derivation of the aggregate electrical dynamics is considered first for a homogeneous group of devices subsequently a perturbation analysis yields the dynamics for a nonhomogeneous group the homogeneons group aggregrate load model is a system of coupled ordinary and partial differential equations fokker planck equations it is obtained by writing evolution equations for the probability density of a hybrid state markov system used to model the switching dynamics of individual devices this result is new and could give a clue to the analysis of a broad class of hybrid state stochastic systems in turn this could provide a new impetus not only in the area of electric load modeling but other areas such as power system reliability and the design of relay control systems where stochastic hybrid state models occur frequently simulation results which illustrate the dynamical properties of the model are presented

an interesting property of the husimi function and its implications we prove that after the transformation q p to lambda q lambda p where 0 lambda 1 every husimi function with appropriate renormalization remains in the class of husimi distributions we discuss some implications of this fact on the problem of the phase distribution of a quantum state we show that wigner and p functions do not have this property

on the influence of noise on jump linear systems jump linear systems are considered in a random environment where they are subject to additive and multiplicative noises stochastic notions of stabilizability and detectability are introduced to characterize the asymptotic behavior of the optimal jump linear quadratic gaussian regulator and a dual kalman filter

quantum states which behave classically we give a definition of quantum states which behave classically based on minimal number of physically reasonable requirements we prove that an infinite unique class of states exists which satisfies this definition and we show that every state from this class may be generated in the unique way departing from some corresponding strictly quantum state we discuss some implications of the obtained results

optimal feedback production planning in a stochastic n machine flowshop we consider a production planning problem in an n machine flowshop subject to breakdown and repair of machines and to non negativity constraints on work in process the machine capacities and demand processes are assumed to be finite state markov chains the problem is to choose the rates of production on the n machines over time to minimize the expected discounted cost of production and inventory backlog over an infinite horizon it is formulated as a stochastic dynamic programming problem we show that the value function of the problem is locally lipschitz and is a solution to a dynamic programming equation together with a certain boundary condition we provide an interpretation of the boundary condition we also prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the value function finally we obtain a deterministic optimal control problem that is equivalent to the stochastic production planning problem under consideration

global weak solutions in a three dimensional keller segel navier stokes system with nonlinear diffusion abstract the coupled quasilinear keller segel navier stokes system ksnf n t u n n m n c x t 0 c t u c c c n x t 0 u t u u p u n x t 0 u 0 x t 0 is considered under neumann boundary conditions for n and c and no slip boundary conditions for u in three dimensional bounded domains r 3 with smooth boundary where m 0 r are given constants w 1 if m 2 then for all reasonably regular initial data a corresponding initial boundary value problem for ksnf possesses a globally defined weak solution

an asymptotic analysis of hierarchical control of manufacturing systems under uncertainty this paper presents an asymptotic analysis of a hierarchical manufacturing system with machines subject to breakdown and repair the rate of change in machine states is much larger than the rate of fluctuation in demand and the rate of discounting of costs and this gives rise to a limiting problem in which the stochastic machine availability is replaced by the equilibrium mean availability the value function for the original problem converges to the value function of the limiting problem moreover the control for the original problem can be constructed from the optimal controls of the limiting problem in a way which guarantees asymptotic optimality of the value function the limiting problem is computationally more tractable and sometimes has a closed form solution

a manufacturing system with general stationary failure process stability and ipa of hedging control policies this paper concerns a new methodology for the adaptive optimization of piecewise deterministic non markovian systems via a simple example of interest in manufacturing this methodology takes into account the fact that piecewise deterministic systems are rarely markovian and that classical control theory based on dynamic programming of markovian systems cannot provide quantitative answers in most realistic situations the example considered is that of a single machine single part production system from the point of view of the control theory by kimemia and gershwin 1983 we obtain stochastic gradient estimates via the perturbation analysis of ho and cao 1991 by the regenerative method of konstantopoulos and zazanis 1992 in view of stochastic optimization its mathematical justification requires a careful study of the regenerative structure of the process in particular we give the necessary and sufficient conditions of stability of this system via the method of loynes 1962

jump linear quadratic control with random state discontinuities abstract in a random environment jump linear quadratic control problems are studied random state discontinuities are included in the analysis and the corresponding optimal regulator is obtained the introduction of stochastic notions of stabilizability and detectability gives a direct characterization of the asymptotic behaviour of the optimal system

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

optimal control for continuous time linear quadratic problems with infinite markov jump parameters the subject matter of this paper is the optimal control problem for continuous time linear systems subject to markovian jumps in the parameters and the usual infinite time horizon quadratic cost what essentially distinguishes our problem from previous ones inter alia is that the markov chain takes values on a countably infinite set to tackle our problem we make use of powerful tools from semigroup theory in banach space and a decomplexification technique the solution for the problem relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution of the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd these concepts are couched into the theory of operators in banach space and parallel to the classical linear quadratic lq case bound up with the spectrum of a certain infinite dimensional linear operator

ergodicity of hedging control policies in single part multiple state manufacturing systems the markov renewal viewpoint of single part multiple state manufacturing systems under hedging control policies subjected to a constant rate of demand for parts is used to derive sufficient criteria to guarantee the ergodicity of the resulting parts surplus process the criteria are simple and directly verifiable from an analysis of the markov chain characterizing the dynamics of the discrete manufacturing system production state a key intermediate result in reaching these criteria is a potentially very useful system of linear differential equations with boundary conditions which can be generalized to permit computation of moments of arbitrary order for sojourn times in the regions between successive hedging points in the parts surplus space

when does a given function in phase space belong to the class of husimi distributions the problem of finding a density matrix corresponding to a husimi distribution is solved in a simple new way it is shown how the proposed procedure may be effectively used to answer the question raised in the title

boundedness vs blow up in a chemotaxis system abstract we determine the critical blow up exponent for a keller segel type chemotaxis model where the chemotactic sensitivity equals some nonlinear function of the particle density assuming some growth conditions for the chemotactic sensitivity function we establish an a priori estimate for the solution of the problem considered and conclude the global existence and boundedness of the solution furthermore we prove the existence of solutions that become unbounded in finite or infinite time in that situation where this a priori estimate fails

perturbation analysis for the design of flexible manufacturing system flow controllers dynamic allocation of stochastic capacity among competing activities in a just in time manufacturing environment is addressed by optimal flow control optimal policies are characterized by generally intractable bellman equations a near optimal controller design technique is proposed it provides an approximate numerical solution to the bellman equation a tight lower bound for the optimality gap of tractable near optimal controller designs and a building block for improved near optimal controller designs that rely on the decomposition of a multiple part type problem to smaller two or three part type problems computational experience is reported for two and three part type problems

discounted stochastic fluid programs we consider optimal control problems for stochastic fluid models of the following type suppose z t is a continuous time markov chain with finite state space as long asz t z the dynamics of the system at timet are given by a functionb z u i whereu is a control we have to choose a cost rate functionc is given depending on the state and the action we want to control the system in such a way as to minimize the expected discounted cost over an infinite horizon we will call a problem of this type astochastic fluid program sfp they typically appear in production and telecommunication systems we formulate the optimization problem as a discrete time markov decision process and give conditions under which an optimal stationary policy exists furthermore we show how to solve sfps numerically using kushner s approximating markov chain approach last but not least we apply our results to a multiproduct manufacturing system without backlog

adaptive control for manufacturing systems using infinitesimal perturbation analysis combining infinitesimal perturbation analysis ipa with stochastic approximation gives identification algorithms to estimate the optimal threshold value for failure prone manufacturing systems consisting of one machine producing one part type two adaptive control schemes are proposed the adaptive control schemes do not require the knowledge of the distribution functions of the up and down times under some appropriate conditions the strong consistency as well as the convergence rates of the identification algorithms and the cost function is established for the adaptive control schemes in particular it is shown that central limit theorems hold for the identification algorithms

production control of a manufacturing system with multiple machine states the production control of a single product manufacturing system with arbitrary number of machine states failure modes is discussed the objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost the optimal production policy has a special structure and is called a hedging point policy if the hedging points are known the optimal production rate is readily specified assuming a set of tentative hedging points the simple structure of the optimal policy is utilized to find the steady state probability distribution of the surplus inventory or backlog once this function is determined the average surplus cost is easily calculated in terms of the values of the hedging points the average cost is then minimized to find the optimum hedging points

global solvability and large time behavior to a three dimensional chemotaxis stokes system modeling coral fertilization abstract we consider the chemotaxis stokes system n t u n n n c c m n x t 0 m t u m m n m x t 0 c t u c c c m x t 0 u t u p n m x t 0 u 0 x t 0 under homogenous neumann boundary conditions in a three dimensional bounded domain r 3 with smooth boundary here is a nondecreasing function on 0 it is shown that if k 0 k 0 2 27 with k 0 max c 0 l m 0 l then the system possesses a globally bounded classical solution

a renewal theoretic analysis of a class of manufacturing systems the authors present the partial differential equations pdes describing the transients of the probability density functions pdfs characterizing the statistical evolution of a manufacturing system producing a single product under hedging point control policies the authors demonstrate the markov renewal nature of the dynamics of the controlled process and use the system of pdes to compute the transition kernel of that renewal process this markov renewal viewpoint is particularly useful in discussing ergodicity in view of the abundant literature on the asymptotic behavior of markov renewal processes moreover besides allowing direct determination of system steady state when it exists it permits the computation of various statistics as well as in some cases the derivation of bounds on the speed of convergence to steady state

probabilistic reachability and safety for controlled discrete time stochastic hybrid systems in this work probabilistic reachability over a finite horizon is investigated for a class of discrete time stochastic hybrid systems with control inputs a suitable embedding of the reachability problem in a stochastic control framework reveals that it is amenable to two complementary interpretations leading to dual algorithms for reachability computations in particular the set of initial conditions providing a certain probabilistic guarantee that the system will keep evolving within a desired safe region of the state space is characterized in terms of a value function and maximally safe markov policies are determined via dynamic programming these results are of interest not only for safety analysis and design but also for solving those regulation and stabilization problems that can be reinterpreted as safety problems the temperature regulation problem presented in the paper as a case study is one such case

production control of manufacturing systems a multiple time scale approach in this note a stochastic production model containing processes with different time scales is developed it is shown that if the time scales of the processes are very different some hierarchical algorithms that are much more efficient than the standard policy iteration method can be developed to find the optimal production control moreover if the time scales fall far apart the optimal control of a deterministic limiting problem depending only on the mean characteristics of the processes can be used to approximate the optimal control of the original problem the limiting problem has much lower dimension than its original counterpart and thus is much easier to solve a numerical example is used to illustrate the potential of the proposed approach

unreliable production inventory model with a two phase erlang demand arrival process a production inventory system is studied in which an unreliable machine is susceptible to failure following which it must be repaired to make it operative again the demand for the product is governed by a two phase erlang process and demand sizes are independent and identically distributed random variables a two critical number policy m m is used to control a machine s setups and shutdowns namely the machine is shut down whenever the inventory level reaches m and is resumed to operate only when the inventory level falls below the critical number m m m we obtain the steady state distribution of the inventory process and some performance measures of the process

pade approximants for the transient optimization of hedging control policies in manufacturing part production is considered over a finite horizon in a single part multiple failure mode manufacturing system when the rate of demand for parts is constant for markovian machine mode dynamics and for convex running cost functions associated with part inventories or backlogs it is known that optimal part production policies are of the so called hedging type for the infinite horizon case such policies are characterized by a set of constant critical machine mode dependent inventory levels that must be aimed at and maintained whenever possible for the finite horizon transient case the critical levels still exist but they are now time varying and in general very difficult to characterize thus in an attempt to render the problem tractable transient production optimization is sought within the suboptimal class of time invariant hedging control policies a renewal equation is developed for the cost functional over finite horizon under an arbitrary time invariant hedging control policy

the relation between the scaling of husimi functions and the linear phase insensitive amplification of the corresponding quantum states and its implications using the description of the linear phase insensitive amplification of a quantum state available in the literature we prove that to every state produced from the initial state by such amplification there corresponds a phase space distribution where is the husimi function of the initial state the scaling parameter satisfies the relation and decreases with time while as we have shown earlier the scaled function is again a husimi distribution we prove using these facts that if the definition of the phase insensitive amplification is physically correct then the distribution of the phase of a state is unambiguously given as the corresponding marginal distribution obtained from its husimi distribution represented in polar coordinates

global existence and boundedness in a keller segel navier stokes system with signal dependent sensitivity abstract in this paper we consider the following keller segel navier stokes system n t u n n n c c x t 0 c t u c c c n x t 0 u t u u u p n x t 0 u 0 x t 0 where r n n 2 3 is a bounded domain with smooth boundary r and c is assumed to generalize the prototype c 0 1 c 2 c 0 it is proved that i for 0 and n 2 or 0 and n 2 3 the corresponding initial boundary problem admits a unique global classical solution which is bounded ii for 0 and n 3 the corresponding initial boundary problem possesses at least one global weak solution

a numerical method to approximate optimal production and maintenance plan in a flexible manufacturing system abstract the simultaneous planning of the production and the maintenance in a flexible manufacturing system is considered in this paper the manufacturing system is composed of one machine that produces a single product there is a preventive maintenance plan to reduce the failure rate of the machine this paper is different from the previous researches in this area in two separate ways first the failure rate of the machine is supposed to be a function of its age second we assume that the demand of the manufacturing product is time dependent and its rate depends on the level of advertisement on that product the objective is to maximize the expected discounted total profit of the firm over an infinite time horizon in the process of finding a solution to the problem we first characterize an optimal control by introducing a set of hamilton jacobi bellman partial differential equations then we realize that under practical assumptions this set of equations can not be solved analytically thus to find a suboptimal control we approximate the original stochastic optimal control model by a discrete time deterministic optimal control problem then proposing a numerical method to solve the steady state riccati equation we approximate a suboptimal solution to the problem

circulant preconditioners for failure prone manufacturing systems this paper studies the application of preconditioned conjugate gradient methods in solving for the steady state probability distribution of manufacturing systems we consider the optimal hedging policy for a failure prone one machine system the machine produces one type of product and its demand has finite batch arrival the machine states and the inventory levels are modeled as markovian processes we construct the generator matrix for the machine inventory system the preconditioner is constructed by taking the circulant approximation of the near toeplitz structure of the generator matrix we prove that the preconditioned linear system has singular values clustered around one when the number of inventory levels tends to infinity hence conjugate gradient methods will converge very fast when applied to solving the preconditioned linear system numerical examples are given to verify our claim the average running cost for the system can be written in terms of the steady state probability distribution the optimal hedging point can then be obtained by varying different values of the hedging point

asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers we consider a production planning problem for a jobshop with unreliable machines producing a number of products there are upper and lower bounds on intermediate parts and an upper bound on finished parts the machine capacities are modelled as finite state markov chains the objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production finding an optimal control policy for this problem is difficult instead we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity the asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities the value function for the original problem is shown to converge to the value function of the limiting problem the convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established

stochastic dynamic job shops and hierarchical production planning this paper presents an asymptotic analysis of hierarchical production planning in a general manufacturing system consisting of a network of unreliable machines producing a variety of products the concept of a dynamic job shop is introduced by interpreting the system as a directed graph and the structure of the system dynamics is characterized for its use in the asymptotic analysis the optimal control problem for the system is a state constrained problem since the number of parts in any buffer between any two machines must remain nonnegative a limiting problem is introduced in which the stochastic machine capacities are replaced by corresponding equilibrium mean capacities as the rate of change in machine states approaches infinity the value function of the original problem is shown to converge to that of the limiting problem and the convergence rate is obtained furthermore near optimal controls for the original problem are constructed from near optimal controls of the limiting problem and an error estimate is obtained on the near optimality of the constructed controls

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques