Event-triggered model predictive control of positive systems with random actuator saturation

Area of Science:

• Control Engineering
• Systems Theory
• Applied Mathematics

Background:

• Positive systems are crucial in various fields, including biology and economics.
• Actuator saturation and system uncertainties pose significant challenges in control design.
• Existing control methods often lack generality in handling saturation phenomena.

Purpose of the Study:

• To develop an event-triggered model predictive control (MPC) strategy for positive systems.
• To address actuator saturation using a more general probabilistic model.
• To ensure system positivity and stability under interval and polytopic uncertainties.

Main Methods:

• A novel model incorporating actuator saturation based on Bernoulli distribution is established.
• A linear event-triggering condition is designed using system state and error signals.
• An interval estimation approach and linear programming are employed for controller synthesis.

Main Results:

• The proposed event-triggered control ensures positivity and stability of the system.
• Actuator saturation is effectively handled by transforming it into a non-saturation problem.
• A predictive algorithm computes the event-triggered controller gain and attraction domain.

Conclusions:

• The developed event-triggered MPC is effective for positive systems with actuator saturation.
• The probabilistic saturation model offers improved generality and performance.
• The method provides a robust framework for controlling uncertain positive systems.