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Impulsive Control Under Event-Triggered Mechanism for Reaction-Diffusion Systems With Impulsive Disturbances
This study ensures reaction-diffusion systems remain stable despite impulsive disturbances by developing Zeno-free event-triggered control. This practical approach is validated using an atmospheric pollution model.
Area of Science:
- Control Theory
- Dynamical Systems
- Environmental Science
Background:
- Reaction-diffusion systems (RDSs) are fundamental in modeling spatio-temporal phenomena.
- Impulsive disturbances can destabilize systems and cause Zeno behavior in control mechanisms.
- Event-triggered mechanisms (ETMs) offer efficiency but require careful design to avoid Zeno issues.
Purpose of the Study:
- To develop Zeno-free conditions for event-triggered control (ETM) in reaction-diffusion systems (RDSs) under impulsive disturbances.
- To establish sufficient conditions for asymptotic stability (AS) of RDSs using impulsive control theory.
- To demonstrate the practical application of the proposed control strategies in an atmospheric pollution model.
Main Methods:
- Utilizing an event-triggered impulsive control (ETIC) method.
- Deriving Zeno-free conditions for the event-triggered mechanism (ETM).
- Applying impulsive control theory to establish sufficient conditions for asymptotic stability (AS).
Main Results:
- Successfully derived Zeno-free conditions for the ETM, preventing premature triggering.
- Established several sufficient conditions for the asymptotic stability (AS) of RDSs under impulsive disturbances.
- Validated the control strategies through a numerical simulation of an atmospheric pollution model.
Conclusions:
- The developed ETIC method provides robust stability for RDSs against impulsive disturbances.
- The Zeno-free conditions are critical for the practical implementation of event-triggered control in real-world systems.
- The study offers valuable theoretical guidance and practical solutions for environmental pollution control.
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