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

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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).