2012/06/21 by Carsten Collon, Joachim Rudolph, Collon, Carsten +1
Engineering · Mathematics · #93B27 #93B51 #93C10 #Adaptive Control of Nonlinear Systems #Control and Stability of Dynamical Systems #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:93B27 #msc:93B51 #msc:93C10
paper · pdf · doi:10.48550/arxiv.1206.4784
arxiv created 2012/06/21 · openalex publication_date 2012/06/21 · arxiv updated 2012/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Symmetries of nonlinear control systems in state representation are considered. To this end, a geometric approach to ordinary differential equations is advocated. Invariant feedback laws for systems with Lie symmetries, i.e. feedback laws that preserve the symmetry group of a considered plant, can be constructed based on invariants of the considered group action. Under minor technical assumptions suitable invariant tracking errors can be determined by following a normalization procedure. The underlying local geometric meaning of this procedure is discussed and it is shown how it can also be applied in order to derive a local, reduced-order system representation. Further, the idea of controlled symmetries, i.e. imposing desired symmetry properties on a given control system by state feedback, is discussed by outlining an exemplary control design for a predator-prey bioreactor.