  This paper studies an optimal consensus problem for a group of heterogeneous
high-order agents with unknown control directions. Compared with existing
consensus results, the consensus point is further required to an optimal
solution to some distributed optimization problem. To solve this problem, we
first augment each agent with an optimal signal generator to reproduce the
global optimal point of the given distributed optimization problem, and then
complete the global optimal consensus design by developing some adaptive
tracking controllers for these augmented agents. Moreover, we present an
extension when only real-time gradients are available. The trajectories of all
agents in both cases are shown to be well-defined and achieve the expected
consensus on the optimal point. Two numerical examples are given to verify the
efficacy of our algorithms.
