Data-driven adaptive compensation control for a class of nonlinear discrete-time system with bounded disturbances

Area of Science:

• Control Engineering
• Nonlinear Systems Theory
• Data-Driven Control

Background:

• Nonlinear discrete-time systems often face challenges from bounded disturbances.
• Accurate system models are frequently unavailable or impractical for real-world applications.
• Disturbances can be measurable (MD) or unmeasurable (UD), complicating control design.

Purpose of the Study:

• To develop novel data-driven adaptive controllers for nonlinear discrete-time systems with bounded disturbances.
• To address the compensation control problem for both measurable and unmeasurable disturbances within a unified framework.
• To design controllers that do not require prior knowledge of the system's internal dynamics.

Main Methods:

• Dynamic Linearization Technique (DLT) to establish an equivalent data model of the disturbed system.
• Design of two data-driven controllers using disturbance-related compact-form and partial-form DLT.
• Adaptive gain update mechanisms that utilize input-output data without system model information.

Main Results:

• Two purely data-driven adaptive disturbance compensation controllers were designed and theoretically validated.
• The controllers effectively handle both measurable and unmeasurable disturbances in a unified approach.
• Time-varying adaptive gains dynamically incorporate system dynamics, especially for unknown disturbances.

Conclusions:

• The proposed data-driven controllers ensure strict stability for nonlinear discrete-time systems under bounded disturbances.
• The effectiveness and practical applicability of the controllers were demonstrated through numerical simulations and a distillation column experiment.
• This research offers a robust solution for adaptive disturbance compensation using only operational data.