Bounds on the optimal performance of pulse-controlled linear systems

The optimal performance of linear pulse-frequency-modulated (PFM) control systems is investigated. A performance index consisting of a weighted sum of the quadratic terminal state error and fuel consumption is used. The direct synthesis of optimal PFM control systems is difficult, but upper and lower bounds on the optimal values of the performance index can be established without difficulty. These bounds are formed by the solutions of two auxiliary optimal control problems. When the upper and lower bounds are close to one another, PFM control may be replaced by a more easily implemented mode of control. Two additional modes-pulse-amplitude modulation and pulse-width modulation-also fall within these bounds.