Guaranteed-cost consensus for multiagent networks with Lipschitz nonlinear dynamics and switching topologies
For researchers in multi-agent systems, this provides a method to achieve consensus with guaranteed cost under switching topologies and nonlinear dynamics, though it is incremental as it extends existing linear results to Lipschitz nonlinearities.
The paper addresses guaranteed-cost consensus for high-order nonlinear multi-agent networks with switching topologies. It decomposes network dynamics into consensus and disagreement parts, linearizes nonlinear impacts via Lipschitz condition, and provides a Riccati-based protocol with minimized cost via LMI, validated by simulation.
Guaranteed-cost consensus for high-order nonlinear multi-agent networks with switching topologies is investigated. By constructing a time-varying nonsingular matrix with a specific structure, the whole dynamics of multi-agent networks is decomposed into the consensus and disagreement parts with nonlinear terms, which is the key challenge to be dealt with. An explicit expression of the consensus dynamics, which contains the nonlinear term, is given and its initial state is determined. Furthermore, by the structure property of the time-varying nonsingular transformation matrix and the Lipschitz condition, the impacts of the nonlinear term on the disagreement dynamics are linearized and the gain matrix of the consensus protocol is determined on the basis of the Riccati equation. Moreover, an approach to minimize the guaranteed cost is given in terms of linear matrix inequalities. Finally, the numerical simulation is shown to demonstrate the effectiveness of theoretical results.