A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control
Artikel i vetenskaplig tidskrift, 2017

Quadratic programs (QP) with an indefinite Hessian matrix arise naturally in some direct optimal control methods, e.g., as subproblems in a sequential quadratic programming scheme. Typically, the Hessian is approximated with a positive de finite matrix to ensure having a unique solution; such a procedure is called regularization. We present a novel regularization method tailored for QPs with optimal control structure. Our approach exhibits three main advantages. First, when the QP satisfies a second order sufficient condition for optimality, the primal solution of the original and the regularized problem are equal. In addition, the algorithm recovers the dual solution in a convenient way. Second, and more importantly, the regularized Hessian bears the same sparsity structure as the original one. This allows for the use of efficient structure-exploiting QP solvers. As a third advantage, the regularization can be performed with a computational complexity that scales linearly in the length of the control horizon. We showcase the properties of our regularization algorithm on a numerical example for nonlinear optimal control. The results are compared to other sparsity preserving regularization methods.

nonlinear mpc

SQP

model-predictive control

1994

v18

hmid c

algorithm

solvers

computers & chemical engineering

regularization

optimization

optimal control

Mathematics

nonlinear predictive control

sqp method

p817

Författare

R. Verschueren

Mario Zanon

Chalmers, Signaler och system, System- och reglerteknik, Mekatronik

R. Quirynen

M. Diehl

SIAM Journal on Optimization

1052-6234 (ISSN) 1095-7189 (eISSN)

Vol. 27 2085-2109

Ämneskategorier

Matematik

DOI

10.1137/16m1081543