Robust Approximate Dynamic Programming for Nonlinear Systems With Both Model Error and External Disturbance

Area of Science:

• Control Theory
• Nonlinear Systems
• Optimization

Background:

• Traditional control methods address model error and external disturbances separately, which is insufficient for complex nonlinear problems.
• Concurrent handling of these uncertainties introduces significant challenges like nonconvexity in performance optimization.
• Existing approaches struggle with simultaneous management of model uncertainties and external disturbances in nonlinear robust control.

Purpose of the Study:

• To develop a unified framework for simultaneously addressing model error and external disturbance in nonlinear robust performance problems.
• To introduce an additional cost function within the augmented Hamilton-Jacobi-Isaacs (HJI) equation to manage concurrent uncertainties.
• To reveal the relationship between the additional cost function and model uncertainty for satisfying the Hamilton-Jacobi inequality.

Main Methods:

• Augmented Hamilton-Jacobi-Isaacs (HJI) equation incorporating an additional cost function.
• A critic online learning algorithm utilizing Lyapunov stabilizing terms and historical states.
• Construction of a joint Lyapunov candidate for stability and convergence analysis.

Main Results:

• The proposed method effectively manages both model error and external disturbance in nonlinear systems.
• The critic online learning algorithm approximates the solution to the augmented HJI equation.
• Stability and convergence are proven using the second method of Lyapunov, with historical data reducing system and critic errors.

Conclusions:

• The introduced additional cost function in the augmented HJI equation provides a viable solution for nonlinear robust performance.
• The critic online learning algorithm ensures stability and convergence while handling uncertainties.
• The method demonstrates effectiveness through numerical examples, offering improved system performance bounds.