Self-learning robust optimal control for continuous-time nonlinear systems with mismatched disturbances.

Area of Science:

• Control Theory
• Nonlinear Systems
• Adaptive Dynamic Programming

Background:

• Mismatched disturbances in continuous-time nonlinear systems pose significant control challenges.
• Existing robust optimal control methods often require strict initial conditions and persistent excitation.

Purpose of the Study:

• To develop a novel adaptive dynamic programming (ADP)-based self-learning robust optimal control scheme.
• To address input-affine continuous-time nonlinear systems with mismatched disturbances.
• To relax restrictive conditions associated with traditional control methods.

Main Methods:

• Designing a stabilizing feedback controller by modifying an auxiliary system's optimal control law.
• Utilizing a single critic network within ADP to solve the Hamilton-Jacobi-Bellman equation.
• Employing an indicator function and concurrent learning for critic network weight updates.

Main Results:

• The proposed controller optimizes a specified value function for the original nonlinear system.
• Restrictive conditions like initial admissible control and persistence of excitation are relaxed.
• Stability of the closed-loop auxiliary system is guaranteed, with all signals uniformly ultimately bounded.

Conclusions:

• The developed ADP-based self-learning robust optimal control strategy is effective for nonlinear systems with disturbances.
• The method demonstrates applicability through simulations on unstable nonlinear plants and power systems.
• This approach offers a more flexible and robust control solution for complex systems.