Optimal control of fractional differential equations with interval uncertainty

Abstract

The purpose of this paper is to obtain numerical solutions of fractional interval optimal control problems. To do so, first, we obtain a system of fractional interval differential equations through necessary conditions for the optimality of these problems, via the interval calculus of variations in the presence of interval constraint arithmetic. Relying on the trapezoidal rule, we obtain a numerical approximation for the interval Caputo fractional derivative. This approach causes the obtained conditions to be converted to a set of algebraic equations which can be solved using an iterative method such as the interval Gaussian elimination method and interval Newton method. Finally, we solve some examples of fractional interval optimal control problems in order to evaluate the performance of the suggested method and compare the past and present achievements in this manuscript.