Session: MSNDC-01-01: Computational Methods and Software Tools in Multibody Systems and Nonlinear Dynamics

Paper Number: 89376

89376 - A Pnh-Adaptive Refinement Procedure for Numerical Optimal Control Problems 

This paper presents an automatic procedure to enhance the accuracy of the numerical solution of an optimal control problem (OCP) discretized via direct collocation at Gauss-Legendre points. First, a numerical solution is obtained by solving a nonlinear program (NLP). Then, the method evaluates its accuracy and adaptively changes both the degree of the approximating polynomial within each mesh interval and the number of mesh intervals until a prescribed accuracy is met. The number of mesh intervals is increased for all state vector components alike, in a classical fashion. Instead, improving on state-of-the-art procedures, the degrees of the polynomials approximating the different components of the state vector are allowed to assume, in each finite element, distinct values. This explains the pnh definition, where n is the state dimension. Instead, in the literature, the degree is always raised to the highest order for all the state components, with a clear waste of resources. Numerical tests on three OCP problems highlight that, under the same maximum allowable error, by independently selecting the degree of the polynomial for each state, our method effectively picks lower degrees for some of the states, thus reducing the overall number of variables in the NLP. Accordingly, various advantages are brought about, the most remarkable being: (i) an increased computational efficiency for the final enhanced mesh with solution accuracy still within the specified tolerance, (ii) a reduced risk of being trapped by local minima due to the reduced NLP size.

Presenting Author: Lorenzo Bartali Università di Pisa

Presenting Author Biography: Lorenzo Bartali received his BS and MS degree (cum Laude) both from the University of Pisa, Pisa, Italy, in 2017 and 2020. He is currently pursuing a PhD in Vehicle Dynamics at the Department of Civil and Industrial Engineering of the University of Pisa. His interests include Optimal Control, Autonomous Driving and Lap-Time Optimization.

Authors:

Lorenzo Bartali Università di Pisa
Marco Gabiccini Università di Pisa
Massimo Guiggiani Università di Pisa