Fault-compensation-based boundary control for hyperbolic PDEs: An adaptive iterative learning scheme

In this paper, a fault-compensation-based boundary control strategy is developed for a class of distributed parameter systems expressed by second-order hyperbolic Partial Differential Equations (PDEs), in the case of actuator faults. Considering multiplicative actuator faults and additive actuator faults simultaneously, we put forward a hierarchical fault compensation scheme, i.e., an adaptive iterative learning boundary control technique. Lyapunov-Like analysis method and a variation of Wirtinger's inequality are used to design a boundary control scheme with an adaptive law, guaranteeing the asymptotical stability of the closed-loop hyperbolic PDE system with multiplicative faults. An iterative learning term is proposed to boost the performance of the system under both multiplicative faults and additive faults, and a composite energy function is used in analysis. With the proposed fault-compensation-based adaptive iterative learning boundary control technique, multiplicative faults are redeemed towards the time horizon and additive faults are compensated towards the iteration horizon. An active acoustic noise reduction process is presented to illustrate the merit and effectiveness of the designed adaptive iterative learning boundary control technique.