Adaptive and optimal regulation controller design for fractional linear multi‐agent systems

Summary This express brief is concerned with the adaptive and optimal regulation control for fractional linear multi‐agent systems (MASs). Firstly, the adaptive control strategy is applied to address the regulation issue for fractional linear MASs with time varying edges. Under the designed adaptive control protocols with adaptive edge‐dependent synchronization gain, the regulation condition is achieved by constructing a Lyapunov functional with the edges. Secondly, the optimal control approach is used to solve the regulation issue for fractional linear MASs with constant edges. The optimization gain is chosen by minimizing an appropriate performance function. Moreover, the synchronization objectives are also achieved based on the proposed the regulation conditions. Finally, the correctness of the theoretical analysis and the feasibility of the designed controllers are verified by two numerical examples.