OPTIMAL IMPULSIVE LINEAR-SYSTEMS - SUFFICIENT CONDITIONS AND MAXIMUM NUMBER OF IMPULSES

The optimal control of a linear system with impulsive force control in puts is considered. The cost functional to be minimized is the integra l of the magnitude of the control force per unit mass, which is equiva lent to the sum of the magnitudes of the discontinuities in the veloci ty vector caused by the force impulses. Previously derived necessary c onditions for an optimal solution are shown to also be sufficient cond itions for a global minimum. A proof is also given that there exists a maximum number q of impulses required for any solution that satisfies the specified boundary conditions. The value of q is equal to the num ber of specified final state variables and thus the optimal solution r equires at most q impulses. In addition, a procedure is derived and il lustrated whereby a solution using more than q impulses can be reduced to a q-impulse solution of equal or lower cost.