Static Output-Feedback <formula> <tex>${H}_{&#x221E;}$</tex> </formula> Control Design Procedures for Continuous-Time Systems With Different Levels of Model Knowledge

Shai A. Arogeti, Frank L. Lewis

Research output: Contribution to journalArticlepeer-review

Abstract

This article suggests a collection of model-based and model-free output-feedback optimal solutions to a general <formula> <tex>${H_{&#x221E;}}$</tex> </formula> control design criterion of a continuous-time linear system. The goal is to obtain a static output-feedback controller while the design criterion is formulated with an exponential term, divergent or convergent, depending on the designer's choice. Two offline policy-iteration algorithms are presented first, which form the foundations for a family of online off-policy designs. These algorithms cover all different cases of partial or complete model knowledge and provide the designer with a collection of design alternatives. It is shown that such a design for partial model knowledge can reduce the number of unknown matrices to be solved online. In particular, if the disturbance input matrix of the model is given, off-policy learning can be done with no disturbance excitation. This alternative is useful in situations where a measurable disturbance is not available in the learning phase. The utility of these design procedures is demonstrated for the case of an optimal lane tracking controller of an automated car.

Original languageEnglish
JournalIEEE Transactions on Cybernetics
DOIs
StateAccepted/In press - 1 Jan 2021

Keywords

  • Attenuation
  • Control design
  • Convergence
  • H&#x221E; optimal control
  • Linear systems
  • Optimal control
  • Riccati equations
  • Standards
  • off-policy reinforcement learning (RL)
  • static output feedback

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