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A [K,KL] sector based control design for nonlinear system.

Ankit Sachan1, Shyam Kamal1, Devender Singh1

  • 1Department of Electrical Engineering, Indian Institute of Technology (BHU), Varanasi, U.P., India.

ISA Transactions
|January 2, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a novel lazy control strategy for stabilizing nonlinear systems. The approach ensures asymptotic stability by activating control only when necessary, saving energy and reducing control effort.

Keywords:
sectorAsymptotic stabilityControl-Lyapunov functionLazy or Hands-Off control

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Systems Engineering

Background:

  • Asymptotic stabilization of nonlinear systems is crucial for many engineering applications.
  • Existing methods may involve excessive control actions, leading to inefficiency.
  • Input-affine nonlinear systems present unique challenges in control design.

Purpose of the Study:

  • To develop a new, energy-efficient approach for asymptotic stabilization of general input-affine nonlinear systems.
  • To introduce a 'Lazy' or 'Hands-Off' control strategy that minimizes control effort.
  • To ensure the stability of nonlinear systems using a novel sector-based control design.

Main Methods:

  • Utilizing Matrosov's theorem for decomposing the state space.
  • Constructing a [K,KL] sector using a control-Lyapunov function.
  • Employing comparison functions for uniform solution analysis.
  • Designing a switching controller activated outside the [K,KL] sector.

Main Results:

  • The proposed method achieves asymptotic stabilization for general input-affine nonlinear systems.
  • A novel 'Lazy' control scheme is successfully implemented, reducing superfluous control actions.
  • The effectiveness of the approach is demonstrated through simulation of an illustrative example.

Conclusions:

  • The developed control strategy provides an effective and efficient method for stabilizing nonlinear systems.
  • The 'Lazy' control concept offers significant advantages in terms of energy savings and reduced control effort.
  • This approach represents a promising advancement in the field of nonlinear control systems.