Robust preview control for a class of uncertain discrete-time systems with time-varying delay

Area of Science:

• Control Systems Engineering
• Systems Theory
• Automation and Robotics

Background:

• Discrete-time systems with time-varying delays present significant control challenges.
• Uncertainty in system dynamics complicates robust controller design.
• Preview control offers potential for improved tracking performance by utilizing future reference information.

Purpose of the Study:

• To develop a robust preview tracking control strategy for uncertain discrete-time systems with time-varying delays.
• To transform the complex tracking problem into a more manageable regulator problem.
• To provide a systematic design method for the proposed preview controller.

Main Methods:

• Model transformation to handle time-varying delays.
• Introduction of auxiliary variables to create an augmented error system incorporating future reference signals.
• Application of the scaled small gain theorem and linear matrix inequality (LMI) techniques.
• Derivation of a sufficient condition for asymptotic stability of the augmented error system.

Main Results:

• A novel robust preview tracking controller design is proposed.
• The controller design effectively addresses uncertainties and time-varying delays.
• The method simplifies the augmented error system structure and handles time-varying matrices.
• Numerical simulations validate the effectiveness of the proposed control strategy.

Conclusions:

• The proposed method provides a robust solution for preview tracking control in uncertain discrete-time systems with time-varying delays.
• The use of LMIs and the scaled small gain theorem offers a computationally tractable approach.
• The technique enhances system stability and tracking performance despite system uncertainties and delays.