Nonlinear noncausal optimal control of wave energy converters via approximate dynamic programming

This article proposes a novel nonlinear receding horizon optimal control algorithm for wave energy converter (WECs) with nonlinear dynamics. It is well accepted that the WEC control problem is essentially a noncausal constrained optimal control problem, where the energy output can be improved by incorporating the short-term wave prediction into the control synthesis. Inspired by this fact, we suggest a new nonlinear noncausal optimal control (NNOC) for WECs based on the principle of approximate dynamic programming, which can, first, explicitly use the wave prediction to improve the energy conversion efficiency; second, handle the state and control input constraints; third, reduce the computational burden. Different to the existing linear noncausal optimal control, the derived Hamilton-Jacobi-Bellman equation for NNOC does not have an analytic solution. To tackle this problem, a critic neural network (NN) is adopted to approximate its solution in a receding horizon manor. The weights of NN are determined via a policy iteration algorithm. The resulting NNOC consists of a causal state feedback part and a noncausal feedforward part to explicit incorporate wave prediction information. Numerical simulations are provided to verify the efficacy of the proposed NNOC method.