Abstract
A new iterative method based on gradient function is proposed for solving bang-bang control problems. The proposed algorithm is outlined as follows. Assume any bang-bang function as an initial guess and calculate the gradient function for the control. The control function is improved succesively via the gradient function also in this method, but unlike the conventional gradient method, the time interval in which the control is improved is small and control is varied as large as admissible during that interval. Thus the improved control is again a bang-bann control.
The control after improvement is shown to give surely a less value of cost functional than before improvement. The convergent control obtained from this algorithm satisfies the local optimal condition. It is examined whether the characteristics of the gradient function with continuous control function will still hold for this case. With regard to this point, the derivation and calculation of the gradient function are also mentioned.
The usefulness of the proposed algorithm is illustrated by numerical examples. It should be remarked that the algorithm needs no assumption of switching times of optimal control function.
