Fault Recoverability Analysis of Nonlinear Systems: A Piecewise Affine System Approach

The recoverability reflects the capability of the system to tolerate the worst faults over a prescribed set under admissible energy constrains. In this paper, a piecewise affine (PWA) controller is designed for a piecewise affine approximation of the nonlinear dynamics, which can stabilize the original nonlinear system under some conditions. By analyzing the upper hound of the piecewise linear quadratic control performance of the PWA system, a novel fault recoverability evaluation scheme is further proposed for the nonlinear system with respect to the given limit of admissible control performance. A longitudinal flight control example is taken to show the effectiveness of the proposed method.