Optimal control of nonlinear fractional systems with multiple pantograph‐delays.

• A numerical integration scheme is proposed to solve the fractional pantograph-delay systems. • A gradient computation procedure is presented for computing the gradients of the cost function. • A gradient optimization is developed for fractional pantograph-delay optimal control problems. In this paper, we consider optimal control of nonlinear fractional-order systems with multiple pantograph-delays, where the fractional-order derivatives are expressed in the Caputo sense. For this problem, we first propose an explicit integration scheme to numerically solve the nonlinear fractional-order system with multiple pantograph-delays and approximate the cost functional using the trapezoidal rule. This yields a series of nonlinear parameter optimization problems. Then, we derive gradients of the cost functions in the resulting problems. Furthermore, we present a gradient-based optimization approach to solve the fractional pantograph-delay optimal control problem. Finally, we validate the proposed solution approach by solving three numerical examples. [ABSTRACT FROM AUTHOR]