NDLI: Globally Optimal Feedback Control Law of the Underactuated Heisenberg System by Generating Functions

Content Provider	IEEE Xplore Digital Library
Author	Chandeok Park Scheeres, D.J. Guibout, V. Bloch, A.
Copyright Year	2006
Description	Author affiliation: Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI (Chandeok Park; Scheeres, D.J.)
Abstract	We present a global solution for an optimal feedback control problem of the underactuated Heisenberg system or nonholonomic integrator. Set in the general framework of the Hamilton-Jacobi theory, this work demonstrates the potential applicability of our methodology to general underactuated optimal control problems. We incorporate the Heisenberg system into a typical optimal control formulation called the hard constraint problem, and transform into a two point boundary value problem for a Hamiltonian system. It is viewed as a canonical transformation in itself, to which we apply our recently developed technique based on generating functions appearing in the Hamilton-Jacobi theory. It is first recognized that our previously developed procedure for solving fully-actuated optimal control problems is not directly applicable due to a singularity caused by underactuation. However, within the same framework of generating functions we are provided with a way to circumvent this singularity by algebraic manipulations linked with the underactuated coordinate. This results in a scalar transcendental equation whose solution ultimately leads to a nonlinear optimal feedback control law in an analytical form. We illustrate our solution by numerical examples
Starting Page	2687
Ending Page	2692
File Size	241322
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377608
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Feedback control Optimal control Control systems Boundary value problems Nonlinear equations USA Councils Power generation Navigation Mathematics Orbital robotics Underactuated System Generating Function Heisenberg System Hamilton-Jacobi Equation Optimal Feedback Control
Content Type	Text
Resource Type	Article

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