Article thumbnail

Unified Riccati theory for optimal permanent and sampled-data control problems in finite and infinite time horizons

By Loïc Bourdin and Emmanuel Trélat

Abstract

We revisit and extend the Riccati theory, unifying continuous-time linear-quadratic optimal permanent and sampled-data control problems, in finite and infinite time horizons. In a nutshell, we prove that:-- when the time horizon T tends to $+\infty$, one passes from the Sampled-Data Difference Riccati Equation (SD-DRE) to the Sampled-Data Algebraic Riccati Equation (SD-ARE), and from the Permanent Differential Riccati Equation (P-DRE) to the Permanent Algebraic Riccati Equation (P-ARE);-- when the maximal step of the time partition $\Delta$ tends to $0$, one passes from (SD-DRE) to (P-DRE), and from (SD-ARE) to (P-ARE).Our notations and analysis provide a unified framework in order to settle all corresponding results

Topics: Mathematics - Optimization and Control
Year: 2020
OAI identifier: oai:arXiv.org:2002.04246
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/2002.0424... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.