Adaptive distributed observer-based cooperative control for noncanonical nonlinear multi-agent systems modeled by RHONNs.

Different from traditional distributed control for multi-agent systems (MASs) composed of linear systems or nonlinear systems in canonical form, for MASs where followers have noncanonical nonlinear dynamics with implicit relative degree, there are two main challenges. Firstly, under the condition of only local interaction, each follower needs to obtain the high-order derivative information of the reference signal and apply it to the controller design. Secondly, the implicit system structure makes it impossible to carry out backstepping design. To achieve output consensus in such MASs, the two aforementioned issues are addressed as follows. For the first issue, a novel filter is designed to indirectly obtain the high-order derivatives of the observation signals. For the second issue, a recurrent high-order neural network (RHONN) is employed to approximate the original system, and an augmented error-based stability analysis method is adopted. By combining the new filter with the augmented error-based analysis method, we propose an effective control scheme and a complete analysis process for the cooperative problem of multiple noncanonical nonlinear systems, with the results guaranteeing the boundedness of all closed-loop signals and the asymptotic output consensus tracking. These theoretical findings are well verified by simulation tests.