Fractional Order Optimal Control Problems with Free Terminal Time

TL;DR

This paper investigates fractional order optimal control problems with free terminal time, deriving necessary and sufficient conditions for optimality, and presents numerical methods with simulations.

Contribution

It introduces new optimality conditions for fractional order control problems with free terminal time, including cases with endpoint constraints, and provides numerical solution techniques.

Findings

Derived necessary optimality conditions for fractional control problems.

Established sufficiency of conditions under certain assumptions.

Presented numerical methods and simulations for solving these problems.

Abstract

We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be optimal are obtained. Situations with constraints present at the end time are also considered. Under appropriate assumptions, it is shown that the obtained necessary optimality conditions become sufficient. Numerical methods to solve the problems are presented, and some computational simulations are discussed in detail.