TY - JOUR
T1 - On the geometric construction of a stabilizing time-invariant state feedback controller for the nonholonomic integrator
AU - Zeng, Shen
N1 - Funding Information:
Section 2 of the present manuscript is adapted from Section 2 in the conference paper Zeng (2019) . This work was supported by the NSF grant CMMI-1933976 . The material in this paper was partially presented at the 11th IFAC Symposium on Nonlinear Control Systems (NOLCOS), September 4–6, 2019, Vienna, Austria. This paper was recommended for publication in revised form by Associate Editor Aneel Tanwani under the direction of Editor Daniel Liberzon.
Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2022/2
Y1 - 2022/2
N2 - The paper presents a rather natural and elementary geometric construction of a stabilizing time-invariant state feedback law for the nonholonomic integrator. The key features of the particular construction are the direct inclusion of certain classical optimality considerations pertaining to the geodesics of the nonholonomic integrator, the confinement of all discontinuities in the feedback law to the z-axis, as well as a uniform exponential convergence result for the closed-loop system. The results of this treatment also have interesting implications for the control of nonholonomic systems in general, e.g., they highlight that for nonholonomic systems even the most natural seeming stabilizing feedback laws may not be amenable to a closed-form expression and may need to be formulated in more elaborate and implicit terms.
AB - The paper presents a rather natural and elementary geometric construction of a stabilizing time-invariant state feedback law for the nonholonomic integrator. The key features of the particular construction are the direct inclusion of certain classical optimality considerations pertaining to the geodesics of the nonholonomic integrator, the confinement of all discontinuities in the feedback law to the z-axis, as well as a uniform exponential convergence result for the closed-loop system. The results of this treatment also have interesting implications for the control of nonholonomic systems in general, e.g., they highlight that for nonholonomic systems even the most natural seeming stabilizing feedback laws may not be amenable to a closed-form expression and may need to be formulated in more elaborate and implicit terms.
KW - Feedback stabilization
KW - Nonholonomic systems
KW - Nonlinear control
UR - http://www.scopus.com/inward/record.url?scp=85121241185&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2021.110073
DO - 10.1016/j.automatica.2021.110073
M3 - Article
AN - SCOPUS:85121241185
SN - 0005-1098
VL - 136
JO - Automatica
JF - Automatica
M1 - 110073
ER -