DocumentCode :
3113964
Title :
Formulation of a Hamiltonian Cauchy Problem for Solving Optimal Feedback Control Problems
Author :
Park, Chandeok ; Scheeres, Daniel J.
Author_Institution :
graduate student in the department of Aerospace Engineering, University of Michigan at Ann Arbor, Ann Arbor, MI, 48109 (chandeok@umich.edu)
fYear :
2005
fDate :
12-15 Dec. 2005
Firstpage :
2793
Lastpage :
2798
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 non-analytic cost function.
Keywords :
Cauchy Problem; Generating Function; Hamilton-Jacobi Equation; Hamiltonian System; Optimal Feedback Control; Boundary conditions; Boundary value problems; Cost function; Differential equations; Dynamic programming; Employment; Feedback control; Logic programming; Optimal control; Partial differential equations; Cauchy Problem; Generating Function; Hamilton-Jacobi Equation; Hamiltonian System; Optimal Feedback Control;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on
Print_ISBN :
0-7803-9567-0
Type :
conf
DOI :
10.1109/CDC.2005.1582586
Filename :
1582586
Link To Document :
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