SINGULAR CONTROL OF STOCHASTIC VOLTERRA INTEGRAL EQUATIONS

This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s),u(s))dB(s)+∫_(0)^(t)h(t,s)dξ(s).by Here d B(s)denotes the Brownian motion It?type differential,ξdenotes the singular control(singular in time t with respect to Lebesgue measure)and u denotes the regular control(absolutely continuous with respect to Lebesgue measure).Such systems may for example be used to model harvesting of populations with memory,where X(t)represents the population density at time t,and the singular control processξrepresents the harvesting effort rate.The total income from the harvesting is represented by J(u, ξ) = E[∫_(0)^(t) f_(0)(t,X(t), u(t))dt + ∫_(0)^(t)f_(1)(t,X(t))dξ(t) + g(X(T))] for the given functions f0,f1 and g,where T>0 is a constant denoting the terminal time of the harvesting.Note that it is important to allow the controls to be singular,because in some cases the optimal controls are of this type.Using Hida-Malliavin calculus,we prove sufficient conditions and necessary conditions of optimality of controls.As a consequence,we obtain a new type of backward stochastic Volterra integral equations with singular drift.Finally,to illustrate our results,we apply them to discuss optimal harvesting problems with possibly density dependent prices.

Patients Transportation in Surgery Scheduling Problem

The scheduling problem in surgery is difficult because, in addition of the planning of the operating rooms which are the most expensive resources in hospitals, each surgery requires a combination of human and material resources. In this paper, the authors address a surgery scheduling problem which arises in operated health care facility. Moreover, the authors consider simultaneously materiel and human resources. This problem is a three-stages flow shop scheduling environment. The first stage(ward) contains a limited number of resources of the same type(beds);The second stage contains different resources with limited capacity(operating rooms, surgeons, nurses, anesthesiologists)and the third stage contains a limited number of recovery beds. There is also a limited number of transporters(porters) between the ward and the other stages. The objective of the problem is to minimize the completion time of the last patient(makespan). The authors formulate this NP-Hard problem in a mixed integer programming model and conduct computational experiments to evaluate the performance of the proposed model.

Distributed order estimation for continuous-time stochastic systems

In this paper,we investigate the distributed estimation problem of continuous-time stochastic dynamic systems over sensor networks when both the system order and parameters are unknown.We propose a local information criterion(LIC)based on the L_(0)penalty term.By minimizing LIC at the diffusion time instant and utilizing the continuous-time diffusion least squares algorithm,we obtain a distributed estimation algorithm to simultaneously estimate the unknown order and the parameters of the system.By dealing with the effect of the system noises and the coupling relationship between estimation of system orders and parameters,we establish the almost sure convergence results of the proposed distributed estimation algorithm.Furthermore,we give a simulation example to verify the effectiveness of the distributed algorithm in estimating the system order and parameters.

Credit Scoring Based on the Set-Valued Identification Method

Credit scoring is one of the key problems in financial risk managements.This paper studies the credit scoring problem based on the set-valued identification method,which is used to explain the relation between the individual attribute vectors and classification for the credit worthy and credit worthless lenders.In particular,system parameters are estimated by the set-valued identification algorithm based on a given recognition criteria.In order to illustrate the efficiency of the proposed method,practical experiments are conducted for credit card applicants of Australia and credit card holders from Taiwan,respectively.The empirical results show that the set-valued model has a higher prediction accuracy on both small and large numbers of data set compared with logistic regression model.Furthermore,parameters estimated by the set-valued identification method are more stable,which provide a meaningful and logical explanation for extracting factors that influence the borrowers’credit scorings.

Optimal Control Using Microscopic Models for a Pollutant Elimination Problem

Optimal control problem with partial derivative equation(PDE) constraint is a numericalwise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a new approach to solve this type of problem by space discretization and transform it into a standard optimal control for a multi-agent system. This resulting problem is formulated from a microscopic perspective while the solution only needs limited the macroscopic measurement due to the approach of Hamilton-Jacobi-Bellman(HJB) equation approximation. For solving the problem, only an HJB equation(a PDE with only terminal boundary condition) needs to be solved, although the dimension of that PDE is increased as a drawback. A pollutant elimination problem is considered as an example and solved by this approach. A numerical method for solving the HJB equation is proposed and a simulation is carried out.

Discrete-time inverse linear quadratic optimal control over fnite time-horizon under noisy output measurements

In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is considered.Our goal is to recover the corresponding quadratic objective function using noisy observations.First,the identifability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifable.Next,we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown,yet the exact observations on the initial states are available.We formulate the problem as a risk minimization problem and approximate the problem using empirical average.It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees.We then study the case where the exact observations on the initial states are not available,yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian(with unknown mean and covariance).EM-algorithm is used to estimate the parameters in the objective function.The efectiveness of our results are demonstrated by numerical examples.

Consistent Kalman flters for nonlinear uncertain systems over sensor networks

In this paper,we study how to design filters for nonlinear uncertain systems over sensor networks.We intoduce two Kalmantype nonlinear fitrs in centralied and dstrbute frameworks.Moreover,the tuning method for the parameters of the filteres is established to ensure the consistency,i.e..the mean square error is upper bounded by a known parameter matrix at each time.We apply the consistent fiters to the track to-track association analysis of multi targets with uncertain dynamics.A novel track to-track asocaion algoritm is proposed to idenify whether two tracks are from the same target.It is proven that the resulting probability of mis.asociation is lower than the desired threshold.Numerical simulations on track.to track association are given to show the ffetives of the methods.

Identifiability and Solvability in Inverse Linear Quadratic Optimal Control Problems

In this paper, the inverse linear quadratic(LQ) problem over finite time-horizon is studied.Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by considering the inverse problem as an identification problem, its model structure is shown to be strictly globally identifiable under the assumption of system invertibility. Next, in the noiseless case a necessary and sufficient condition is proposed for the solvability of a positive semidefinite weighting matrix and its unique solution is obtained with two proposed algorithms under the condition of persistent excitation. Furthermore, a residual optimization problem is also formulated to solve a best-fit approximate cost function from sub-optimal observations. Finally, numerical simulations are used to demonstrate the effectiveness of the proposed methods.