Optimal control of a class of Caputo fractional systems

This article introduces a broad formulation of fractional optimal control issues characterized by a class of Caputo fractional systems within Hilbert spaces. Through a variational method, the Pontryagin maximum principle (PMP) is established as a set of essential conditions for optimality. Following this, the Hamilton–Jacobi–Bellman (HJB) equations are derived based on the derived PMP. In conclusion, it is established that the value function serves as a viscosity solution of the HJB equation. Numerical example is finally provided to exemplify the theory developed.