Other examples are the the manufacturing experiments at University of Michigan and the PATH program at UC Berkeley. Recognizing the difference between regulation and tracking For linear control systems, regulation and tracking are essentially identical. For nonlinear systems, and particularly motion control systems , the problem of tracking is significantly different and considerably harder. The role of trajectory generation is very important in nonlinear problems and is the motivation for much of our work in differential flatness , nonholonomic motion planning , and mechanical systems with symmetries . Exploiting special structure to synthesize controllers You can't build a theory for nonlinear control that works for everything.
Nonlinear systems are a lot more complicated than that.
Concentrating on special classes of systems, like mechanical systems and propulsion systems , is the most likely way make significant progress in synthesizing nonlinear controllers. I think that a really good example is some of the work that Blaise Morton has done at Honeywell on the use of dynamic inversion for pitch control of an F14. Finding nonlinear normal systems for control Most of the research in nonlinear control to date has concentrated on extending linear methodologies to nonlinear problems. In essense, we convert or approximate nonlinear systems by linear ones and then applying traditional ideas. Even more nonlinear approaches like backstepping really only apply to problems that are absolutely equivalent to linear systems.