Conversion of Optimal Control Problems with Free Initial State into Optimal Control Problems with Fixed Initial State.
RICE UNIV HOUSTON TEX AERO-ASTRONAUTICS GROUP
Pagination or Media Count:
This paper considers optimal control problems involving the minimization of a functional subject to differential constraints, nondifferential constraints, initial conditions, and final conditions. The initial conditions can be partly fixed and partly free. Transformation techniques are suggested, by means of which problems with free initial state are converted into problems with fixed initial state. Thereby, it becomes possible to employ, without change, some of the algorithms already developed for optimal control problems with fixed initial state for instance, the sequential gradient-restoration algorithm. The transformations introduced are two 1 a linear transformation and 2 a nonlinear transformation. In the linear-quadratic case, the former preserves unchanged the basic structure of the optimization problem, while this is not the case with the latter.
- Theoretical Mathematics