Each dynamic job shop can be represented as a network of queues, in which each service station indicates a machine or a production department. Now, assume that the service rates of these service stations can be CONTROLled. In this paper, a new model is developed for bicriteria OPTIMAL CONTROL of service rates of all service stations in a class of Jackson networks, in which the expected value of the shortest path of the network and, also, the total operating costs of all service stations of the network, per period, are minimized. The expected value of the shortest path of such a network of queues is equal to the expected value of the time that the first product is completed.This is an important factor in production systems, because, related to design and manufacture of a new product, the first manufactured product often has the maximum flow time, in effect, which can be minimized through the model. The networks of queues analyzed in this paper, have all the specifications of Jackson networks, except for not containing M/M /C queueing systems.

Singular systems have been studied extensively during the last two decades due to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking PROBLEM for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the OPTIMAL CONTROL and associated trajectory. Two methods are presented for solving these trajectories. The first method uses the concept of the Drazin inverse, and the second involves the derivation and solution of a Riccati equation. Similar to the linear regulator PROBLEM, necessary and sufficient conditions for existence and uniqueness of a solution are stated.

OPTIMAL CONTROL theory is a branch of mathematics. It is developed to find OPTIMAL ways to CONTROL a dynamic system. In 1957, R.Bellman applied dynamic programming to solve OPTIMAL CONTROL of discrete-time systems. His procedure resulted in closed-loop,  generally nonlinear, and feedback schemes. OPTIMAL CONTROL PROBLEMs which will be tackled involve the minimization of a cost function subject to constraints on the state vector and the CONTROL. Lagrange multipliers provide a method of converting a constrained minimization PROBLEM into an unconstrained minimization PROBLEM of higher order. The necessary condition for OPTIMALity can be obtained as the solution of the unconstrained optimization PROBLEM of the Lagrange function and the bordered Hessian matrix is used for the second-derivative test. A spectral method for solving OPTIMAL CONTROL PROBLEMs is presented. The method is based on Bernoulli polynomials approximation. By using the Bernoulli operational matrix of integration and the Lagrangian function, stochastic OPTIMAL CONTROL is transformed into an optimisation PROBLEM, where the unknown Bernoulli coefficients are determined by using Newton's iterative method. The convergence analysis of the proposed method is given. The simulation results based on the Monte-Carlo technique prove the performance of the proposed method. Some error estimations are provided and illustrative examples are also included to demonstrate the efficiency and applicability of the proposed method.

In this study, an indirect method is proposed based on the Chebyshev pseudo-spectral method for solving OPTIMAL CONTROL PROBLEMs governed by Burgers' equation. Pseudo-spectral methods are one of the most accurate methods for solving nonlinear continuous-time PROBLEMs, specially OPTIMAL CONTROL PROBLEMs. By using OPTIMALity conditions, the original OPTIMAL CONTROL PROBLEM is  rst reduced to a system of partial differential equations with boundary conditions. CONTROL and state functions are then approximated by interpolating polynomials. The convergence is analyzed, and some numerical examples are solved to show the efficiency and capability of the method.

In this paper we consider an OPTIMAL CONTROL PROBLEM for an inhomogeneous Heat equation. We transfer the PROBLEM into a moment PROBLEM. Then this moment PROBLEM is changed to measure theoretic CONTROL PROBLEM, and the new PROBLEM is converted to an infinite dimensional linear programming PROBLEM. Finally we approximate the infinite dimensional linear programming PROBLEM to a finite dimensional one and the solution to this PROBLEM is used to find a piecewise constant CONTROL for the original PROBLEM