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

This paper considers the distributed robust suboptimal consensus control problem of linear multi-agent systems, with both H-2 and H-infinity performance requirements. A novel two-step complementary design approach is proposed. In the first step, a distributed control law is designed for the nominal multi-agent 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-infinity 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 trade-off, and can be expected to be much less conservative than the trade-off design such as the mixed H-2/H-infinity 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