Optimal Control of Hysteresis in Smart Actuators: A Viscosity Solutions Approach

Abstract

Hysteresis in smart materials hinders their wider applicability in actuators. The low dimensional hysteresis models for these materials are hybrid systems with both controlled switching and autonomous switching. In particular, they belong to the class of Duhem hysteresis models and can be formulated as systems with both continuous and switching controls. In this paper, we study the control methodology for smart actuators through the example of controlling a commercially available magnetostrictive actuator. For illustrative purposes, an infinite horizon optimal control problem is considered. We show that the value function satisfies a Hamilton-Jacobi-Bellman equation (HJB) of a hybrid form in the viscosity sense. We further prove uniqueness of the viscosity solution to the (HJB), and provide a numerical scheme to approximate the solution together with a sub-optimal controller synthesis method. Numerical and experimental results based on this approach are presented.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2002
Accession Number
ADA439782

Entities

People

  • John Baras
  • Xiaobo Tan

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Actuators
  • Closed Loop Systems
  • Computational Fluid Dynamics
  • Differential Equations
  • Domain Walls
  • Dynamic Programming
  • Equations
  • Ferromagnetic Materials
  • Frequency
  • Hybrid Systems
  • Hysteresis
  • Magnetic Fields
  • Magnetic Properties
  • Materials
  • Military Research
  • Simulations
  • Viscosity

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Materials Science and Engineering.
  • Mathematical Modeling and Probability Theory.