Position tracking of multi double-integrator dynamics by bounded distributed control without velocity measurements

The position tracking problem of multi double-integrator dynamics without velocity measurements is considered. To ensure the feedback signal is prior bounded, the notion of local neighborhood synchronization error (LNSE) is extended to the nonlinear case by hyperbolic tangent functions of position errors. A condition, under which the convergence of the position error can be concluded from the convergence of the extended LNSE, is identified. A continuous bounded distributed controller is designed with the extended notion and the output of an auxiliary system. This control scheme can serve as a unified approach for solving the rotating consensus problems in both 2-dimensional and 3-dimensional space. Numerical examples are provided to validate this point.