Output‐feedback boundary adaptive fault‐tolerant control for scalar hyperbolic partial differential equation systems with actuator faults

Abstract

SummaryThis article studies the output‐feedback adaptive fault‐tolerant boundary control problem for scalar hyperbolic partial differential equation systems with actuator faults. All the coefficients of the controlled plant are unknown, and two types of actuator faults, that is, multiplicative faults and additive faults, are considered simultaneously. For the state estimation problem, two filters are constructed, based on which an observer is obtained to estimate the system state. A parametric model is established for actuator faults, based on which the parameter updating laws of gradient type are then developed to identify actuator faults and to estimate the unknown system coefficients. With the observer and the parameter updating laws, an output‐feedback adaptive fault‐tolerant boundary control law is developed via infinite‐dimensional backstepping method. The boundness of all the signals involved in the control design is guaranteed and the convergence of system states is also confirmed. Finally, the simulation results are given to testify the effectiveness of the proposed control scheme.