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Area of Science:

  • Control Theory
  • System Dynamics
  • Robust Control

Background:

  • Parameter-varying systems present significant challenges in control design due to unpredictable dynamics.
  • Ensuring safety and stability in the presence of nonlinear, time-varying uncertainties is a critical problem.

Purpose of the Study:

  • To develop robust control barrier functions for uncertain parameter-varying control affine systems.
  • To design methods that maintain linearity in control inputs despite nonlinear uncertainties.
  • To reduce conservatism in robust control approaches through advanced parameter estimation.

Main Methods:

  • Utilizing mixed-monotone decomposition and concave bounding for robust control barrier functions.
  • Designing robust control Lyapunov functions with linear control input dependency.
  • Implementing set-membership parameter estimation using polyhedral intersections and interval observers.

Main Results:

  • Controlled invariance conditions remain linear in control inputs, simplifying online computation.
  • Coupling robust control barrier and Lyapunov functions yields a solvable quadratic program.
  • Proposed parameter estimation methods effectively reduce conservatism in robust control.

Conclusions:

  • The developed robust control barrier functions offer reliable safety guarantees for uncertain systems.
  • Performance is comparable to adaptive methods, with enhanced robustness.
  • The approach provides a practical framework for designing safe and stable controllers for complex systems.