A switching-free multiple-model approach for adaptive FTC of non-Lipschitz nonlinear uncertain systems under persistent actuator failures

A novel actuator failure compensation scheme is proposed for affine nonlinear uncertain systems (not necessarily Lipschitz) subject to persistent/intermittent actuator faults/failures unknown in time, magnitude and pattern. The proposed control methodology satisfies the nonlinear separation principle through a modular backstepping control. The controller is then augmented with multiple estimation models to estimate failure induced parametric uncertainties and unknown system parameters. The output transient performance at start up and post-failure instances, is improved on account of a two layer adaptation which enhances the convergence speed and accuracy of parameter estimates. The proposed fault tolerant control (FTC) method yields a faithful accommodation of uncertain finite as well as infinite/intermittent/persistent actuator failures while ensuring satisfactory output transient and steady state performances. Further, compared to existing multiple model based adaptive fault tolerant control design for nonlinear systems, the proposed methodology circumvents the issues of stability due to switching between different models and utilizes a minimum number of estimation models for parameter estimation without compromising on the output performance. Consequently, the computational burden is also reduced. Compared to multiple model adaptive control based FTC strategies proposed earlier which assume finite actuator failures and Lipschitz nonlinear system, the proposed method is applicable to both Lipschitz and non-Lipschitz nonlinear systems affected by intermittent actuator failures. Using the concepts from stability analysis in random nonlinear impulsive systems, the $L_{\infty }$ and $L_2$ bounds on tracking error for all future time are derived in the case of intermittent/persistent actuator failures obtained using the proposed fault-tolerant controller. The improvement of output transient performance in the proposed control scheme in comparison with controller with single identifier, is theoretically proved and quantified.