Distributed optimal nonlinear dynamic inversion for multi-agents consensus

In this paper, we propose an optimal distributed controller based on Nonlinear Dynamic Inversion (NDI) theory and apply it to solve the consensus of nonlinear multi-agent systems (MASs). Our proposed method addresses the limitations of existing Distributed Nonlinear Dynamic Inversion (DNDI) techniques, which only apply to agents with square output. We formulated an optimal control problem to minimize a quadratic cost function while satisfying a set of linear constraints derived by simplifying the enforced consensus error dynamics. By relaxing the previous limitation, we introduced a distributed optimal framework called Distributed Optimal NDI (DONDI). This framework achieves consensus and incorporates additional objectives, such as minimizing control energy. The design of Optimal DNDI inherits all the advantages of NDI and provides an optimized allocation of control for achieving consensus in MAS. Also, we have shown how the controller handles the communication noise. This approach represents a significant advancement in multi-agent control, and our experimental results demonstrate its satisfactory performance and effectiveness.