Stochastic optimal control of a heave point wave energy converter based on a modified LQG approach

The optimal control constrain problem of a wave energy point absorber is constrained due to limited stroke and saturation of the control force actuator. The basic idea of this paper is to control the motion of the absorber by a modified LQG control where the constraints on the displacement and actuator force are approximately considered by counteracting the absorbed power in the objective quadratic functional. Based on rational approximations to the radiation force and the wave load, the integrated dynamic system can be reformulated as a linear stochastic differential equation which is driven by a unit intensity Gaussian white noise. The optimal LQG control force becomes a linear function of the state vector of the integrated system, which can only be partially observed. In order to remedy this problem, the control is combined with a Kalman filter observer. The obtained sub-optimal solution has been compared to the numerical optimal solution obtained by nonlinear programming. With suitable calculated gain parameters, the LQG controller can provide approximately the amount of the averaged absorbed power as that of the numerical optimum.