Neural-network-based robust critic learning control with advanced value iteration for continuous-time dynamical...

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear Dynamics

Background:

• Designing controllers for continuous-time nonlinear systems presents significant challenges.
• Traditional value iteration (VI) methods often require strict initial conditions and can suffer from slow convergence.
• Robust control is crucial for systems operating under uncertainty.

Purpose of the Study:

• To develop a novel neural-network-based robust critic learning method for controller design in continuous-time nonlinear systems.
• To overcome limitations of traditional VI, such as stringent initial condition requirements and slow convergence.
• To analyze approximation errors and introduce a relaxation factor for improved performance and implementation.

Main Methods:

• A robust critic learning algorithm is developed using advanced value iteration (VI).
• The method eliminates the need for an initial admissible control law, relaxing starting conditions.
• A relaxation factor is introduced to accelerate convergence, and approximation error analysis is performed.

Main Results:

• The developed scheme significantly relaxes the initial conditions required for iteration.
• Convergence is accelerated by a relaxation factor, outperforming traditional VI algorithms.
• Detailed proofs are provided for the algorithm's convergence and system stability.
• Three examples demonstrate the effectiveness of the proposed approach.

Conclusions:

• The novel neural-network-based robust critic learning method offers an effective solution for controller design in continuous-time nonlinear systems.
• The approach relaxes initial conditions, accelerates convergence, and provides robust performance.
• The theoretical analysis and practical examples validate the algorithm's efficacy and stability guarantees.