optimal birth control for an age dependent n dimensional food chain model abstract in this paper we investigate optimal policies for an age dependent n dimensional food chain model which is controlled by fertility by using dubovitskii milyutin s general theory the maximum principles are obtained for problems with free terminal states infinite horizon and target sets respectively

a meshless local collocation method for time fractional diffusion wave equation abstract in this manuscript we present a radial basis function based local collocation method for solving time fractional diffusion wave equation the advantage of the local collocation method is only the discretization points located in each sub domain surrounding the collocation point need to be considered it also avoids the ill conditioning problem arises due to the use of global collocation method the theoretical stability and convergence of the proposed time semi discrete scheme are also discussed numerical experiments for one dimension and two dimension problems are carried out it is shown that the present method is efficient and numerical results have nice agreements with theoretical result

hermite birkhoff interpolation on scattered data on the sphere and other manifolds abstract the hermite birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered each proposed interpolant is expressed as a linear combination of basis functions the combination coefficients being incomplete taylor expansions of the interpolated function at the interpolation points the basis functions depend on the geodesic distance are orthonormal with respect to the point evaluation functionals and have all derivatives equal zero up to a certain order at the interpolation points a remarkable feature of such interpolants which belong to the class of partition of unity methods is that their construction does not require solving linear systems numerical tests are given to show the interpolation performance

a prediction error and stepwise regression estimation algorithm for non linear systems the identification of non linear systems based on a narmax non linear autoregressive moving average model with exogenous inputs model representation is considered and a combined stepwise regression prediction error estimation algorithm is derived the stepwise regression routine determines the model structure by detecting significant terms in the model while the prediction error algorithm provides optimal estimates of the final model parameters implementation of the algorithms is discussed in detail and several simulated examples and industrial applications are included to illustrate that parsimonious models of non linear systems can be identified using the algorithm

on the controllability of the lotka mckendrick model of population dynamics abstract in this work we consider the problem of exact controllability of the linear lotka mckendrick model of population dynamics we establish an observability inequality and show that any initial condition can be steered into any quasi steady state by a distributed control except for a small interval of ages near zero in contrast with that we observe that the boundary control is more efficient in the sense that it controls the entire population the biological implication of our conclusions is that a closed population is more efficiently controlled through birth control as opposed to migration and eradication in particular this supports the trap alter release method for controlling a population of stray cats as opposed to the trap and kill method

on a distributed control problem arising in dynamic optimization of a fixed size population the practical motivation for this paper is provided by the recruitment problem faced by many organizations of fixed size to keep the average age young and thus keep innovation and productivity high while at the same time keeping levels of recruitment high a typical example is an academy of sciences the problem is formalized by an infinite horizon optimal control model for a first order pde with nonlocal dynamics a mckendrick type equation based on the nonstandard necessary optimality condition proved in the paper the following results are established i stationarity of the optimal recruitment density ii strong ergodicity of the optimal solution iii principle of bipolar recruitment in the case where the productivity of the organization is measured by the average age of the members the analysis involves a new type of transversality condition for the costate system the stability with respect to perturbations of the optimal solution of a noncoercive bang bang type problem boundedness and stability of the solution of a specific volterra integral equation of the second kind

new coordination strategy for on line hierarchical optimizing control of large scale industrial processes abstract a new coordination strategy for hierarchical optimizing control is presented unlike the price coordination method this approach is not a primal and dual method and its convergence behaviour does not depend on the feature of the saddle point of the problem lagrangian compared with the price coordination method this approach has two advantages firstly its applicability conditions are easier to satisfy and secondly its convergence behaviour is more desirable in terms of convergence rate and insensitivity of the hessian structure of the problem a variable augmentation technique is employed to increase the flexibility of the iterative gain selection and to improve further the convergence behaviour of the method optimality and convergence analysis are provided for each different version of the algorithm presented a comparative study between different versions of the algorithm presented and a single iterative integrated system optimization and parameter estimation isope method with global fee

an interval for the shape parameter in radial basis function approximation the radial basis functions rbfs depend on an auxiliary parameter called the shape parameter great theoretical and numerical efforts have been made to find the relationship between the accuracy of the rbf approximations and the value of the shape parameter in many cases the numerical approaches are based on minimization of an estimation of the error function such as rippa s approach and its modifications these approaches determine a value for the shape parameter in this paper we propose a practical approach to determine an interval instead of a value without any minimization and estimation of error function the idea is based on adding a loop on the shape parameter but not to minimize an error norm suitable values of the shape parameter are determined by take into account the practical convergence behavior of the problem the proposed method is applied to some illustrative examples including one and two dimensional interpolation and partial differential equations the results of the method are compared with those of some other approaches to confirm the reliability of the method furthermore numerical stability of the method of line respect to the shape parameter is considered for time dependent pdes the results show that the proposed method can be used as an independent method to find a shape parameter and also as an alternative for investigating the validity of the values of the other methods

optimal birth control of age dependent competitive species abstract this work is concerned with optimal policies for two age structured biological populations in a competing system which is controlled by fertilities the maximum principles for problems with free terminal infinite horizon and target sets are obtained respectively via dubovitskii milyutin s general extremal theory

optimal control for age structured population dynamics of incomplete data we are concerned with the control question for linear age structured population dynamics of incomplete initial data more precisely the initial population age distribution is supposed to be unknown we here generalize the notion of no regret control of lions 1992 10 to such singular population dynamics following the method by nakoulima omrane and velin 2000 16 we prove that the problem we are considering has a unique no regret control that we characterize by a singular optimality system

optimal birth control of population dynamics abstract we study optimal birth control policies for an age structured population of mckendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control the functional analytic approach of dubovitskii and milyutin is adopted in the investigation maximum principles for problems with a free end condition a fixed final horizon are developed and the time optimal control problem the problem with target sets and the infinite planning horizon case are investigated

a numerical scheme for solving a class of logarithmic integral equations arisen from two dimensional helmholtz equations using local thin plate splines abstract this paper presents a numerical method for solving logarithmic fredholm integral equations which occur as a reformulation of two dimensional helmholtz equations over the unit circle with the robin boundary conditions the method approximates the solution utilizing the discrete collocation method based on the locally supported thin plate splines as a type of free shape parameter radial basis functions the local thin plate splines establish an efficient and stable technique to estimate an unknown function by a small set of nodes instead of all points over the solution domain to compute logarithm like singular integrals appeared in the method we use a particular nonuniform gauss legendre quadrature rule since the scheme does not require any mesh generations on the domain it can be identified as a meshless method the error estimate of the proposed method is presented numerical results are included to show the validity and efficiency of the new technique these results also confirm that the proposed method uses much less computer memory in comparison with the method established on the globally supported thin plate splines moreover it seems that the algorithm of the presented approach is attractive and easy to implement on computers

improvements in the formulation and solution approach for stochastic optimizing control of steady state industrial processes an improved formulation for stochastic steady state optimizing control problems is presented owing to its different structure it is applicable to a larger group of practical problems than an earlier version lin et al 1989 a theoretical analysis is carried out to investigate the viability of the new formulation a modified approach to stochastic steady state optimizing control problems under such a formulation is also presented here a modified steady state identification technique is employed to estimate the mean derivative that is required in calculating the modifier the dynamic information acquired from the real process between any two successive controller set point changes is used the advantage of this approach is that it significantly reduces the required number of controller set point changes and is much less sensitive to noise than the modified two step methods optimality and global convergence conditions are provided consistency and asymptotic behaviour of the modified steady state iden

new approach to stochastic optimizing control of steady state systems using dynamic information an underlying relationship between a dynamic stochastic control system and its steady state counterpart is thoroughly investigated a novel approach which uses both dynamic and steady state information for solving the stochastic steady state optimizing control problem is presented a two stage steady state system identification technique is proposed and employed in the presented approach to estimate the expectation of the real process derivative compared with integrated system optimization and parameter estimation isope methods this new approach has reduced significantly the required controller set point changes and is much less sensitive when subjected to noise optimality of the algorithm is examined and sufficient conditions for global convergence are provided consistency and asymptotic behaviour of the two stage identification method are also investigated computer simulations are provided and comparisons are made between the isope method and the presented approach simulation results show that t

optimal birth control problems for a nonlinear vermin population model with size structure abstract in this paper we investigate theoretically the least cost size problem and the least cost deviation problem for a nonlinear size structured vermin population model with separable mortality which takes fertility rate as the control variable we obtain the existence of a unique non negative solution by considering the separable solution of the model which is crucial to obtain the optimal control strategy we also illustrate the continuous dependence of the population density on initial value and control parameter finally we study the least cost size problem and the least cost deviation problem our conclusion would be useful for managing the vermin

a two stage adaptive scheme based on rbf collocation for solving elliptic pdes abstract in this paper we present a new adaptive two stage algorithm for solving elliptic partial differential equations via a radial basis function collocation method our adaptive meshless scheme is based at first on the use of a leave one out cross validation technique and then on a residual subsampling method each of phases is characterized by different error indicators and refinement strategies the combination of these computational approaches allows us to detect the areas that need to be refined also including the chance to further add or remove adaptively any points the resulting algorithm turns out to be flexible and effective through a good interaction between error indicators and refinement procedures several numerical experiments support our study by illustrating the performance of our two stage scheme finally the latter is also compared with an efficient adaptive finite element method

modelling and analysis of non linear time series the modelling of non linear time series is reviewed and new results are introduced by employing some ideas from the identification of non linear control systems both global and local conditions for stationary and invertibility are established for the general non linear time series model and it is shown how these results provide a framework for time series estimators methods of computing multistep ahead predictions are studied and the usefulness of polynomial models is discussed

hierarchical integrated identification and optimization approach for on line stochastic optimizing control of large scale steady state industrial processes based on a centralized formulation for stochastic steady state optimizing control problems a hierarchical formulation for such problems is proposed and analysed a hierarchical joint system identification and set point optimization approach is devised and implemented with two different iterative strategies for on line stochastic optimizing control of large scale steady state industrial processes the optimality and convergence of the approach are examined joint dynamic and steady state simulation studies are provided showing that the approach is very efficient and reliable

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

a pontryagin maximum principle for infinite dimensional problems a basic idea of the classical approach for obtaining necessary optimality conditions in optimal control is to construct suitable needle like control variations we use this idea to prove the main result of the present paper a pontryagin maximum principle for infinite dimensional optimal control problems with pointwise terminal constraints in arbitrary banach state space by refining the classical variational technique we are able to replace the differentiability of the norm of the state space guaranteed by the strict convexity of its dual norm which is assumed in the known results by a separation argument we also drop another key assumption which is common in the existing literature on infinite dimensional control problems that the set of variations in the state space of the state trajectory s endpoint resulting from the control variations be finite codimensional instead we require only that it has nonempty interior in its closed affine hull as an application of the abstract result we present an illustrative example an optimal control problem for an age structured system with pointwise terminal state constraints

optimal birth control of age dependent competitive species ii free horizon problems we study optimal birth policies for two age dependent populations in a competing system which is controlled by fertilities new results on problems with free final time and integral phase constraints are presented and the approximate controllability of system is discussed

implicit local radial basis function interpolations based on function values in this paper we propose two fast localized radial basis function fitting algorithms for solving large scale scattered data interpolation problems for each given point in the given data set a local influence domain containing a small number of nearest neighboring points is established and a global interpolation is performed within this restricted domain a sparse matrix is formulated based on the global interpolation in these local influence domains the proposed methods have achieved both low computational cost and minimal memory storage in comparison with the compactly supported radial basis functions the proposed fitting algorithms are highly accurate the numerical examples have provided strong evidence that the two proposed algorithms are indeed highly efficient and accurate in the two proposed algorithms we have successfully solved a large scale interpolation problem with 225 000 interpolation points in two dimensional space

optimal harvesting for a nonlinear age dependent population dynamics here we investigate an optimal harvesting problem for a nonlinear age dependent population dynamics existence and uniqueness of a positive solution for the model are demonstrated the structure of the solution is also investigated we establish the existence of the optimal control and the convergence of a certain fractional step scheme for some approximating problems we obtain the optimal controllers in feedback form via the dynamic programming method

overtaking optimal control problem for an age dependent competition system of n species abstract in this paper the overtaking optimal control problem for an age dependent competition model of n species with unbounded time interval is considered the existence of overtaking optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions weak and strong turnpike properties of optimal trajectories are established

on a population dynamics control problem with age dependence and spatial structure we consider the control problem for a population dynamics model with age dependence spatial structure and a nonlocal birth process arising as a boundary condition we examine the controllability at a given time t and show that approximate controllability holds for every fixed finite time t as a consequence a new uniqueness condition continuation result is proved

overtaking optimal control problem of age dependent populations with infinite horizon abstract the optimal birth control of an age dependent population model with unbounded time interval is considered the minimum principle which must be satisfied by the overtaking optimal control is established large time behaviour and the turnpike property of the overtaking optimal trajectory are studied existence results are also presented

optimal birth control of age dependent competitive species iii overtaking problem a study is made of an overtaking optimal problem for a population system consisting of two competing species which is controlled by fertilities the existence of optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions weak and strong turnpike properties of optimal trajectories are established

optimal harvesting for periodic age dependent population dynamics here we investigate the optimal harvesting problem for some periodic age dependent population dynamics namely we consider the linear lotka mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations existence and uniqueness of a positive periodic solution are demonstrated and the existence and uniqueness of the optimal control are established we also state necessary optimality conditions a numerical algorithm is developed to approximate the optimal control and the optimal harvest some numerical results are presented

optimality conditions for age structured control systems abstract we consider a fairly general model extension of the gurtin maccamy model of population dynamics of an age structured control system with nonlocal dynamics and nonlocal boundary conditions a necessary optimality condition is obtained in the form of pontryagin s maximum principle which is applicable to a number of practically meaningful models where the previously known results fail we discuss such models an epidemic control and a capital accumulation model as illustrations

optimal birth control of population dynamics ii problems with free final time phase constraints and mini max costs abstract we study optimal birth control of population systems of mckendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control new results on problems with free final time phase constraints and mini max costs are presented

extension of integrated system optimization and parameter estimation to hierarchical control of steady state systems with output dependent constraints this paper proposes an alternative hierarchical integrated system optimization and parameter estimation technique obtained by combining a modified two step method with the price method the aim is to find a general hierarchical approach for the case where inequality constraints are output dependent in this algorithm a new modifier is introduced to cope with the output dependent constraints this algorithm has the advantages that the existence of the model based optimal solution is ensured during the course of iteration and the model optimization is simplified considerably this technique uses an output feedback structure and a single loop iteration strategy optimality properties and convergence conditions are investigated a simulation study is also presented