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Safety-critical controller design for nonlinear systems: Stabilization and robustness.

Mohammad Hosein Sabzalian¹

¹Department of Mechanical Engineering, Faculty of Engineering, University of Santiago of Chile (USACH), Avenida Libertador Bernardo O'Higgins 3363, Santiago, 9170022, Santiago, Chile.

ISA Transactions

|May 14, 2025

Summary

This summary is machine-generated.

This study introduces novel closed-form solutions for safe controller design in nonlinear systems, replacing complex real-time optimization. The method ensures system stability and safety without computational burden.

Keywords:

Control barrier function Control lyapunov function Disturbed nonlinear systems Nonlinear control systems Safety-critical control

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Area of Science:

Control Systems Engineering
Nonlinear Dynamics
Robotics

Background:

Designing safe controllers for nonlinear systems is challenging due to computational complexity.
Real-time optimization methods like quadratic programming can be computationally intensive for fast dynamics.

Purpose of the Study:

To develop innovative closed-form solutions for safe controller design in nonlinear affine control systems.
To eliminate the need for real-time quadratic programming optimization in safety-critical applications.

Main Methods:

Utilizing a Lyapunov-based control law (unsafe control) and an additional state variable with a safeguarding control.
Ensuring the derivative of a control Lyapunov function remains negative semi-definite.
Extending the approach to robust safety control for systems with external disturbances.

Main Results:

Proposed closed-form scheme guarantees safe operation by limiting the impact of safeguarding control.
User-defined parameters offer flexibility in managing safety constraints.
Achieved input-to-state stability for nonlinear systems under disturbances.

Conclusions:

The developed controllers maintain safety and stability without the computational load of real-time quadratic programming.
The method is adaptable and suitable for systems with fast dynamics.
Validated through three case studies for real-world applicability.