Output feedback based PD-type robust iterative learning control for uncertain spatially interconnected systems

Spatially interconnected systems (SISs) are formed by a chain of subsystems or units with the same or similar structure, all of which directly interact with their neighbors. For robust tracking of SISs subject to both polytopic uncertainty and external disturbances, a PD-type iterative learning control (ILC) algorithm integrated with real-time output feedback is proposed in the absence of accurate state measurement. By lifting along the spatial variable, the SISs are first transformed into an equivalent one-dimensional (1D) state-space model. Then, the transformed 1D system, together with the learning law, is reformulated as an equivalent discrete repetitive process model. Based on the Lyapunov theory, sufficient conditions in terms of bilinear matrix inequalities (BMIs) are established to ensure the robust stability of the resulting ILC system along the trial. To circumvent computation problem of BMIs, a two-stage heuristic approach is developed to derive ILC gains iteratively. Finally, the validity of the proposed method is verified by the comparative simulation of temperature distribution model of the metal rod.