Regularization of Linear-Quadratic Control Problems with L 1 -Control Cost

作者: Christopher Schneider , Walter Alt

DOI: 10.1007/978-3-662-45504-3_29

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摘要: We analyze \(L^2\)-regularization of a class linear-quadratic optimal control problems with an additional \(L^1\)-control cost depending on parameter \(\beta \). To deal this nonsmooth problem we use augmentation approach known from linear programming in which the number variables is doubled. It shown that if for given ^*\ge 0\) bang-zero-bang, solutions are continuous functions \) and regularization \(\alpha Moreover derive error estimates Euler discretization.

参考文章(18)
W. Alt, M. Seydenschwanz, Regularization and discretization of linear-quadratic control problems Control and Cybernetics. ,vol. 40, pp. 903- 920 ,(2011)
Walter Alt, Christopher Schneider, Linear‐quadratic control problems with L1‐control cost Optimal Control Applications & Methods. ,vol. 36, pp. 512- 534 ,(2015) , 10.1002/OCA.2126
Ivar Ekeland, Roger Téman, Convex analysis and variational problems ,(1976)
Eduardo Casas, Roland Herzog, Gerd Wachsmuth, Approximation of sparse controls in semilinear equations by piecewise linear functions Numerische Mathematik. ,vol. 122, pp. 645- 669 ,(2012) , 10.1007/S00211-012-0475-7
Georg Stadler, Elliptic optimal control problems with L1-control cost and applications for the placement of control devices Computational Optimization and Applications. ,vol. 44, pp. 159- 181 ,(2009) , 10.1007/S10589-007-9150-9
G. Vossen, H. Maurer, On L1‐minimization in optimal control and applications to robotics Optimal Control Applications & Methods. ,vol. 27, pp. 301- 321 ,(2006) , 10.1002/OCA.781
Klaus Deckelnick, Michael Hinze, A note on the approximation of elliptic control problems with bang-bang controls Computational Optimization and Applications. ,vol. 51, pp. 931- 939 ,(2012) , 10.1007/S10589-010-9365-Z