Distributed Constrained Optimization Algorithm for Higher-Order Multi-Agent Systems

The distributed nonsmooth constrained optimization problems over higher-order systems are investigated in this study. The challenges lies in the fact that the output of the agent is directly controlled by the state variable rather than the control input. Compared to existing works, the local objective function is merely assumed to be nonsmooth. Firstly, an initialization-free fully distributed derivative feedback control scheme is developed for the known objective function over double-integrator systems. The local generic constraint is addressed by an adaptive nonnegative penalty factor. Secondly, an initialization-free fully distributed state feedback control scheme is proposed for the unknown objective function over double-integrator systems. Addressing the local box constraint involves incorporating an adaptive penalty factor. Thirdly, the above two algorithms are extended to the general higher-order systems using the tracking control method. In addition, the above-developed methods are proved to be asymptotically convergent under certain conditions. Eventually, the efficiency of the above-produced methods is shown via four simulation cases.