Riemann–Liouville spatial fractional optimal control for a class of bilinear systems with Caputo time-fractional derivatives

Abstract

The objective of this study is to address a space-fractional optimal control problem for a class of bilinear systems involving a fractional time derivative of order α. The problem is formulated as the minimization of a cost functional that accounts for both the control energy and the fractional deviation between the desired and actual state over a given time interval. By employing Fréchet differentiability, we establish the existence of optimal controls that may vary in both time and space. Moreover, we examine the properties of the optimal distributed control under various admissible control sets. An algorithm is also proposed, and numerical simulations are carried out to illustrate and validate the theoretical results.