TY - JOUR
T1 - Non-unique and non-bang-bang controls in some linear time-optimal problems
AU - Nosov, V. R.
AU - Meda-Campaña, J. A.
AU - Gómez-Mancilla, J. C.
N1 - Funding Information:
This work was partially supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) through scholarship Sistema Nacional de Investigadores (SNI) and by Instituto Politécnico Nacional (IPN) through research projects 20110250 and 20110812, and scholarships EDI and COFFA.
PY - 2012/6
Y1 - 2012/6
N2 - In this paper, the time-optimal control for multidimensional linear systems is studied in cases when Kalman controllability conditions does hold, but Gramkrelidze generic position condition does not. The main contribution of this study is the demonstration that time-optimal control for multidimensional linear systems is not restricted to the classical discontinuous bang-bang form with a finite number of switching points. Instead, an infinite number of controls, including continuous ones, can be used to take the system to the origin in minimum time. As an illustrative example for this class of problems, the controllable movement of material point in multidimensional space is considered.
AB - In this paper, the time-optimal control for multidimensional linear systems is studied in cases when Kalman controllability conditions does hold, but Gramkrelidze generic position condition does not. The main contribution of this study is the demonstration that time-optimal control for multidimensional linear systems is not restricted to the classical discontinuous bang-bang form with a finite number of switching points. Instead, an infinite number of controls, including continuous ones, can be used to take the system to the origin in minimum time. As an illustrative example for this class of problems, the controllable movement of material point in multidimensional space is considered.
KW - controllability
KW - generic position conditions
KW - multidimensional linear systems
KW - time-optimal control
UR - http://www.scopus.com/inward/record.url?scp=84863601416&partnerID=8YFLogxK
U2 - 10.1093/imamci/dnr042
DO - 10.1093/imamci/dnr042
M3 - Artículo
SN - 0265-0754
VL - 29
SP - 259
EP - 269
JO - IMA Journal of Mathematical Control and Information
JF - IMA Journal of Mathematical Control and Information
IS - 2
ER -