scholarly journals Observability and Symmetries of Linear Control Systems

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 953
Author(s):  
Víctor Ayala ◽  
Heriberto Román-Flores ◽  
María Torreblanca Todco ◽  
Erika Zapana
Keyword(s):  
Euclidean Space ◽  
Control Systems ◽  
Lie Groups ◽  
Lie Group ◽  
Linear Control ◽  
Linear Control Systems ◽  
Euclidean Spaces ◽  
General Setup ◽  
Connected Lie Group

The goal of this article is to compare the observability properties of the class of linear control systems in two different manifolds: on the Euclidean space R n and, in a more general setup, on a connected Lie group G. For that, we establish well-known results. The symmetries involved in this theory allow characterizing the observability property on Euclidean spaces and the local observability property 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 Toward Applications of Linear Control Systems on the Real World and Theoretical Challenges

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 167
Author(s):  
Víctor Ayala ◽  
María Torreblanca ◽  
William Valdivia
Keyword(s):  
Maximum Principle ◽  
Control Systems ◽  
Lie Group ◽  
Real World ◽  
Pontryagin Maximum Principle ◽  
Optimization Problems ◽  
Linear Control ◽  
Linear Control Systems ◽  
Open Problems ◽  
The Pontryagin Maximum Principle

Many significant real world challenges arise as optimization problems on different classes of control systems. In particular, ordinary differential equations with symmetries. The purpose of this review article is twofold. First, we give the information we have about the class of Linear Control Systems ΣG on a low dimension matrix Lie group G. Second, we invite the Mathematical community to consider possible applications through the Pontryagin Maximum Principle for ΣG. In addition, we challenge some theoretical open problems. The class ΣG is a perfect generalization of the classical Linear Control System on the Abelian group Rn. Let G be a Lie group of dimension two or three. Related to ΣG, this review describes the actual results about controllability, the time-optimal Hamiltonian equations and, the Pontryagin Maximum Principle. We show how to build ΣG, through several examples on low dimensional matrix groups.

scholarly journals About the solutions of linear control systems on Lie groups

2016 ◽  
Vol 35 (4) ◽  
pp. 491-503 ◽  
Author(s):  
Victor Ayala ◽  
Adriano Da Silva ◽  
EyUp ]Kizil
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Linear Control ◽  
Linear Control Systems ◽  
Systems On Lie Groups

Fractional Vector-Order h-Realisation of the Impulse Response Function

2020 ◽  
Vol 14 (2) ◽  
pp. 108-113
Author(s):  
Ewa Pawłuszewicz
Keyword(s):  
Control Systems ◽  
Impulse Response ◽  
Response Function ◽  
Impulse Response Function ◽  
Linear Control ◽  
Linear Control Systems

AbstractThe problem of realisation of linear control systems with the h–difference of Caputo-, Riemann–Liouville- and Grünwald–Letnikov-type fractional vector-order operators is studied. The problem of existing minimal realisation is discussed.

Sign in / Sign up

Export Citation Format

Share Document