Lie groups underlying fault avoidance in dynamical control systems

2006 ◽  
pp. 174-181
Author(s):  
Dahlard L. Lukes
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Dynamical Control

scholarly journals Optimal control of affine connection control systems from the point of view of Lie algebroids

2014 ◽  
Vol 11 (09) ◽  
pp. 1450038 ◽  
Author(s):  
Lígia Abrunheiro ◽  
Margarida Camarinha
Keyword(s):  
Optimal Control ◽  
Vector Field ◽  
Control Systems ◽  
Lie Groups ◽  
Optimal Control Problems ◽  
Affine Connection ◽  
Point Of View ◽  
Lie Algebroids ◽  
Control Problems ◽  
Hamiltonian Vector Field

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems (OCPs) for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

scholarly journals Control systems on nilpotent Lie groups of dimension ≤4: Equivalence and classification

2017 ◽  
Vol 54 ◽  
pp. 282-297 ◽  
Author(s):  
Catherine E. Bartlett ◽  
Rory Biggs ◽  
Claudiu C. Remsing
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Nilpotent Lie Groups

A COMPOSITIONAL METHOD USING AN EVOLUTIONARY ALGORITHM FOR FINDING FUZZY RULES IN 3-LAYERED HIERARCHICAL FUZZY STRUCTURE

2009 ◽  
Vol 08 (04) ◽  
pp. 467-485 ◽  
Author(s):  
J. ZAJACZKOWSKI ◽  
B. VERMA
Keyword(s):  
Evolutionary Algorithm ◽  
Control Systems ◽  
Initial Conditions ◽  
Fuzzy Rules ◽  
Large Set ◽  
Multi Objective ◽  
Wide Range ◽  
Dynamical Control ◽  
Better Than ◽  
Compositional Method

This paper presents a novel compositional method for finding fuzzy rules in a three-layered hierarchical fuzzy structure. The proposed method incorporates a multi-objective evolutionary algorithm and a large set of initial conditions, including dynamical conditions of the system under investigation. The proposed method is focused on handling the large set of initial conditions by a multi-objective evolutionary algorithm and it can be applied to a wide range of dynamical control systems in robotics. The method has been evaluated on a dynamical system such as the inverted pendulum. The experimental results and analysis showed that the proposed method is much better than the existing methods such as amalgamation and single objective evolutionary algorithm based methods.

On the Observability of Semilinear Fuzzy Dynamical Control Systems

2009 ◽  
pp. 611-619
Author(s):  
Young Chel Kwun ◽  
Eun Hye Choi ◽  
Jong Seo Park ◽  
Jin Han Park
Keyword(s):  
Control Systems ◽  
Dynamical Control

Nonlinear Dynamical Control Systems

1990 ◽  
Author(s):  
Henk Nijmeijer ◽  
Arjan van der Schaft
Keyword(s):  
Control Systems ◽  
Nonlinear Dynamical ◽  
Dynamical Control

Optimal multiplexing of discrete-time constrained control systems on matrix Lie groups

2020 ◽  
pp. 1-1
Author(s):  
Chinmay Maheshwari ◽  
Sukumar Srikant ◽  
Debasish Chatterjee
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Discrete Time ◽  
Constrained Control

Cost-Extended Control Systems on Lie Groups

2013 ◽  
Vol 11 (1) ◽  
pp. 193-215 ◽  
Author(s):  
R. Biggs ◽  
C. C. Remsing
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Systems On Lie Groups

A minimal realization for affine control systems on connected Lie groups

2017 ◽  
Vol 14 (09) ◽  
pp. 1750126
Author(s):  
A. Kara Hansen ◽  
S. Selcuk Sutlu
Keyword(s):  
Control System ◽  
Control Systems ◽  
Lie Groups ◽  
Lie Group ◽  
Canonical Projection ◽  
Minimal Realization ◽  
Realization Problem ◽  
Affine Control Systems ◽  
Affine Control System ◽  
Connected Lie Group

In this work, we study minimal realization problem for an affine control system [Formula: see text] on a connected Lie group [Formula: see text]. We construct a minimal realization by using a canonical projection and by characterizing indistinguishable points of the system.

scholarly journals Attainable sets and one-parameter semigroups of sets

1991 ◽  
Vol 33 (2) ◽  
pp. 187-201 ◽  
Author(s):  
I. Chon ◽  
J. D. Lawson
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Vector Fields ◽  
Geometric Control ◽  
Lie Theory ◽  
Attainable Sets ◽  
Widespread Application ◽  
Close Relationship ◽  
Basic Facts ◽  
Systems On Lie Groups

The methods of Lie theory have found widespread application in the study of the Lie algebras of vector fields on manifolds that arise naturally in geometric control theory (for some such applications, see [1]). Control systems on Lie groups themselves also have received considerable attention (see, for example, [9]). After reviewing basic facts about control systems on Lie groups, we derive the close relationship between attainable sets and Rådström's theory [12] of one-parameter semigroups of sets (Section 2). These ideas are then linked to the recently emerging Lie theory of semigroups [5]. The authors are indebted to the referee for pointing out some of the pertinent literature and analogous results from the area of geometric control.

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