Fixed-final-time optimal control of nonlinear systems with terminal constraints

Area of Science:

• Control Theory
• Artificial Intelligence
• Machine Learning

Background:

• Optimal control problems for nonlinear systems are challenging, especially with fixed-final-time and terminal constraints.
• Existing methods may struggle with the complexity and adaptability required for diverse scenarios.

Purpose of the Study:

• To develop a model-based reinforcement learning algorithm for fixed-final-time optimal control of nonlinear systems.
• To address both soft and hard terminal constraints within the control framework.
• To create a versatile neurocontroller applicable to various initial conditions, final times, and constraint surfaces.

Main Methods:

• A model-based reinforcement learning algorithm is designed.
• Convergence is proven for linear neural networks by demonstrating the training algorithm as a contraction mapping.
• The trained neurocontroller is evaluated on three distinct examples.

Main Results:

• The algorithm successfully achieves fixed-final-time optimal control for nonlinear systems.
• Convergence of the reinforcement learning algorithm is mathematically proven.
• Numerical results confirm the neurocontroller's versatility across different initial conditions, final times, and terminal constraints.

Conclusions:

• The developed neurocontroller offers a robust and adaptable solution for fixed-final-time optimal control of nonlinear systems.
• The technique shows significant potential for practical applications requiring precise control under complex constraints.
• The mathematical proof of convergence supports the reliability of the proposed reinforcement learning approach.