A time-varying observer design for synchronization with an uncertain target and its applications in coordinated mission rendezvous

Coordinated mission rendezvous is the most fundamental and crucial issue in the application of cooperative search and rescue, forest fire fighting, and target hunting even tactical simulation and drill. The biggest challenge is how to schedule the limited resource to carry out cooperative mission rendezvous against uncertain targets with unknown external inputs and heterogeneous system dynamics. Three fundamental challenges are addressed: (1) how to accurately estimate the motion trajectory of an uncertain target; (2) how to design a pre-action mission rendezvous framework to create the rendezvous region; and (3) how to enhance the difficulty of interception but improve the accuracy of rendezvous. To do this, this paper first proposes a time-varying observer design for synchronization with an uncertain target over a dual design framework. By introducing proper assumptions, a novel condition of dwell time of switching communication topologies can be constructed, from which a synchronization algorithm is developed to achieve the cooperative behaviors between the trackers and distributed observers such that they eventually synchronize to their target signal. With the application of multi-missile systems, the time-varying formation techniques will be further developed for an uncertain mission rendezvoustarget. Specifically, this paper proposes a novel multi-stage cooperative mission rendezvous strategy that includes preparation and execution phases. In the preparation stage, the trackers will maintain a specified altitude to pre-construct the mission rendezvous region. In the execution stage, the trackers are in time-varying formation attitudes to approach the uncertain target over time-varying observers to accomplish the cooperative mission rendezvous. Specifically, the cases of chattering reduction and synchronization for general heterogeneous systems are discussed, respectively. At last, two simulations with uncertain moving targets, i.e., the ground vehicle and robotic with unknown input signals, are presented to demonstrate the proposed theories and chattering-free controllers.