Robust SDRE filter design for nonlinear uncertain systems with an H∞ performance criterion

Area of Science:

• Control Systems Engineering
• Nonlinear System Analysis
• Robust Filtering Theory

Background:

• Standard state-dependent Riccati equation (SDRE) filters are susceptible to modeling uncertainties, measurement noise, and input disturbances.
• These factors degrade the performance and reliability of state estimation in nonlinear systems.
• Developing robust filtering techniques is crucial for practical applications involving uncertain dynamic systems.

Purpose of the Study:

• To design a novel robust H(∞) SDRE filter to mitigate the adverse effects of uncertainties and noise.
• To ensure effective state estimation for nonlinear uncertain systems subjected to unknown disturbance inputs.
• To guarantee a modified H(∞) performance index under a mild Lipschitz condition.

Main Methods:

• Development of a robust H(∞) SDRE filter based on infinity-norm minimization.
• Application of a mild Lipschitz condition on the state-dependent coefficient form.
• Validation through numerical simulations comparing the proposed filter against the conventional SDRE filter.

Main Results:

• The proposed H(∞) SDRE filter demonstrates superior performance in estimating system states under model uncertainties, disturbance, and measurement noise.
• Numerical simulations confirm a significant reduction in estimation error compared to the standard SDRE filter.
• The robust filter exhibits an improved region of convergence.

Conclusions:

• The developed robust H(∞) SDRE filter effectively addresses performance degradation caused by uncertainties and noise in nonlinear systems.
• The filter provides a reliable solution for state estimation in challenging dynamic environments.
• The findings highlight the practical advantages of the robust H(∞) SDRE filter over conventional approaches.