Stabilization via Event-Triggered Impulsive Control With Constraints for Switched Stochastic Systems.

Area of Science:

• Control Theory
• Stochastic Systems
• System Stability

Background:

• Switched stochastic systems (SSSs) present unique control challenges.
• Event-triggered impulsive control (ETIC) offers potential for efficient system stabilization.
• Existing ETIC schemes may lack robustness or efficiency in constrained environments.

Purpose of the Study:

• To develop and analyze an event-triggered impulsive control (ETIC) scheme with constraints for switched stochastic systems (SSSs).
• To ensure the stabilization of SSSs under defined constraints using the proposed ETIC.
• To investigate the performance and properties of the constrained ETIC, including its robustness and impulse frequency.

Main Methods:

• Design of a constrained ETIC scheme using a multi-index event-triggering mechanism (threshold value, control-free index, check period, constraint index).
• Analysis of system stabilization in terms of p th moment exponential stability and almost exponential stability, considering activation and transition probabilities.
• Development of sampling-based and random ETIC strategies derived from the constrained ETIC framework.

Main Results:

• The proposed ETIC with constraints guarantees p th moment exponential stability and almost exponential stability for SSSs.
• The constrained ETIC is demonstrated to be non-Zeno and robust against time delays.
• The constrained ETIC achieves a lower impulse frequency compared to traditional time-based impulsive control and other ETIC methods.

Conclusions:

• The developed ETIC with constraints is an effective and efficient control strategy for switched stochastic systems.
• The method offers significant advantages in terms of impulse frequency reduction and robustness.
• The study validates the effectiveness of the constrained ETIC through theoretical derivations and practical examples.