This paper addresses the issue of real-time control for applications, subject to physical constraints, involving an energy maximization objective. Typical application areas include renewable energy systems where, in spite of the fact that the raw energy resource is free, the capital and operational costs associated with the energy conversion process are not. In addition, economic energy delivery can only be achieved if the conversion device is operated efficiently. Previous approaches to this problem include model predictive control (MPC), but the computational cost associated with MPC can be high. Pseudospectral solutions show considerable promise in achieving a good balance between performance and computation, but currently available solutions deal with fixed-period optimization. In this paper, a receding horizon real-time pseudospectral control is developed, based on half-range Chebyshev Fourier basis functions, which can accurately represent harmonic signals in the application domain, while also efficiently dealing with the signal truncation effects associated with a receding horizon formulation. An application example, based on a wave energy converter, is used to illustrate the new control algorithm.