scholarly journals Approximate Input-state Feedback Linearization for Non-linear Systems and Control for the Acrobot

2003 ◽  
Vol 69 (688) ◽  
pp. 3301-3308
Author(s):  
Kou YAMADA ◽  
Atsuyuki YUZAWA ◽  
Kouji NITTA ◽  
Wataru KINOSHITA
Keyword(s):  
Linear Systems ◽  
Feedback Linearization ◽  
State Feedback ◽  
Input State ◽  
Systems And Control ◽  
Non Linear ◽  
Non Linear Systems ◽  
And Control

scholarly journals Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2092
Author(s):  
Simone Fiori
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Linear Control Systems ◽  
First Order ◽  
Curved Manifolds ◽  
Non Linear ◽  
Covariant Derivation ◽  
Non Linear Systems ◽  
And Control

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

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