Optimal prediction is a method to approximate the average solution of a large system of ordinary differential equations by a smaller system. In this thesis we show how optimal prediction can be applied in the field of molecular dynamics in order to reduce the number of particles. We apply optimal prediction to a model problem describing a surface coating process and show how asymptotic methods ...

In this paper, the nonlinear optimal control problem is formulated for the position control of an electrohydraulic servo system. The optimal control is given by the solution to the Hamilton-Jacobi-Bellman equation, which in this case cannot be solved explicitly. An alternative method, based upon successive Galerkin approximation, is used to obtain an approximate optimal solution. Preliminary si...

the purpose of the matching interdiction problem in a weighted graph is to findtwo vertices such that the weight of the maximum matching in the graph withoutthese vertices is minimized. an approximate solution for this problem has beenpresented. in this paper, we consider dendrimers as graphs such that the weightsof edges are the bond lengths. we obtain the maximum matching in some types ofdend...

In this paper, Homotopy perturbation method is used to find the approximate solution of the optimal control of linear systems. In this method the initial approximations are freely chosen, and a Homotopy is constructed with an embedding parameter   0,1 p , which is considered as a “small parameter”. Some examples are given in order to find the approximate solution and verify the efficiency of...

We consider the generalized airfoil equation in the situation where the index of the problem is −1. We periodize the problem, then discretize it by a fully discrete version of the trigonometric collocation method and apply the conjugate gradient method to solve the discretized problem. The approximate solution appears to be of optimal accuracy in a scale of Sobolev norms, and the N parameters o...

An online adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem for continuous-time uncertain nonlinear systems. A novel actor–critic–identifier (ACI) is proposed to approximate the Hamilton–Jacobi–Bellman equation using three neural network (NN) structures—actor and critic NNs approximate the optimal control and the optimal value function,...

This paper presenting case studies in modern large scale constrained optimization, the purpose of which is to illustrate how recent advances in algorithms and modelling languages have made it easy to solve difficult optimization problems using of software. In this paper we use measure theory technique and iterative dynamic programming algorithm for solving of a trajectory optimization problem: ...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

The purpose of this article is to review the literature on the topic of deterministic vehicle routing problem (VRP) and to give a review on the exact and approximate solution techniques. More specifically the approximate (meta-heuristic) solution techniques are classified into: tabu search, simulated annealing, genetic algorithm, evolutionary algorithm, hybrid algorithm, and Ant Colony Opti...