Adaptive distributed control of uncertain multi-agent systems in the power-chained form

Power-chained form systems are a generalization of strict-feedback and pure-feedback systems since integrators with positive odd-powers can appear in the dynamics (chain of positive-odd power integrators) and they are extremely challenging to deal with, as their linearized dynamics might possess uncontrollable modes whose eigenvalues are in the right-hand-side plane, making standard feedback linearization or standard backstepping methodologies fail. The adding-one-power-integrator technique was proposed to handle power-chained formsystems. Progress made for power-chained formsystems includes employing universal approximators to handle completely unknown nonlinearities. However, state-of-the-art results on power-chained form systems are mainly focused on the single-agent case since a direct extension of the existing design to a distributed setting is not very meaningful on account of the facts that: i) the control gain of each virtual control is incorporated into the next virtual control law iteratively, possibly leading to high-gain issues; ii) state-of-the-art results rely on the assumption that the agents’ control directions are known a priori and are available for control design; iii) universal approximators often used in the adding-one-power-integrator procedure inevitably increase the complexity in the sense that extra adaptive parameters have to be updated (i.e. extra nonlinear differential equations need to be solved numerically), thus making their distributed implementation difficult.