The conjugate-gradient method for optimal control problems with undetermined final time†

Abstract

For solving non-linear control problems several methods exist, the conjugate-gradient method being one of the most successful. Gradient and conjugate-gradient methods have also been extended to treat control problems with undetermined final time. Two basic approaches have been suggested; one in which the final time in each iteration is determined by a search and the other in which the final time for the next iteration is computed. In both approaches the number of steps in the numerical integration procedure is variable. In this paper an alternative approach is suggested. By augmenting the control vector with one additional component the problem with undetermined final time is transformed to a problem with fixed final time. A fixed number of steps can then be used. The same approach can be applied to the determination of unknown constant system parameters or unknown initial conditions of the state vector and for the computation of the on-off control.

Notes

†Communicated by the Author.