A method for constructing multiply closed strategies in the problem of minimizing the total control impulse in a linear system with disturbance

This paper deals with an optimal control problem for a linear discrete-time system subject to unknown bounded disturbance. It is required to steer the system robustly to a terminal set with the smallest total impulse of the control function. A problem of constructing an optimal multiply closed control strategy is formulated. It is assumed that the system states are measured and the control is corrected at some future times. A method for calculating an optimal strategy based on reducing the formulated problems to linear programs is proposed.