Optimal control of nonlinear continuous-time systems in strict-feedback form.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Artificial Intelligence in Control

Background:

• Nonlinear systems with uncertain dynamics pose significant control challenges.
• Optimal tracking control is crucial for performance in many engineering applications.
• Existing methods often require known system dynamics or initial admissible controllers.

Purpose of the Study:

• To develop a novel optimal tracking control scheme for nonlinear continuous-time systems with uncertain dynamics.
• To address systems in strict-feedback form using adaptive and neural network-based approaches.
• To ensure system stability without the need for an initial admissible controller.

Main Methods:

• Transformation of optimal tracking to optimal regulation via modified backstepping.
• Utilizing neural networks to estimate the infinite-horizon cost function (value function).
• Designing an observer for optimal output feedback control, validated by Lyapunov stability theory.

Main Results:

• A novel optimal tracking control scheme for nonlinear systems in strict-feedback form.
• Demonstration of minimizing Hamilton-Jacobi-Bellman estimation error without iterations.
• Proven overall stability of the proposed control and observer schemes.

Conclusions:

• The proposed method effectively achieves optimal tracking control for uncertain nonlinear systems.
• The approach offers stability guarantees and avoids the need for initial controllers.
• Simulation results confirm the theoretical validity and practical applicability of the scheme.