Control reconfigurability of nonlinear system based on control redundancy

This paper presents the analysis of reconfiguration of control law (control reconfigurability) in nonlinear system. A reconfigurable closed-loop control circuit is constructed for a normal nonlinear system, with three components, i.e. a nominal controller, a reconfiguration block and a faulty module to be controlled. The whole circuit is described with corresponding state spaces of these components. The Lie algebra (Lie derivative and Lie brackets) is used for linearizing the system to study its controllability and observability. By referring to the feedback control of pole placement method in linear system and the construction of objective function, ensuring the asymptotic stability, the stabilizability and detectability are studied. After that, the control redundancies are proposed, i.e. the controllable redundancy, observable redundancy, stabilizable redundancy and detectable redundancy. Furthermore, the causalities between control redundancies and control reconfigurability are summarized as means to estimate whether the system is reconfigurable or not. Finally, a real example of multiple input multiple output (MIMO) nonlinear system is used to testify the validity of the conclusions.