B-spline based certificates of positivity with applications in engineering.

In various engineering applications, including optimal control, explicit model predictive control, and robust design, optimization problems featuring infinitely many constraints emerge. In order to solve such optimization problems, the infinite constraint set is commonly replaced by a more restrictive finite set of constraints using Polyas theorem or sum-of-squares certificates of positivity. As neither of these relaxation strategies can cope with the complexity of engineering applications, this research project aims at novel relaxation strategies through B-spline based certificates of positivity. The theoretical advances required to reach this objective are tied to methodological developments in two application areas and the development of a software toolbox for spline manipulations and optimization.

Keywords:engineering

Disciplines:Manufacturing engineering, Other mechanical and manufacturing engineering, Product development