Error bounds for Euler approximation of linearquadratic control problems with bangbang solutions
W. Alt, R. Baier, M. Gerdts, F. Lempio:
Error bounds for Euler approximation of linearquadratic control problems with bangbang solutions
Numerical Algebra, Control and Optimization
2
(3),
547  570,
2012,
A special issue Dedicated to Professor Helmut Maurer on the occasion of his 65th birthday. Submitted in July 2011.
DOI:
10.3934/naco.2012.2.547
MR Nummer:
2970902
Zentralblattnummer:
1259.49003
Keywords: linearquadratic optimal control; bangbang control; discretization
Mathematics Subject Classification Code: 49J15 (49M25 49N10 49J30)
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Abstract:
We analyze the Euler discretization to a class of linearquadratic optimal control problems. First we show convergence of order h for the optimal values, where h is the mesh size. Under the additional assumption that the optimal control has bangbang structure we show that the discrete and the continuous controls coincide except on a set of measure O(sqrt(h)). Under a slightly stronger assumption on the smoothness of the coefficients of the system equation we obtain an error estmate of order O(h).
Contents:
1.  Introduction  
2.  Euler Approximation  
3.  Error Estimates for Optimal Values  
4. 
Error Estimates for BangBang Solutions


5.  Structural Stability and Improved Error Estimates  
6.  Numerical Results 