Reinforcement learning based adaptive optimal control for constrained nonlinear system via a novel state-dependent...

Area of Science:

• Control Theory
• Nonlinear Systems
• Adaptive Control

Background:

• Existing state-constrained control schemes often require feasibility conditions or sacrifice optimality.
• Strict-feedback nonlinear systems present challenges in control design due to inherent constraints.

Purpose of the Study:

• To develop an adaptive optimal control scheme for strict-feedback nonlinear systems with state constraints.
• To address the limitations of existing methods by eliminating feasibility requirements and maintaining optimality.

Main Methods:

• A novel nonlinear state-dependent function (NSDF) transforms the constrained system into an unconstrained one.
• Reinforcement learning (RL) is employed to design an adaptive optimal controller for the transformed system.
• Actor and critic neural networks are updated using modified adaptive laws to approximate optimal controllers.

Main Results:

• The proposed scheme effectively handles state constraints without imposing feasibility conditions.
• All signals within the closed-loop system are proven to be bounded.
• The output tracking error converges to an adjustable neighborhood of the origin, independent of the NSDF.

Conclusions:

• The developed adaptive optimal control scheme offers a robust solution for state-constrained nonlinear systems.
• The integration of NSDF and RL provides a novel approach to achieve both optimality and constraint satisfaction.
• Simulation results validate the effectiveness and performance of the proposed control strategy.