Distributed Optimal Control With Recovered Robustness for Uncertain Network Systems: A Complementary Design Approach

This article considers the distributed robust suboptimal consensus control problem of uncertain linear multiagent systems, with both
$H_{2}$
and
$H_\infty$
performance requirements. A novel two-step complementary design approach is proposed. In the first step, a distributed control law is designed for the nominal multiagent system to achieve consensus with a prescribed
$H_{2}$
performance. In the second step, an extra control input, depending on some carefully chosen residual signals indicating the modeling mismatch, is designed to complement the
$H_{2}$
performance by providing robustness guarantee in terms of
$H_\infty$
requirement with respect to disturbances or uncertainties. The proposed complementary design approach provides an additional degree of freedom for design, having two separate controls to deal with the
$H_{2}$
performance and the robustness of consensus, respectively. Thereby, it does not need to make much tradeoff, and can be expected to be much less conservative than the tradeoff design, such as the mixed
$H_{2}/H_\infty$
control method. Besides, this complementary approach will recover the achievable
$H_{2}$
performance when external disturbances or uncertainties do not exist. The effectiveness of the theoretical results and the advantages of the complementary approach are validated via numerical simulations.