Linear systems on Lie groups and almost-Riemannian structures

• Grant number: 16/11135-2
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2016
• End date: June 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Adriano João da Silva
• Grantee: Adriano João da Silva
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The main aim of the present project is to give a contribution to the geometric control theory through the class of linear control systems on Lie groups (LCS). Our objective is to approach both, classical problems of control theory and more contemporary problems involving almost-Riemannian geometry. (AU)

Scientific publications

(11)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

AYALA, VICTOR; DA SILVA, ADRIANO; SAN MARTIN, LUIZ A. B.. CONTROL SYSTEMS ON FLAG MANIFOLDS AND THEIR CHAIN CONTROL SETS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 37, n. 5, p. 2301-2313, MAY 2017. (12/18780-0, 16/11135-2, 13/19756-8)

AYAL, VICTOR; DA SILVA, ADRIANO. On the characterization of the controllability property for linear control systems on nonnilpotent, solvable three-dimensional Lie groups. Journal of Differential Equations, v. 266, n. 12, p. 8233-8257, JUN 5 2019. (18/10696-6, 16/11135-2)

KAWAN, CHRISTOPH; DA SILVA, ADRIANO. Invariance entropy for a class of partially hyperbolic sets. Mathematics of Control, Signals, and Systems (MCSS), v. 30, n. 4, DEC 2018. (16/11135-2)

AYALA, VICTOR; DA SILVA, ADRIANO; FERREIRA, MAX. Affine and bilinear systems on Lie groups. SYSTEMS & CONTROL LETTERS, v. 117, p. 23-29, JUL 2018. (16/11135-2)

DA SILVA, ADRIANO; KAWAN, CHRISTOPH. Robustness of critical bit rates for practical stabilization of networked control systems. AUTOMATICA, v. 93, p. 397-406, JUL 2018. (16/11135-2)

DA SILVA, ADRIANO; IEEE. Affine systems on Lie groups and invariance entropy. 2016 IEEE 55TH CONFERENCE ON DECISION AND CONTROL (CDC), v. N/A, p. 6-pg., 2016-01-01. (13/19756-8, 16/11135-2)

DA SILVA, ADRIANO; KAWAN, CHRISTOPH. Lyapunov exponents and partial hyperbolicity of chain control sets on flag manifolds. Israel Journal of Mathematics, v. 232, n. 2, p. 947-1000, AUG 2019. (16/11135-2)

AYALA, VICTOR; DA SILVA, ADRIANO; JOUAN, PHILIPPE; ZSIGMOND, GUILHERME. Control sets of linear systems on semi-simple Lie groups. Journal of Differential Equations, v. 269, n. 1, p. 449-466, JUN 15 2020. (16/11135-2, 18/10696-6)

AYALA, VICTOR; DA SILVA, ADRIANO. A semigroup associated to a linear control system on a Lie group. SYSTEMS & CONTROL LETTERS, v. 98, p. 33-36, DEC 2016. (16/11135-2)

VICTOR AYALA; ADRIANO DA SILVA; EYUP ]KIZIL. About the solutions of linear control systems on Lie groups. Proyecciones, v. 35, n. 4, p. 491-503, 2016-12-30. (16/11135-2)

AYALA, VICTOR; ROMAN-FLORES, HERIBERTO; DA SILVA, ADRIANO. The dynamic of a Lie group endomorphism. OPEN MATHEMATICS, v. 15, p. 1477-1486, DEC 29 2017. (16/11135-2)