Containment control for stochastic multiagent systems with multiple dynamic leaders and compound noises.

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Stochastic multi-agent systems (SMASs) are susceptible to compound noise (additive and multiplicative), degrading stability, especially in containment control with dynamic leaders.
• Existing error analysis methods fail with multiplicative noise in dynamic SMASs, necessitating new approaches for robust control.
• Containment control aims for followers to converge within the convex hull of leaders, a challenge amplified by dynamic leader behaviors and noise.

Purpose of the Study:

• To develop a novel containment control protocol for SMASs under compound noise with multiple dynamic leaders.
• To address the limitations of existing error analysis methods caused by multiplicative noise.
• To establish a weaker control gain condition for achieving containment control.

Main Methods:

• A novel model incorporating compound noises and dynamic leaders was developed.
• A containment control protocol based on the stochastic approximation (SA) technique was designed.
• A novel semi-decomposition technique was proposed to handle the challenges posed by multiplicative noise.

Main Results:

• The proposed method achieves containment control, ensuring followers converge to the convex hull of dynamic leaders.
• A weaker control gain condition (∫₀^∞σ^τ(t)dt<∞, τ=min{2,ρ}>1) was adopted, improving upon existing results.
• Numerical simulations confirmed the feasibility, showing faster leader convergence than followers enhances control.
• Multiplicative noise intensity significantly impacts convergence more than additive noise intensity.

Conclusions:

• The developed containment control protocol effectively manages SMASs with compound noise and multiple dynamic leaders.
• The novel semi-decomposition technique provides a robust framework for analyzing systems with multiplicative noise.
• The findings offer a more flexible control gain condition and practical insights into noise impact for SMASs.