Solutions of the Optimal Feedback Control Problem using Hamiltonian Dynamics and Generating Functions

Chandeok Park, Daniel J. Scheeres

Research output: Contribution to journalConference article

13 Citations (Scopus)

Abstract

We show that the optimal cost function that satisfies the Hamilton-Jacobi-Bellman (HJB) equation is a generating function for a class of canonical transformations for the Hamiltonian dynamical system defined by the necessary conditions for optimality. This result allows us to circumvent the final time singularity in the HJB equation for a finite time problem, and allows us to analytically construct a nonlinear optimal feedback control and cost function that satisfies the HJB equation for a large class of dynamical systems. It also establishes that the optimal cost function can be computed from a large class of solutions to the Hamilton-Jacobi (HJ) equation, many of which do not have singular boundary conditions at the terminal state.

Original languageEnglish
Pages (from-to)1222-1227
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2
Publication statusPublished - 2003 Dec 1
Event42nd IEEE Conference on Decision and Control - Maui, HI, United States
Duration: 2003 Dec 92003 Dec 12

Fingerprint

Optimal Feedback Control
Hamiltonians
Hamiltonian Dynamics
Hamilton-Jacobi-Bellman Equation
Cost functions
Feedback control
Generating Function
Cost Function
Control Problem
Dynamical systems
Dynamical system
Canonical Transformation
Control Function
Hamilton-Jacobi Equation
Optimality
Boundary conditions
Singularity
Necessary Conditions
Class

All Science Journal Classification (ASJC) codes

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

Cite this

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Solutions of the Optimal Feedback Control Problem using Hamiltonian Dynamics and Generating Functions. / Park, Chandeok; Scheeres, Daniel J.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2, 01.12.2003, p. 1222-1227.

Research output: Contribution to journalConference article

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