Optimal linear–quadratic control of asymptotically stabilizable systems using approximations

Hans Zwart, Kirsten A. Morris, Orest V. Iftime*

*Corresponding author for this work

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Abstract

In this paper we study approximations to the infinite-horizon quadratic optimal control problem for linear systems that may be only asymptotically stabilizable. For linear systems, this issue only arises with infinite-dimensional systems. We provide sufficient conditions which guarantee when approximations to the optimal feedback result in the cost converging to the optimal cost. One technique for approximate solution of the optimal control problem is to use Newton–Kleinman iterations for the associated Riccati equation. Some new results in this direction are provided. Several important classes of systems, lightly damped second-order systems and a platoon-type system, are shown to be optimizable. Also, finding an initial stabilizing control for the Newton–Kleinman iteration can be non-trivial. The initial iterate for these classes is described.

Original languageEnglish
Article number104802
JournalSystems and control letters
Volume146
Early online date13 Nov 2020
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Asymptotic stability
  • Infinite-dimensional systems
  • Optimal control
  • Riccati equations

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