Adaptive output feedback containment control for parabolic PDE multi-agent systems

This paper investigates the output feedback containment control problem of multi-agent systems (MASs) with multiple leaders described by partial differential equations (PDEs). In contrast to MASs modeled by ODEs, the PDEs system studied in this paper considers additional spatial variables, which leads to traditional ODEs control design methods inapplicable, then the design of observer based adaptive distributed protocols is more challenging. Considering that leaders may be task-driven, the control inputs of the leaders are non-zero and time-varying. Through the introduction of nonlinear terms in the containment controller to eliminate the influence of leader control inputs, the paper ultimately achieves bounded tracking errors and containment errors for agents under undirected graph topologies. Finally, the designed control scheme is validated through examples.