Fault Recoverability Analysis of Nonlinear Affine Control Systems: A Differential Geometry Approach

Fault recoverability reflects the capability of the system to tolerate faults, which maintains or gracefully degrades original performance under the faulty situation. With full consideration of different recovery objectives for the nonlinear affine control systems, two new concepts, named strict fault recoverability and weak fault recoverability, are defined and deeply analyzed in this paper. The strict fault recoverability is studied by analyzing the equivalence between the faulty system and the original system, which reveals the existence of the diffeomorphism between distributions of the faulty system and the original system; The weak fault recoverability is studied by analyzing whether global controllability or small-time local controllability (STLC) of the original system is maintained, which reveals the existence of the diffeomorphism between the smallest Lie algebras of the faulty system and the original system. A numerical example is given to illustrate the effectiveness of the proposed methods.