Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions

W. Alt, R. Baier, M. Gerdts, F. Lempio: Error bounds for Euler approximation of linear-quadratic control problems with bang-bang 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: linear-quadratic optimal control; bang-bang control; discretization
Mathematics Subject Classification Code: 49J15 (49M25 49N10 49J30)
Download as PDF


Abstract:

We analyze the Euler discretization to a class of linear-quadratic 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 bang-bang 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 Bang-Bang Solutions
4.1 A lower minorant for minimal values
4.2 Hölder type error estimates
5. Structural Stability and Improved Error Estimates
6. Numerical Results

Chair -

|  University of Bayreuth -