GDI 2013 - International Workshop on Generalized Dynamic Inversion: An Evolving Paradigm for Control System Design

The development of Nonlinear Dynamic Inversion (NDI) has contributed substantially towards the advancements in control systems design during the past three decades. The methodology is nowaday simplemented within numerous control systems of the latest state- of the art industrial applications, e.g., civil and military aircraft,spacecraft, electric motors and devices, robots, and chemical plants. Despite of its popularity, NDI has its shortcomings, which are mostly related to the square inversion involved in the methodology. These include singularities of the inverted matrices, cancelations of useful nonlinearities, large control efforts, limited choices of controlled variables due to the zero dynamics, in addition to robustness concerns. The aim of this workshop is to present the newly developed generalized dynamic inversion (GDI) control paradigm, which intends to overcome the drawbacks of classical NDI. In particular, the inversion process that utilizes non-square generalized (pseudo-) inversion will be highlighted, in addition to the associated nullspace parametrization of non-square system matrices. The algebraic and the geometrical features of GDI that facilitate control system design will be emphasized, and the opportunities to employ several well-known control design methodologies in the framework of GDI will be discussed. Finally, the advantages of GDI over classical NDI and other control methodologies will be illustrated by several aerospace,electrical, and mechanical engineering examples.
Outline:
Overview of classical Nonlinear Dynamic Inversion (NDI)
Summary of the NDImethodology and feedback linearization
Shortcomings and drawbacks of NDI
Generalized Dynamic Inversion (GDI)
Mathematical preliminaries
Feedback linearization of non-square systems
Nullspace parametrization of nonsquare system matrices
Semi-definite Lyapunov functions and Null-control vector design
Augmenting control methodologies in the GDI control design framework
Examples, applications, and open problems