Stochastic $\varepsilon$-Optimal Linear Quadratic Adaptation: An Alternating Controls Policy: An alternating controls policy

Peter E. Caines, David Levanony

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

This paper presents a continuous time stochastic linear quadratic (LQ) adaptive control algorithm for completely observed linear stochastic systems with unknown parameters. Based on a certainty equivalence approach, we propose to utilize an alternating controls policy, whereby the linear feedback matrix is switched between two \surd \varepsilon -apart distinct matrices Ki, i = 1, 2. The associated adaptive estimation algorithm is designed so that it drives the maximum likelihood based estimate into the sets \scrI i, i = 1, 2, and consequently into \scrI 1 \cap \scrI 2, with \scrI i corresponding to the true closed loop dynamics under the ith control. A mild geometric assumption is shown to guarantee that \scrI 1 \cap \scrI 2 = \theta \ast , the true parameter. This strongly consistent estimation, coupled with the alternating controls policy, then yields \varepsilon -optimal long-run LQ closed loop performance.

Original languageEnglish
Pages (from-to)1094-1126
Number of pages33
JournalSIAM Journal on Control and Optimization
Volume57
Issue number2
DOIs
StatePublished - 1 Jan 2019

Keywords

  • Adaptive stochastic control
  • Alternating controls
  • Bayesian embedding
  • Certainty equievalence
  • Linear quadratic control
  • Persistent excitation

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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