Abstract
The paper presents a sufficient condition for strong metric sub-regularity (SMsR) of the system of first order optimality conditions (optimality system) for a Mayer-type optimal control problem with a dynamics affine with respect to the control. The SMsR property at a reference solution means that any solution of the optimality system, subjected to “small” disturbances, which is close enough to the reference one is at a distance to it, at most proportional to the size of the disturbance. The property is well understood for problems satisfying certain coercivity conditions, which however, are not fulfilled for affine problems.
This research is supported by the Austrian Science Foundation (FWF) under grant No P31400-N32.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Applied to a, for example, this means that for every bounded set
there exists a function (called modulus of continuity) \(\omega : (0, +\infty ) \rightarrow [0,+\infty )\) with \(\lim _{s \rightarrow 0} \omega (s) = 0\), such that \(|a(t,x') - a(t,x)| \le \omega (|x'-x|)\) for every \(t \in [0,T]\) and \(x, \, x' \in S\).
there exists a function (called modulus of continuity) References
Alt, W., Felgenhauer, U., Seydenschwanz, M.: Euler discretization for a class of nonlinear optimal control problems with control appearing linearly. Comput. Optim. Appl. 69, 825–856 (2018)
Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings: A View from Variational Analysis, 2nd edn. Springer, New York (2014)
Osmolovskii, N.P., Veliov, V.M.: Metric sub-regularity in optimal control of affine problems with free end state. Submitted; available as Research Report 2019–04, ORCOS, TU Wien (2019). https://orcos.tuwien.ac.at/research/research_reports
Preininger, J., Scarinci, T., Veliov, V.M.: Metric regularity properties inbang-bang type linear-quadratic optimal control problems. Set-Valued Var. Anal. 27, 381–404 (2019). https://doi.org/10.1007/s11228-018-0488-1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Osmolovskii, N.P., Veliov, V.M. (2020). On the Regularity of Mayer-Type Affine Optimal Control Problems. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2019. Lecture Notes in Computer Science(), vol 11958. Springer, Cham. https://doi.org/10.1007/978-3-030-41032-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-41032-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41031-5
Online ISBN: 978-3-030-41032-2
eBook Packages: Computer ScienceComputer Science (R0)