Formulation of a hamiltonian cauchy problem for solving optimal feedback control problems

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 research, we formulate the problem as 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 equation for generating functions we derive a set of 1st order quasilinear partial differential equations with the appropriate initial or terminal conditions, which forms the well-known Cauchy problem. These equations can also be derived by applying the invariant imbedding technique to the two point boundary value problem. The solution to this Cauchy problem is utilized for solving the Hamiltonian two point boundary value problem as well as the optimal feedback control problem with hard and soft constraint boundary conditions. As suggested by the illustrative examples given, 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 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages2793-2798
Number of pages6
DOIs
Publication statusPublished - 2005 Dec 1
Event44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain
Duration: 2005 Dec 122005 Dec 15

Publication series

NameProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume2005

Other

Other44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
CountrySpain
CitySeville
Period05/12/1205/12/15

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Park, C., & Scheeres, D. J. (2005). Formulation of a hamiltonian cauchy problem for solving optimal feedback control problems. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 2793-2798). [1582586] (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1582586
Park, Chandeok ; Scheeres, Daniel J. / Formulation of a hamiltonian cauchy problem for solving optimal feedback control problems. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. pp. 2793-2798 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05).
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Park, C & Scheeres, DJ 2005, Formulation of a hamiltonian cauchy problem for solving optimal feedback control problems. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1582586, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 2793-2798, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 05/12/12. https://doi.org/10.1109/CDC.2005.1582586

Formulation of a hamiltonian cauchy problem for solving optimal feedback control problems. / Park, Chandeok; Scheeres, Daniel J.

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 2793-2798 1582586 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

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

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Park C, Scheeres DJ. Formulation of a hamiltonian cauchy problem for solving optimal feedback control problems. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 2793-2798. 1582586. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). https://doi.org/10.1109/CDC.2005.1582586