Nonconvex optimal control problems for semi-linear neutral integro-differential systems with infinite delay

In this work, by using the theory of fundamental solution and resolvent operators, we investigate the existence of solutions for Bolza optimal control problems for a semi-linear neutral integro-differential equation with infinite delay. It is stressed that both the integral cost functional and the admissible set do not require convexity conditions other than the existing literature. Meanwhile, the existence of time optimal control to a target set is also considered and obtained by limit arguments. Finally, we provide a example to demonstrate the applications of our main results.