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Karmvir Singh Phogat1, Dong Eui Chang2

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This study introduces novel partial differential equations for optimal tracking control, enhancing system performance and computational efficiency. The method generalizes control for systems on manifolds, achieving asymptotic output regulation.

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Area of Science:

  • Control Theory
  • Differential Geometry
  • Robotics

Background:

  • Tracking exogenous signals is a fundamental challenge in control theory, often addressed via optimal regulation.
  • Exogenous signals are typically generated by external systems known as exosystems.
  • Designing optimal tracking control laws is crucial for system performance.

Purpose of the Study:

  • To derive a computationally efficient set of partial differential equations for optimal output regulation.
  • To generalize optimal regulation techniques from Euclidean space to systems on manifolds.
  • To demonstrate the efficacy of the proposed method in practical applications.

Main Methods:

  • Derivation of a reduced set of Francis-Byrnes-Isidori partial differential equations.
  • Generalization of optimal regulation to systems residing on manifolds via stable embedding into Euclidean space.
  • Design of optimal feedback control laws using established Euclidean space techniques.

Main Results:

  • The derived equations achieve asymptotic output regulation efficiently.
  • The technique successfully extends optimal regulation to manifold-based systems.
  • Numerical studies on quadcopter and rigid body tracking confirm asymptotic regulation.

Conclusions:

  • The proposed method offers an effective and computationally efficient approach to output regulation for complex systems.
  • Generalizing control to manifolds provides a powerful framework for advanced robotic and mechanical systems.
  • The technique outperforms classical approaches in achieving asymptotic output regulation.