The present tutorial paper constitutes the second of a series of tutorials on manifold calculus with applications in system theory and control. The aim of the present tutorial, in particular, is to explain and illustrate some key concepts in manifold calculus such as covariant derivation and manifold curvature. Such key concepts are then applied to the formulation, to the control, and to the analysis of non-linear dynamical systems whose state-space are smooth (Riemannian) manifolds. The main flow of exposition is enriched by a number of examples whose aim is to clarify the notation used and the main theoretical findings through practical calculations.
Manifold Calculus in System Theory and Control—Second Order Structures and Systems
Fiori S.
Primo
Formal Analysis
2022-01-01
Abstract
The present tutorial paper constitutes the second of a series of tutorials on manifold calculus with applications in system theory and control. The aim of the present tutorial, in particular, is to explain and illustrate some key concepts in manifold calculus such as covariant derivation and manifold curvature. Such key concepts are then applied to the formulation, to the control, and to the analysis of non-linear dynamical systems whose state-space are smooth (Riemannian) manifolds. The main flow of exposition is enriched by a number of examples whose aim is to clarify the notation used and the main theoretical findings through practical calculations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
