Solving optimal feedback control problems by the Hamilton-Jacobi theory

Chandeok Park, Daniel J. Scheeres

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

Abstract

We propose a novel approach for solving the optimal feedback control problem. Following our previous researches, we construct a Hamiltonian system by using the necessary conditions for optimality, and treat the resultant phase flow as a canonical transformation. Then starting from the Hamilton-Jacobi equations for generating functions we derive a set of 1st order quasilinear partial differential equations with the relevant terminal conditions, which forms the well-known Cauchy problem. These equations can also be obtained by applying the invariant imbedding technique to the two point boundary value problem. The solution to this Cauchy problem is utilized for solving the optimal feedback control problem with hard and soft constraint boundary conditions. As suggested by the illustrative examples, this method is promising for solving problems with control constraints, non-smooth control logic, and nonanalytic cost function.

Original languageEnglish
Title of host publicationProceedings of the 2006 American Control Conference
Pages2406-2411
Number of pages6
Publication statusPublished - 2006 Dec 1
Event2006 American Control Conference - Minneapolis, MN, United States
Duration: 2006 Jun 142006 Jun 16

Publication series

NameProceedings of the American Control Conference
Volume2006
ISSN (Print)0743-1619

Other

Other2006 American Control Conference
CountryUnited States
CityMinneapolis, MN
Period06/6/1406/6/16

Fingerprint

Feedback control
Hamiltonians
Cost functions
Boundary value problems
Partial differential equations
Boundary conditions

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Park, C., & Scheeres, D. J. (2006). Solving optimal feedback control problems by the Hamilton-Jacobi theory. In Proceedings of the 2006 American Control Conference (pp. 2406-2411). [1656580] (Proceedings of the American Control Conference; Vol. 2006).
Park, Chandeok ; Scheeres, Daniel J. / Solving optimal feedback control problems by the Hamilton-Jacobi theory. Proceedings of the 2006 American Control Conference. 2006. pp. 2406-2411 (Proceedings of the American Control Conference).
@inproceedings{34e27639b3214356a7badaf0d3ae0010,
title = "Solving optimal feedback control problems by the Hamilton-Jacobi theory",
abstract = "We propose a novel approach for solving the optimal feedback control problem. Following our previous researches, we construct a Hamiltonian system by using the necessary conditions for optimality, and treat the resultant phase flow as a canonical transformation. Then starting from the Hamilton-Jacobi equations for generating functions we derive a set of 1st order quasilinear partial differential equations with the relevant terminal conditions, which forms the well-known Cauchy problem. These equations can also be obtained by applying the invariant imbedding technique to the two point boundary value problem. The solution to this Cauchy problem is utilized for solving the optimal feedback control problem with hard and soft constraint boundary conditions. As suggested by the illustrative examples, this method is promising for solving problems with control constraints, non-smooth control logic, and nonanalytic cost function.",
author = "Chandeok Park and Scheeres, {Daniel J.}",
year = "2006",
month = "12",
day = "1",
language = "English",
isbn = "1424402107",
series = "Proceedings of the American Control Conference",
pages = "2406--2411",
booktitle = "Proceedings of the 2006 American Control Conference",

}

Park, C & Scheeres, DJ 2006, Solving optimal feedback control problems by the Hamilton-Jacobi theory. in Proceedings of the 2006 American Control Conference., 1656580, Proceedings of the American Control Conference, vol. 2006, pp. 2406-2411, 2006 American Control Conference, Minneapolis, MN, United States, 06/6/14.

Solving optimal feedback control problems by the Hamilton-Jacobi theory. / Park, Chandeok; Scheeres, Daniel J.

Proceedings of the 2006 American Control Conference. 2006. p. 2406-2411 1656580 (Proceedings of the American Control Conference; Vol. 2006).

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

TY - GEN

T1 - Solving optimal feedback control problems by the Hamilton-Jacobi theory

AU - Park, Chandeok

AU - Scheeres, Daniel J.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - We propose a novel approach for solving the optimal feedback control problem. Following our previous researches, we construct a Hamiltonian system by using the necessary conditions for optimality, and treat the resultant phase flow as a canonical transformation. Then starting from the Hamilton-Jacobi equations for generating functions we derive a set of 1st order quasilinear partial differential equations with the relevant terminal conditions, which forms the well-known Cauchy problem. These equations can also be obtained by applying the invariant imbedding technique to the two point boundary value problem. The solution to this Cauchy problem is utilized for solving the optimal feedback control problem with hard and soft constraint boundary conditions. As suggested by the illustrative examples, this method is promising for solving problems with control constraints, non-smooth control logic, and nonanalytic cost function.

AB - We propose a novel approach for solving the optimal feedback control problem. Following our previous researches, we construct a Hamiltonian system by using the necessary conditions for optimality, and treat the resultant phase flow as a canonical transformation. Then starting from the Hamilton-Jacobi equations for generating functions we derive a set of 1st order quasilinear partial differential equations with the relevant terminal conditions, which forms the well-known Cauchy problem. These equations can also be obtained by applying the invariant imbedding technique to the two point boundary value problem. The solution to this Cauchy problem is utilized for solving the optimal feedback control problem with hard and soft constraint boundary conditions. As suggested by the illustrative examples, this method is promising for solving problems with control constraints, non-smooth control logic, and nonanalytic cost function.

UR - http://www.scopus.com/inward/record.url?scp=34047233355&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047233355&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:34047233355

SN - 1424402107

SN - 9781424402106

T3 - Proceedings of the American Control Conference

SP - 2406

EP - 2411

BT - Proceedings of the 2006 American Control Conference

ER -

Park C, Scheeres DJ. Solving optimal feedback control problems by the Hamilton-Jacobi theory. In Proceedings of the 2006 American Control Conference. 2006. p. 2406-2411. 1656580. (Proceedings of the American Control Conference).