Manoeuvrable multi-agent formation control via time-varying flocking and iterative learning tracking

Manoeuvrable (or time-varying) formation control of second-order integral multi-agent networks with single virtual leaders is contrived by incorporating time-varying weighting matrices into flocking algorithms. Existence and properties are examined, including control bounded-ness, average trajectory and formation manoeuvrability with respect to the weighting matrices and virtual leader reference input. More specifically, it is shown that under the time-varying flocking algorithms, the multi-agents ultimately run into lattice formations and their kinematical features in terms of orientation, scaling, subspace specification and homogeneous/heterogeneous consensus can be manoeuvred. Moreover, by gain-scheduling assignment for the leader-average dynamics via the variation-of-constant formula and iterative learning optimisation, trajectory-tracking manoeuvrable formation control can be achieved. Technical advantages include: flexible formations rather than rigid ones can be dealt with; formation and trajectory tracking can be designed separately and implemented simultaneously; diverse formations are achievable by selecting the weighting matrices; trajectory-tracking control is independent of trajectory modelling. Numerical examples are illustrated to show the main results.