In this paper, we formulate an optimal control problem for an SIR epidemic model with saturated incidence and saturated treatment. Two main efforts, namely treatment and vaccination are considered to limit the disease transmission. The impacts of vaccination and treatment on the disease transmission are discussed through the basic reproduction number. Then to achieve control of the disease, a c...

We present a model for an SIR epidemic in a population consisting of two components—locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2-group population in a very simple form. Finally we support our analysis by numerical simulation using the...

An optimal stochastic control problem is considered for systems with unbounded controls satisfying an integral constraint. It is shown that there exists an optimal control within the class of generalized controls leading to impulse actions. Applying an approach of time transformation, developed recently for deterministic systems, the original control problem is shown to be equivalent to an opti...

We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the many-server heavy traffic regime for parallel server systems when the service times are only server pool dependent and exponenti...

There has been much progress in the development of a model of motor control in the brain in the last decade; from the improved method for mathematically extracting the predicted movement direction from a population of neurons to the application of optimal control theory to motor control models, much work has been done to further our understanding of this area. In this paper recent literature is...

The paper provides a systematic way for finding a partial differential equation that directly characterizes the optimal control, in the framework of one–dimensional stochastic control problems of Mayer type, with no constraints on the controls. The results obtained are applied to continuous–time portfolio problems.

The paper describes the analysis, design and control of two new versions of spherical permanent magnet motor, which are capable of two and three degrees-of-freedom of controlled motion, and have a high specific torque capability. Their magnetic field distribution is established using an analytical technique formulated in spherical coordinates. This enables the torque vector and back-emf to be d...

Market segmentation has emerged as the primary means by which firms achieve optimal production policy. In this paper, we use market segmentation approach in multi-product inventory system with inventory-level-dependent demand. The objective is to make use of optimal control theory to solve the inventory-production problem and develop an optimal production policy that minimizes the total cost as...

We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged ...

In this paper, we relax the assumption of a known time horizon in optimal control models.