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Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 1: Error Estimates

Title data

Baier, Robert ; Le, Thuy Thi Thien:
Construction of the Minimum Time Function Via Reachable Sets of Linear Control Systems. Part 1: Error Estimates.
University of Bayreuth, Germany; Università di Padova, Italy
Bayreuth ; Padova , 2015 . - 30 p.

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Project information

Project title:
Project's official titleProject's id
PhD fellowship for foreign students at the Università di PadovaNo information

Project financing: Andere
Fondazione CARIPARO

Abstract in another language

The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In particular, in this paper the theoretical justification of the proposed approach is restricted to a class of linear control systems. The error estimate of the fully discrete reachable set is provided by employing the Hausdorff distance to the continuous-time reachable set. The detailed procedure solving the corresponding discrete set-valued problem is described. Under standard assumptions, by means of convex analysis and knowledge of the regularity of the true minimum time function, we estimate the error of its approximation. Numerical examples are included in the second part.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
Refereed: Yes
Additional notes: Contents:
1. Introduction
2. Preliminaries
3. Approximation of the minimum time function
3.1 Set-valued discretization methods
3.2 Implementation and error estimate of the reachable set approximation
3.3 Error estimate of the minimum time function
3.4 Convergence and reconstruction of discrete optimal trajectories

published in arXiv at December 2015
Keywords: minimum time function; reachable sets; linear control problems; set-valued Runge-Kutta methods
Subject classification: Mathematics Subject Classification Code: 49N60 93B03 (49N05 49M25 52A27)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 11 Jan 2016 08:10
Last Modified: 25 Mar 2019 14:08
URI: https://eref.uni-bayreuth.de/id/eprint/29585