Abstract:
The proposed methods to solve optimal control problems are
classified as direct methods and indirect methods. This thesis is based on
solving optimal control problems using direct methods in which an
optimal control problem is converted into a mathematical programming
problem. The direct methods can be employed by using the
parameterization technique which can be applied in three different ways:
control parameterization, control-state parameterization and state
parameterization. Here, we used control-state parameterization.
This thesis presents numerical methods to solve unconstrained
optimal control problems. The solution method is based on using the
iteration approach to replace the nonlinear optimal control problem by a
sequence of time-varying linear quadratic optimal control problems. Each
of these problems is solved by converting it into quadratic programming
problem. The control-state parameterization technique is done by using
the Legendre polynomials to approximate the system state variables.
The proposed method has been applied on several examples and
we find that it gives acceptable results compared with some other
methods.
