Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input.

Area of Science:

• Control Theory
• Nonlinear Systems
• Artificial Intelligence

Background:

• Controlling continuous-time nonaffine nonlinear systems with saturated control signals presents significant challenges.
• Traditional methods often require precise knowledge of system dynamics, which is frequently unavailable in real-world applications.
• The Hamilton-Jacobi-Bellman (HJB) equation is central to optimal control but difficult to solve for complex systems.

Purpose of the Study:

• To develop an online, near-optimal control strategy for continuous-time nonaffine nonlinear systems with control saturation.
• To address the challenge of unknown system dynamics by employing adaptive neural network techniques.
• To ensure the control signal remains within specified saturation bounds while maintaining system stability.

Main Methods:

• An identifier-critic structure utilizing two Neural Networks (NNs) is proposed.
• The identifier NN approximates unknown system dynamics, while the critic NN approximates the value function by solving the HJB equation.
• Online simultaneous tuning of NN weights ensures accurate approximation and adherence to control saturation limits, validated by Lyapunov's direct method.

Main Results:

• The proposed method successfully derives a near-optimal controller without prior knowledge of system dynamics.
• Simultaneous online tuning of identifier and critic NNs guarantees accurate approximation of unknown terms and keeps the control signal within saturation bounds.
• Convergence of NN weights, identification error, and system states is mathematically proven using Lyapunov's direct method.

Conclusions:

• The identifier-critic structure with neural networks provides an effective solution for controlling nonlinear systems with control saturation.
• The adaptive nature of the NNs allows for online learning and control, making the strategy robust to uncertainties.
• Simulation results on two nonlinear systems validate the effectiveness and practical applicability of the proposed control strategy.