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A Sparsity Preserving Convexification Procedure for Indefinite Quadratic Programs Arising in Direct Optimal Control

R. Verschueren ; Mario Zanon (Institutionen för signaler och system, Mekatronik) ; R. Quirynen ; M. Diehl
Siam Journal on Optimization (1052-6234). Vol. 27 (2017), 3, p. 2085-2109.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: regularization, nonlinear predictive control, SQP, optimal control, model-predictive control, nonlinear mpc, sqp method, optimization, algorithm, solvers, Mathematics, hmid c, 1994, computers & chemical engineering, v18, p817



Denna post skapades 2017-10-25.
CPL Pubid: 252771

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Mekatronik (2005-2017)

Ämnesområden

Matematik

Chalmers infrastruktur