Decoupling Partially Unknown Dynamical Systems by State Feedback Equations

Abstract

One problem for efficient control of complex systems is to take into account the influence of unknown dynamics in interaction with a fixed defined one by a set of defined time varying parameters behaviour coming from coupling partially unknown dynamics. Under the assumption of robust model, nonlinear state feedback decoupling methods can be used for the control of such systems. We show in our paper, that if these parameters are slowly varying in time before the main dynamics (the exact mathematical meaning of this notion is given in the article), the classical decoupling methods remain valid with parameterized laws, but if parameters dynamic are non negligible before the main dynamic, we are in the fast varying parameters case, and we show that in this case decoupling methods operators must be changed in order to include these dynamical effects. We show also that in this case the use of classical decoupling methods, leads to non effcient control and multiple spurious effects. The computation of the static and dynamic feedback laws, in case of fast varying parameters, are given, for nonlinear decoupling methods, linearization and rejection of perturbations, as the research of the functional invariants of the output. A robust example in robotics is given, and the contribution of parameters dynamic is shown.