Energy maximising robust control for spectral and pseudospectral methods with application to wave energy systems

Spectral and Pseudospectral methods have been widely considered in diverse optimal control applications, usually where energy optimisation is required. Although such methods are a good way to ensure a good balance between performance and computational effort, in most of the literature, nominal mathematical models are considered without taking into account possible dynamic deviations from the nominal case. The main aim of this study is to propose a novel framework where spectral and pseudospectral problems include some structured uncertainty, achieving robust optimal control designs guaranteeing the 'best worst-case performance'. In this paper, the objective function used for optimisation is inspired by wave energy converters. Two solution methodologies are developed. Firstly, an analytical solution, for circular and convex polytopic uncertainty boundaries, is proposed. Then, a numerical formulation is introduced to consider uncertainty sets of arbitrary shape, adding the ability to consider physical system constraints. Finally, an application example shows the benefit of this new control formulation.

Automated summary

This study proposes a novel framework where spectral and pseudospectral methods include structured uncertainty, ensuring robust optimal control designs. Two solution methodologies, analytical and numerical, are developed to handle uncertainty sets of different shapes and consider physical system constraints. An application example demonstrates the benefits of this new control formulation.