Andrea Zanelli

Tuesday, May 19, 2015, 11:00 - 12:00

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

Exploiting nonlinear model predictive control in embedded applications is gradually becoming a viable technology thanks to the mature algorithms and increasing computational power available. State-of-the-art algorithms and implementations allow one to solve nonlinear optimization problems arising from NMPC formulations in the millisecond timescale. When solving such problems the main computational burden is associated with a discretization phase in which the infinite-dimensional continuous-time formulation has to be recast into a finite-dimensional discrete-time one. This task is carried out by integrating the nonlinear differential equations describing the dynamics with highly
accurate discretization schemes based on implicit Runge-Kutta methods.

In this talk efficient discretization schemes will be presented that allow this computational burden to be decreased due to their lower complexity. Two discretization algorithms based on the Picard iteration are introduced that lead to efficient schemes to be used with sequential quadratic programming or interior point methods. The first method described relies on a transformation that allows one to tackle the integral form of the dynamics in a semi-analytical manner. The second approach consists instead in using the Picard iteration to solve a set of algebraic equations resulting in a simple and efficient scheme.  In both cases it will be shown how the computational burden can be reduced by relying solely on low complexity operations. The presented methods can achieve a complexity reduction of more than an order of magnitude in comparison to the state-of-the-art schemes.