Synthesis of time-optimal control by time interval adjustment

An iterative procedure for time-optimal control of linear plants with constrained control amplitudes is presented. It is assumed that the n th-order state-equation coefficient matrix has real eigenvalues, so that the time-optimal control is of the known bang-bang form with n switchings. The first step in the procedure is to arbitrarily choose n switching times (including the final time), and to calculate a precise constant control function which although not necessarily satisfying the amplitude constraints does bring the plant to the desired terminal state. In the following steps the switching times are systematically adjusted until the control function closely approximates the bang-bang form. The procedure is simple to implement, and experiments have shown fast convergence.