Simplified Optimized Backstepping Control for a Class of Nonlinear Strict-Feedback Systems With Unknown Dynamic...

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Artificial Intelligence

Background:

• Nonlinear strict-feedback systems present significant control challenges due to unknown dynamics.
• Existing reinforcement learning (RL) optimal control methods are often complex, relying on intricate derivations from the Hamilton-Jacobi-Bellman (HJB) equation.
• Traditional methods may require strict conditions like persistence of excitation, limiting their applicability.

Purpose of the Study:

• To develop a simplified and effective optimized backstepping (OB) control scheme for nonlinear strict-feedback systems.
• To integrate reinforcement learning (RL) with neural networks (NNs) for adaptive control of systems with unknown dynamics.
• To alleviate the complexity associated with traditional RL-based optimal control and remove restrictive conditions.

Main Methods:

• An optimized backstepping (OB) control strategy is designed, ensuring virtual and actual controls are optimized solutions.
• A novel reinforcement learning (RL) algorithm is developed using an identifier-critic-actor neural network (NN) architecture.
• Updating laws are derived from the negative gradient of a simplified positive function based on the HJB equation, avoiding complex gradient descent on Bellman errors.

Main Results:

• The proposed method effectively estimates unknown system dynamics and implements optimized control actions.
• The simplified RL algorithm reduces computational complexity compared to existing methods.
• The control scheme successfully operates without the need for persistence of excitation, demonstrating broader applicability.
• Theoretical analysis and simulations confirm the effectiveness of the developed control strategy.

Conclusions:

• The optimized backstepping (OB) control scheme, enhanced by a simplified reinforcement learning (RL) approach, provides an effective solution for controlling nonlinear strict-feedback systems with unknown dynamics.
• This method offers a more tractable and less restrictive alternative to existing RL-based optimal control techniques.
• The successful demonstration through theory and simulation validates the practical utility of this advanced control strategy.