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Abstract
This paper applies a Discontinuous Galerkin (DG) finite element time-stepping method for the numerical solution of optimal and sub-optimal control problems within the framework of the Pontryagin’s Maximum Principle. The local nature of the piecewise polynomial approximation used in the DG method handles easily the case of a large number of switching instants not known a priori. The weakly enforced inter-element continuity allows a simple implementation of element-wise mesh and polynomial refinement. To show the capabilities of the method, an element-wise time-interval refinement algorithm was implemented (the so-called h-refinement) and applied to a classic bang-bang optimal control problem. Finally, the application of the method to a practical problem is discussed: the optimal latching (bang-bang) control of a floating oscillating water column wave energy converter equipped with a self-rectifying air-turbine. The results presented in this study show that the DG method is an efficient alternative to the well-known Pseudo-Spectral methods.
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