박찬덕 교수

The optimal control of a spacecraft as it transitions between specified states using continuous thrust in a fixed amount of time is studied using a recently developed technique based on Hamilton–Jacobi theory. Started from the first-order necessary conditions for optimality, a Hamiltonian system is derived for the state and adjoints with split boundary conditions. Then, with recognition of the two-point boundary-value problem as a canonical transfor-mation, generating functions are employed to f

Given a nonlinear system and performance index to be minimized, we present a general approach to evaluating the optimal feedback control law for this system that can be easily modified to satisfy different types of boundary conditions. Formulated in the context of Hamiltonian systems theory, this work allows us to analytically construct optimal feedback control laws from generating functions. Given our feedback control law solution, our approach enables us to obtain the feedback control for a di

The optimal control of a spacecraft as it transitions between specified states using continuous thrust in a fixed amount of time is studied using a recently developed technique based on Hamilton-Jacobi theory. Starting from the 1st order necessary conditions for optimality, we derive a Hamiltonian system for the state and adjoints with split boundary conditions. Then, recognizing the two point boundary value problem as a canonical transformation, we employ generating functions to find the optima

A fuel-optimal trans-Earth trajectory design for manned lunar missions is presented. The gravitational effects of the Moon, Earth, and Sun constitute a 4-body problem. Imposing maximum thrust, fuel budget, and flight time as design constraints, we formulate a nonlinear constrained fuel-optimal control problem to obtain an optimal trajectory from a low lunar parking orbit to an Earth interface condition. The resulting optimal control problem is solved using Legendre pseudospectral method. An anti

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