Globally optimal feedback control law of the underactuated Heisenberg system by generating functions

Chandeok Park, Daniel J. Scheeres, Vincent Guibout, Anthony Bloch

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

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 fullyactuated 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.

Original languageEnglish
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Pages2687-2692
Number of pages6
Publication statusPublished - 2006 Dec 1
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: 2006 Dec 132006 Dec 15

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
CountryUnited States
CitySan Diego, CA
Period06/12/1306/12/15

Fingerprint

Optimal Feedback Control
Hamilton-Jacobi
Feedback control
Generating Function
Optimal Control Problem
Singularity
Canonical Transformation
Nonholonomic
Transcendental
Two-point Boundary Value Problem
Global Solution
Hamiltonian Systems
Manipulation
Hamiltonians
Control Problem
Optimal Control
Scalar
Transform
Numerical Examples
Boundary value problems

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Park, C., Scheeres, D. J., Guibout, V., & Bloch, A. (2006). Globally optimal feedback control law of the underactuated Heisenberg system by generating functions. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 2687-2692). [4177499]
Park, Chandeok ; Scheeres, Daniel J. ; Guibout, Vincent ; Bloch, Anthony. / Globally optimal feedback control law of the underactuated Heisenberg system by generating functions. Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. 2006. pp. 2687-2692
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Park, C, Scheeres, DJ, Guibout, V & Bloch, A 2006, Globally optimal feedback control law of the underactuated Heisenberg system by generating functions. in Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC., 4177499, pp. 2687-2692, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 06/12/13.

Globally optimal feedback control law of the underactuated Heisenberg system by generating functions. / Park, Chandeok; Scheeres, Daniel J.; Guibout, Vincent; Bloch, Anthony.

Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. 2006. p. 2687-2692 4177499.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Park C, Scheeres DJ, Guibout V, Bloch A. Globally optimal feedback control law of the underactuated Heisenberg system by generating functions. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. 2006. p. 2687-2692. 4177499