  This paper studies the consensus problem of heterogeneous multi-agent systems
by the feedforward control and linear quadratic (LQ) optimal control theory.
Different from the existing consensus control algorithms, which require to
design an additional distributed observer for estimating the leader's
information and to solve a set of regulator equations. In this paper, by
designing a distributed feedforward controller, a non-standard neighbor error
system is transformed into a standard linear system, and then an optimal
consensus controller is designed by minimizing a combined state error with
neighbour agents. The proposed optimal controller is obtained by solving
Riccati equations, and it is shown that the corresponding cost function under
the proposed distributed controllers is asymptotically optimal. The proposed
consensus algorithm can be directly applicable to solve the consensus problem
of homogeneous systems. Simulation example indicates the effectiveness of the
proposed scheme and a much faster convergence speed than the existing
algorithm.
