Scaled consensus for MASs with compound noises over Markovian switched topologies

This article aims to address the stochastic scaled consensus issue in almost surely and mean square sense of stochastic multiagent systems (SMASs) with compound noises in a Markovian switching setting. At first, based on stochastic approximation technique and nearest-neighbor interaction rules, the stochastic scaled consensus controller is built for SMASs in presence of multiplicative and additive noise by designing a time-varying gain. Meanwhile, some consensus criterions of SMASs are addressed if the union of the graph and time-varying gain fulfill some mild requirements. Furthermore, the scaled consensus means that the agents' state variables tend to a prescribed proportion rather than the common value, so this behavior can be seen as non-convergent behavior. The difference with most of excellent literatures is that the coexistence of noncooperative behavior and multiplicative noise generates that it is not easy to transform the multiplicative noise term into the form of an error equation, which means that the Lyapunov methods cannot be directly utilized in our article. To cope with this, we first demonstrate the boundedness for each agent's state, and hence the convergence can be achieved. Finally, in order to reveal the efficiency of our proposed protocol, the corresponding example is given in the simulation part.