We present a global solution for an optimal controller of the underactuated Heisenberg system or nonholonomic integrator. Employing a recently developed technique based on generating functions appearing in the Hamilton-Jacobi theory, we circumvent a singularity caused by underactuation to develop a nonlinear optimal feedback control in an implicitly analytical form. The systematic procedure to deal with underactuation indicates that generating functions should be effective tools for solving general underactuated optimal control problems.
Bibliographical noteFunding Information:
Manuscript received November 01, 2006; revised June 06, 2008. Current version published December 10, 2008. This work was supported by National Science Foundation Grant CMS 0408542, DMS 0305837, and DMS 0604307. Recommended by Associate Editor J. Berg. C. Park and D. J. Scheeres are with the Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109 USA (e-mail: chandeok@umich. edu; firstname.lastname@example.org). V. Guibout is with the Advanced Concepts Department, MBDA, Paris 75016, France (e-mail: email@example.com). A. Bloch is with the Department Mathematics, University of Michigan, Ann Arbor, MI 48109 USA (e-mail: firstname.lastname@example.org). Digital Object Identifier 10.1109/TAC.2008.2007885
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering