Principles of non-linear control

Abstract

The chapter analyzes established concepts in the control of non-linear and PDE dynamical systems. The following main approaches for the control of complex non-linear dynamical systems are considered (i) control with methods of approximate (local) linearization being associated with the solution of the non-linear optimal control problem, (ii) control with methods of exact (global) linearization comprising also adaptive control methods and (iii) control of distributed parameter systems (systems which are described by partial differential equations) and stochastic estimation methods. In (i) one can distinguish a novel non-linear optimal (H-infinity) control method. In (ii) one can distinguish flatness-based control for non-linear dynamical systems with known model and adaptive flatness-based control in the case of systems with the unknown model. In (iii) one can distinguish a flatness-based boundary control approach for PDEs which is implemented in successive loops.