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

In recent years, compound noise, including additive noise and multiplicative noise, has inevitably affected stochastic multi-agent systems (SMASs). These noises introduce unpredictable oscillations that severely degrade system stability. This influence becomes particularly critical in containment control problems where multiple leaders exhibit dynamic behaviors. Therefore, this article addresses this challenge by introducing a novel model that incorporates compound noises and the multiple dynamic leaders can evolve dynamically through interactions with their neighboring leaders. In order to reduce the effect of compound noises, based on stochastic approximation (SA) technique, a novel containment control protocol is designed. Since the introduction of multiplicative noise causes existing error analysis methods to fail for our proposed SMASs with multiple dynamic leaders, a novel semi-decomposition technique is proposed to achieve containment control in a compound noisy environment, where followers converge to the convex hull spanned by dynamic leaders. Additionally, the containment control problem with multiple static leaders scene can be viewed as a special case of our underlying system. Different from existing results for control gain conditions (∫₀^∞σ(t)dt=∞ and ∫₀^∞σ²(t)dt<∞), a weaker condition of ∫₀^∞σ^τ(t)dt<∞ is adopted, where τ=min{2,ρ}>1 rather than 2. Then, three numerical simulations are proposed to illustrate the feasibility of our results. By selecting the control gains as ξ(t)=1/(t+1)^0.8 (leaders' gain) and σ(t)=1/(t+1)^0.6 (followers' gain), that is, the convergence speed of the leaders is faster than that of the followers, the containment control for SMASs with multiple dynamic leaders can be achieved. Additionally, the noise intensities of multiplicative noise have a greater impact on the convergence than those of additive noise.