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Robust induced ℓ<sub>2</sub>-ℓ<sub>∞</sub> optimal control of discrete-time systems having magnitude and rate-bounded actuators.

ISA transactions·2022
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Data-driven H∞ control of constrained systems: An application to bilateral teleoperation system.

Ibrahim Kucukdemiral1, Hakan Yazici2, Bilal Gormus3

  • 1Department of Applied Science, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK.

ISA Transactions
|February 4, 2023
PubMed
Summary

A new data-driven H-infinity control method for discrete-time systems requires only disturbance bounds, not system matrices. This approach yields effective controllers that respect system limitations and track references accurately.

Keywords:
Data-driven controlLinear matrix inequalitiesPhysical constraints and norm-bounded disturbance

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Area of Science:

  • Control Theory
  • System Identification
  • Robotics

Background:

  • Traditional H-infinity control often requires full knowledge of system matrices.
  • Physical limitations and external disturbances pose significant challenges in control system design.
  • Data-driven methods offer an alternative when system identification is difficult or impossible.

Purpose of the Study:

  • To develop an identification-free, data-driven H-infinity control method for discrete-time linear time-invariant systems.
  • To design a static state-feedback controller that operates under physical limitations and norm-bounded disturbances.
  • To ensure controllers do not exceed state and input variable bounds while achieving performance objectives.

Main Methods:

  • Utilizes a data-driven approach without requiring system matrices.
  • Employs closed-loop parametrization with control input and state measurements.
  • Represents disturbances as affine uncertainties via Linear Fractional Transformation (LFT).
  • Applies the full block S-procedure method (FBSPM) with relaxations for reduced conservatism.

Main Results:

  • The proposed method successfully designs static state-feedback controllers.
  • Controllers adhere strictly to specified bounds on states and control signals.
  • Demonstrated effectiveness in numerical illustrations and case studies, including a bilateral teleoperation system.
  • Achieved accurate reference and force tracking.

Conclusions:

  • The identification-free, data-driven H-infinity control method is effective for discrete-time LTI systems.
  • This approach offers a practical solution for systems with unknown dynamics but known disturbance bounds.
  • The method provides robust and performant control under physical constraints.