Linear‐quadratic control problems with L1‐control cost
作者： Walter Alt , Christopher Schneider
DOI: 10.1002/OCA.2126
关键词: Control variable 、 Optimal control 、 Linear quadratic 、 Lipschitz continuity 、 Euler's formula 、 Mathematical optimization 、 Discretization 、 Regularization (mathematics) 、 Linear programming 、 Mathematics
摘要: Summary We analyze a class of linear-quadratic optimal control problems with an additional L1-control cost depending on parameter β. 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 bang-zero-bang and switching function has stable structure, solutions are Lipschitz continuous functions We also show case controls β * with | β − β * | sufficiently small coincide except set measure . Finally, to derive error estimates Euler discretizations. Copyright © 2014 John Wiley & Sons, Ltd.
sci-hub.se 参考文章(16)
W. Alt, M. Seydenschwanz, Regularization and discretization of linear-quadratic control problems Control and Cybernetics. ,vol. 40, pp. 903- 920 ,(2011)
Josef L. Haunschmied, Alain Pietrus, Vladimir M. Veliov, The Euler Method for Linear Control Systems Revisited international conference on large-scale scientific computing. ,vol. 8353, pp. 90- 97 ,(2013) , 10.1007/978-3-662-43880-0_9
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
Yoshiyuki Sakawa, Trajectory planning of a free‐flying robot by using the optimal control Optimal Control Applications & Methods. ,vol. 20, pp. 235- 248 ,(1999) , 10.1002/(SICI)1099-1514(199909/10)20:5<235::AID-OCA658>3.0.CO;2-I
Eduardo Casas, Roland Herzog, Gerd Wachsmuth, Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with $L^1$ Cost Functional Siam Journal on Optimization. ,vol. 22, pp. 795- 820 ,(2012) , 10.1137/110834366
Ursula Felgenhauer, On Stability of Bang-Bang Type Controls Siam Journal on Control and Optimization. ,vol. 41, pp. 1843- 1867 ,(2002) , 10.1137/S0363012901399271
Andreas Wächter, Lorenz T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Mathematical Programming. ,vol. 106, pp. 25- 57 ,(2006) , 10.1007/S10107-004-0559-Y
Gerd Wachsmuth, Daniel Wachsmuth, Convergence and regularization results for optimal control problems with sparsity functional ESAIM: Control, Optimisation and Calculus of Variations. ,vol. 17, pp. 858- 886 ,(2011) , 10.1051/COCV/2010027