The boundary CONTROL of nonlinear parabolic equation with an integral performance criterion and a fixed final state is considered. By means of a well-known process of embedding (used by Rubio and others) for finite-dimensional system, this PROBLEM is replaced by one in which a linear form is minimized over a set of pairs of positive radon measures satisfying linear constraints. The OPTIMAL pair measures are then approximated by a finite combination of atomic measures and the PROBLEM converted to a finite-dimensional linear programming PROBLEM. The solution of this PROBLEM is used to construct a piecewise constant OPTIMAL CONTROL.The Advantages of this formulation are:(i) There is automatic existence theory.(ii) There exists the possibility of using linear functional analysis to developed the theory.(iii) The minimization is global.A numerical example is considered to illustrate the procedure.

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.

Non-cooperative intelligent CONTROL agents (ICAs) with dedicated cost functions, can lead the system to poor performance and in some cases, closed-loop instability. A robust solution to this challenge is to place the ICAs at the feedback Nash equilibrium point (FNEP) of the differential game between them. This paper introduces the designation of a robust decentralized infinite horizon LQR CONTROL system based on the FNEP for a linear time-invariant system. For this purpose, two CONTROL strategies are defined. The first one is a centralized infinite horizon LQR (CIHLQR) PROBLEM (i.e. a supervisory PROBLEM), and the second one is a decentralized CONTROL PROBLEM (i.e. an infinite horizon linear-quadratic differential game). Then, while examining the OPTIMAL solution of each of the above strategies on the performance of the other, the necessary and sufficient conditions for the equivalence of the two PROBLEMs are presented. In the absence of the conditions, by using the least-squares error criterion, an approximated CIHLQR CONTROLler is presented. It is shown that the theorems could be extended from a two-agent CONTROL system to a multi-agent system. Finally, the results are evaluated using the simulation results of a Two-Area non-reheat power system.

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.

In this paper a nonlinear OPTIMAL CONTROL is suggested. Spacecraft intended to rendezvous and dock with the target is CONTROLled by actuators to have a safe and stable course while satisfying requirements. The Nonlinear OPTIMAL CONTROLler is designed using nonlinear equations of relative position and attitude of spacecraft for circular and elliptical orbits with and without reaction wheels. Cost function of the OPTIMAL CONTROL PROBLEM is expressed in the form of nonlinear quadratic regulator and CONTROL constraints are applied to the PROBLEM to gain CONTROLs in the allowable domain which is produced by the wheels. For the sake of robustness to the uncertainties as one of the most important element of the CONTROL design, nonlinear OPTIMAL CONTROL is derived using state dependent Riccatti equation based on analytical method of eigen vectors of Hamiltonian matrix. Simulation results show that this nonlinear CONTROL method achieves a good performance for rendezvous and docking PROBLEM.

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