On Nonlinear Control Perspectives of a Challenging Benchmark

Abstract

Dynamical systems are often nonlinear in nature. It motives people to explore various theoretical nonlinear analysis and control design tools, of which constructive nonlinear design methods are the most celebrated ones. However, applying a constructive tool faces up a big hurdle that the tool deals only with a certain dynamical structure, often not possessed by the natural dynamics. Nonlinear constructive control designs heavily relies on the identification of a particular structure via coordinate transformation and control transformation. To be realistic, these theoretical tools are not general to all of the nonlinear systems. Here, a challenging benchmark example–a four degrees of freedom inverted pendulum under the influence of a planar force–is considered that is nonlinear, multiple input and multiple output, underactuated and unstable. The benchmark is also of practical interests because it is an abstract of several applications. Three challenging control objectives are envisaged for the first time in the literature in order to how to apply various cuttingedge theoretical nonlinear control tools. In fact, the key step of all of the nonlinear designs is to identify spectral structures– certain “normal” forms. From this aspect, a sequence of preliminary designs will accompany the existing tools to construct nonlinear controllers, which is quite different from the linear control designs.