### 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 language | English |
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Pages (from-to) | 1222-1227 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 2 |

Publication status | Published - 2003 Dec 1 |

Event | 42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: 2003 Dec 9 → 2003 Dec 12 |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*2*, 1222-1227.

}

*Proceedings of the IEEE Conference on Decision and Control*, vol. 2, pp. 1222-1227.

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

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Solutions of the Optimal Feedback Control Problem using Hamiltonian Dynamics and Generating Functions

AU - Park, Chandeok

AU - Scheeres, Daniel J.

PY - 2003/12/1

Y1 - 2003/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=1542299121&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542299121&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:1542299121

VL - 2

SP - 1222

EP - 1227

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -