Existence of an optimal feedback control law for time-optimal control of two-input analytic nilpotent systems in dimension three

Guoqing Tang

doi:10.1109/ssst.1998.660073

Existence of an optimal feedback control law for time-optimal control of two-input analytic nilpotent systems in dimension three

Guoqing Tang

Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper we analyze regularity properties of time-optimal trajectories for a class of two-input three-dimensional real-Analytic systems whose accessibility Lie algebra is nilpotent of step 2, and establish the existence of an almost analytic optimal feedback control law. We prove that every time-optimal trajectory is replaceable by a bang-bang trajectory with at most three switchings, and show that there exist a large open dense subset of the state space and an optimal feedback control law which is analytic on the open dense subset.

Original language	English
Title of host publication	30th Southeastern Symposium on System Theory, SSST 1998
Volume	1998-
DOIs	https://doi.org/10.1109/ssst.1998.660073
State	Published - 1998

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10.1109/ssst.1998.660073

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title = "Existence of an optimal feedback control law for time-optimal control of two-input analytic nilpotent systems in dimension three",

abstract = "In this paper we analyze regularity properties of time-optimal trajectories for a class of two-input three-dimensional real-Analytic systems whose accessibility Lie algebra is nilpotent of step 2, and establish the existence of an almost analytic optimal feedback control law. We prove that every time-optimal trajectory is replaceable by a bang-bang trajectory with at most three switchings, and show that there exist a large open dense subset of the state space and an optimal feedback control law which is analytic on the open dense subset.",

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year = "1998",

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language = "English",

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AU - Tang, Guoqing

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N2 - In this paper we analyze regularity properties of time-optimal trajectories for a class of two-input three-dimensional real-Analytic systems whose accessibility Lie algebra is nilpotent of step 2, and establish the existence of an almost analytic optimal feedback control law. We prove that every time-optimal trajectory is replaceable by a bang-bang trajectory with at most three switchings, and show that there exist a large open dense subset of the state space and an optimal feedback control law which is analytic on the open dense subset.

AB - In this paper we analyze regularity properties of time-optimal trajectories for a class of two-input three-dimensional real-Analytic systems whose accessibility Lie algebra is nilpotent of step 2, and establish the existence of an almost analytic optimal feedback control law. We prove that every time-optimal trajectory is replaceable by a bang-bang trajectory with at most three switchings, and show that there exist a large open dense subset of the state space and an optimal feedback control law which is analytic on the open dense subset.

UR - https://dx.doi.org/10.1109/SSST.1998.660073

U2 - 10.1109/ssst.1998.660073

DO - 10.1109/ssst.1998.660073

M3 - Conference contribution

VL - 1998-

BT - 30th Southeastern Symposium on System Theory, SSST 1998

ER -

Existence of an optimal feedback control law for time-optimal control of two-input analytic nilpotent systems in dimension three

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