A method for optimizing control-free costs in systems with linear controllers

Optimization problems for
n
-dimensional systems with
m
linear controls and cost functions not explicitly dependent on the control variables are transformed into equivalent problems involving only (
n-m
) state variables and
m
controls, and cost functions which are dependent on the controls. The equivalent problems can be solved by standard techniques, but at a considerable computational advantage stemming from the reduced dimensionality. An illustrative example is worked out for a discrete linear system.