Formation and trajectory control of multiple dynamical systems

In recent years a lot of effort is put into making the transition from individually operating dy-namical systems to cooperation of multiple dynamical systems within a group. Besides providing straightforward advantages as increased effectiveness and performance, cooperation between sys-tems can also lead to performing complex tasks that cannot be realised with a single system. In this report possibilities of multi-system control are examined with particular focus on movement of individual systems in group formations. The main objective is to present a control strategy that is able to force a group of dynamical systems to move according to a desired trajectory in a desired formation layout and ensure stability of the overall dynamics. The control strategy presented in this report observes the group of dynamical systems as one large single system and moreover separates the overall movement and the formation of the group with each other. This is realised with a coordinate transformation, which transforms the dynamics of the n m-degree-of-freedom (m-DOF) systems into a m-DOF average system and a (n-1)m for-mation system. Here the average system represents the movement of the group and logically the formation system coincides with the dynamics of the group formation. Advantage of thi