Control Oriented Real-Time Nonlinear Dynamic Pseudo-Inverse for Non-Minimum Phase Systems

Abstract

This paper presents a novel algorithm for the dynamic inversion of nonlinear systems within the output tracking control framework, wherein the inverse serves as an open-loop nominal controller to facilitate feedback stabilization of the tracking error dynamics along a nominal trajectory. The desired dynamic response for the open-loop controlled system is treated as a pseudo identity from which the causal and stable inverse is defined. For non-minimum phase systems, the Fliess normal form is used to enable a practical pseudo-inverse design without the need for internal dynamics stabilization or reverse-time previewing. Unlike exact inversion, which can be unstable or anti-causal, the proposed pseudo-inverse is stable and implementable in real time. A nontrivial application example illustrates the algorithm.