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

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.