The CLF-HJ combination, while effective in providing safety guarantees and robust control, has certain limitations that can be addressed for further enhancement:
Conservatism: The method may be conservative in estimating the region of attraction and handling uncertainties, leading to suboptimal performance. This can be addressed by refining the uncertainty modeling and optimization criteria to reduce conservatism while maintaining safety guarantees.
Computational Complexity: The computational burden of solving the optimization problems for CLF and HJ analysis can be high, especially for complex systems. Implementing efficient numerical algorithms and parallel computing techniques can help mitigate this limitation.
Model Mismatch: The approach assumes a perfect knowledge of the system model, which may not hold in practical scenarios. Incorporating adaptive elements to update the model online based on real-time data can improve robustness in the presence of model uncertainties.
Sensitivity to Disturbances: The method's performance may degrade in the presence of unmodeled disturbances or uncertainties beyond the assumed bounds. Implementing robust observer designs or disturbance rejection mechanisms can enhance the system's resilience.
Validation and Verification: Rigorous testing and validation of the control system under various scenarios and uncertainties are essential to ensure its robustness and reliability in real-world applications.