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.
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