Comparison of Several Filtering Methods for Linear Multi-agent Systems with Local Unknown Parametric Couplings

Abstract

In this chapter, several filtering methods for multi-agent systems with coupling uncertainties are investigated. The considered multi-agent system is composed of many agents, each of which evolves with a discrete-time stochastic linear time-varying dynamics, and each agent will be locally influenced by its neighbor agents. So the states evolution of each agent is not only related with its previous states but also related with its neighbors’ previous states. Every agent can only observe its own measurements (outputs) and its neighbor agents’ outputs, while the states are invisible to any agent because of communication limitations existing in the considered multi-agent system. We suppose that each agent has a priori knowledge on the structure of itself and its neighbors, that is to say, the coefficient matrices occurred in the individual dynamic system are available for use by the agent itself and those agents who have interactions with the agent. Because of the information constraints, without knowing the coupling gains of the local interactions, it is not easy for each agent to estimate its states by traditional Kalman filter or other state observers. For the wide applications of multi-agent systems and the existence of coupling uncertainties in many practical applications, the problem of decentralized filtering of multi-agent systems is more important; this chapter introduces one general framework of multi-agent systems for convenience of filtering studies. For the considered coupled linear discrete-time multi-agent system with uncertain linear local couplings, based on the key idea of state augmentation and the certainty equivalence principle borrowed from the area of adaptive control, we introduce several filtering methods to resolve the fundamental problem considered in this chapter. By conducting extensive simulations, the consuming time and estimation errors of every method are compared for one typical example, which suggests which method is more precise and fast.