Extreme solutions in control of moisture transport in concrete carbonation

Sergey A. Timoshin*, Toyohiko Aiki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This paper is concerned with a control system modeling concrete carbonation process when underlying hysteresis effects are taken into account. The system consists of a diffusion equation for moisture and an ordinary differential equation accounting for the hysteresis. We obtain the bang–bang principle for this system asserting the proximity of all attainable states to the so-called bang–bang states. The later are the states reached by controls valued in the extreme points of the control constraint. In our study we are able to dispense with the monotonicity of the right-hand side in the hysteresis equation. This assumption has repeatedly appeared in previous analysis of control systems with hysteresis.

Original languageEnglish
Pages (from-to)446-459
Number of pages14
JournalNonlinear Analysis: Real World Applications
Publication statusPublished - Jun 2019
Externally publishedYes


  • Bang–bang controls
  • Concrete carbonation
  • Control system
  • Hysteresis


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