On necessary optimality conditions and exact penalization for a constrained fractional optimal control problem

Abstract

The purpose of this article is twofold. We first develop the first-order necessary optimality conditions for a general constrained fractional optimal control problem using calculus of variation. These conditions are of the form of fractional ordinary differential equations which reduce to the conventional Euler-Lagrange equations when the dynamical system becomes a first-order one. Then, we prove, via the optimality conditions established, that a popular penalty method used for conventional constrained optimal control and optimization is an "exact" penalty method for the fractional control problem by showing that an optimal solution to the penalized problem satisfies the optimality conditions of the original one when the penalty parameter is sufficiently large. An example is also provided to verify the necessary optimality conditions.

An Integer-Fractional Gradient Algorithm for Back Propagation Neural Networks

“…In addition, many optimal control problems also involve fractional-order differentiation. For example, Wang, Li, and Liu et al [9] focused on establishing necessary optimality conditions and exact penalization techniques for constrained fractional optimal control problems. Bhrawy et al [10] solved fractional optimal control problems using a Chebyshev-Legendre operational technique.…”

Time‐average stochastic control based on a singular local Lévy model for environmental project planning under habit formation

“…Path dependence is a key concept in modeling and controlling system dynamics. Examples include the Asian option wherein the option is valued by a historic mean of the price process [12], the portfolio risk management subject to the past reference points [13], and the fractional optimal control [14]. Another example, focused on in this study, is habit formation wherein the current decision is affected by the past decisions.…”