Adaptive time-varying state safety constraint control for discrete-time nonlinear systems with random actuator failures

This work investigates the adaptive time -varying state safety constraint control problem for a class of discrete -time nonlinear systems subject to large parameter uncertainties and stochastic actuator failures for the first time. The existence of time -varying full -state constraints, large parameter uncertainties and stochastic actuator failures leads to a series of difficulties for realizing all control objectives. Due to the absence of the linearity property of the derivative in discrete -time log type barrier Lyapunov functions, they are not used to deal with the state constraint problem of nonlinear discrete -time systems. The discrete quadratic -fraction timevarying barrier Lyapunov function is employed to guarantee that all states are constrained in the time -varying predefined regions. By virtue of the constructed multiple -model set, an adaptive identification algorithm is developed to deal with large parameter uncertainties and it has a clear advantage that this method does not requires cn (where n is the dimension of the parameter vector and c is an integer) identification models and only relies on n+ 1 identification models, thereby heavily reducing the computational burden. By employing the discrete -time filter and backstepping techniques, the adaptive failure compensation controller is designed to ensure the boundedness in probability of the considered systems with respect to stochastic actuator failures. Finally, the effectiveness of the proposed scheme is proved by two simulation examples.