Online Optimal Adaptive Control of Partially Uncertain Nonlinear Discrete-Time Systems Using Multilayer Neural...

Area of Science:

• Control Engineering
• Artificial Intelligence
• Nonlinear System Dynamics

Background:

• Adaptive control is crucial for systems with unknown or changing dynamics.
• Neural networks offer powerful tools for approximating complex system behaviors.
• Online learning methods are essential for real-time control applications.

Purpose of the Study:

• To develop an online optimal adaptive regulation strategy for nonlinear discrete-time systems.
• To address systems with affine form and partially uncertain dynamics.
• To utilize multilayer neural networks (MNNs) within an actor-critic framework.

Main Methods:

• An actor-critic framework was employed to estimate optimal control inputs and value functions.
• Weights of critic and actor networks were tuned using control input error and temporal difference.
• Lyapunov stability analysis was used to prove boundedness of system states and network weights.
• The method does not require pre-selection of basis functions or their derivatives.

Main Results:

• The proposed method effectively achieves online optimal adaptive regulation.
• Boundedness of the state vector and neural network weights was mathematically proven.
• The approach demonstrated successful application via a simulation example.
• The method is extensible to MNNs with varying numbers of hidden layers.

Conclusions:

• The developed online adaptive control strategy is effective for uncertain nonlinear discrete-time systems.
• The use of MNNs within an actor-critic framework provides a robust solution.
• The approach offers flexibility and theoretical guarantees on stability and boundedness.