On metric controllers and observers for nonlinear systems

While the observer and controller design is well understood and widely used for linear systems, extensions to nonlinear systems have lacked generality. Motivated by fluid dynamics, and following up on our earlier work (1996), this paper further explores the use of so-called Euler coordinates (rather than the usual or Lagrange-based methods) in general nonlinear, non-autonomous systems, and the analysis and design tools they lead to. In this field formulation, a complex plant may be regarded as the superposition of simpler plants, each of them with very specific properties. There are two major classes of simple flow fields in fluid dynamics, namely potential flow and solenoidal flow. Both of them may be associated to an integral formulation of the system equations, leading in turn to a Lyapunov-like function, in the form of of a scalar potential Φ or of stream function Ψ*. These generalized distance functions can be regarded as an extension of the differential concept of length introduced in our earlier work