Adaptive Critic Design for Pure-Feedback Discrete-Time MIMO Systems Preceded by Unknown Backlashlike Hysteresis

Area of Science:

• Control Systems Engineering
• Nonlinear System Analysis
• Artificial Intelligence in Control

Background:

• Adaptive critic design (ACD) is challenging for uncertain nonlinear discrete-time systems.
• Backlash-like hysteresis and nonaffine functions complicate optimal control.
• Existing methods struggle with multi-input multi-output (MIMO) systems in pure-feedback form.

Purpose of the Study:

• To develop an ACD framework for uncertain MIMO nonlinear discrete-time systems with unknown hysteresis.
• To address the complexities arising from nonaffine functions and state-input couplings.
• To ensure system stability and minimize the performance index.

Main Methods:

• Utilizing the mean value theorem to convert systems into input-output models.
• Employing a reinforcement learning algorithm for optimal control strategy development.
• Implementing an actor-critic structure for adaptive control.

Main Results:

• The first ACD framework for MIMO systems with unknown hysteresis is established.
• An adaptive auxiliary signal is introduced to effectively compensate for hysteresis.
• Demonstrated stability and minimized performance index for the considered systems.

Conclusions:

• The proposed ACD method is effective for uncertain MIMO nonlinear discrete-time systems with hysteresis.
• The adaptive auxiliary signal successfully mitigates the impact of unknown hysteresis.
• Numerical simulations validate the proposed control strategy's effectiveness.