Design of optimal dead-beat controllers

The problem of forcing the state of a linear discrete control system to zero in the minimum number of steps is discussed. Among those controllers that achieve the above goal, one is selected which minimizes -in an average sense-a given objective function. Expressions are given for the gradient of the objective function with respect to the parameter vector that determines the dead-beat controller. A minimizing algorithm is then developed to compute the optimal controller. An example is worked out for a third-order case.