Title: Distributed Average Tracking of Heterogeneous Physical Second-order Agents With No Input Signals Constraint,
Abstract: This paper addresses distributed average tracking of physical second-order
agents with heterogeneous nonlinear dynamics, where there is no constraint on
input signals. The nonlinear terms in agents' dynamics are heterogeneous,
satisfying a Lipschitz-like condition that will be defined later and is more
general than the Lipschitz condition. In the proposed algorithm, a control
input and a filter are designed for each agent. Each agent's filter has two
outputs and the idea is that the first output estimates the average of the
input signals and the second output estimates the average of the input
velocities asymptotically. In parallel, each agent's position and velocity are
driven to track, respectively, the first and the second outputs. Having
heterogeneous nonlinear terms in agents' dynamics necessitates designing the
filters for agents. Since the nonlinear terms in agents' dynamics can be
unbounded and the input signals are arbitrary, novel state-dependent
time-varying gains are employed in agents' filters and control inputs to
overcome these unboundedness effects. Finally the results are improved to
achieve the distributed average tracking for a group of double-integrator
agents, where there is no constraint on input signals and the filter is not
required anymore. Numerical simulations are also presented to illustrate the
theoretical results.