A Pseudospectral Method for Continuous-Time Nonlinear Fractional Programming

Abstract

In this paper, we focus on the continuous-time nonlinear fractional programming problems with objective functional given by the ratio of two integrals. Since the standard continuous-time programming theory, such as optimal control theory, cannot be used directly to solve this type of problems, we propose a new numerical method to solve the problem. At first we convert the original problem into an equivalent continuous-time nonfractional problem which is not included integral term. Then, we utilize the Legendre pseudospectral method to discretize the problem. We analyze the feasibility of the obtained discretized problem and the convergence of the method. Finally, we provide two numerical examples to demonstrate the efficiency and capability of the method.