Applied Mathematical Programming Using Algebraic Systems

Applied Mathematical Programming Using Algebraic Systems

Optimal control of switched systems by a modified pseudo spectral method

In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching t...

Shape Optimization of an Arterial Bypass in Cardiovascular Systems

A high performance numerical technique in the study of aorto-coronaric bypass anastomoses configurations using steady Stokes equations is presented. The problem is first expressed as an optimal control problem. Then, by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by ...

A Recurrent Neural Network Model for Solving Linear Semidefinite Programming

In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs). SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations. Then a recurrent neural network...

Estimation of Concentrations in Chemical Systems at Equilibrium Using Geometric Programming

Geometric programming is a mathematical technique, which has been developed for nonlinear optimization problems. This technique is based on the dual program with linear constraints. Determination of species concentrations in chemical equilibrium conditions is one of its applications in chemistry and chemical engineering fields. In this paper, the principles of geometric programming and its comp...