TY - GEN

T1 - Solving optimal feedback control problems by the Hamilton-Jacobi theory

AU - Park, Chandeok

AU - Scheeres, Daniel J.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:34047233355

SN - 1424402107

SN - 9781424402106

T3 - Proceedings of the American Control Conference

SP - 2406

EP - 2411

BT - Proceedings of the 2006 American Control Conference

T2 - 2006 American Control Conference

Y2 - 14 June 2006 through 16 June 2006

ER -