Optimal Control of Bilinear Systems and Its Relation to Lie Algebras

摘要

The minimum fuel problem for a bilinear system is considered. It is shown how to obtain the optimal control by considering the Lie algebra generated by the system matrices. It is noted that an open-loop control depending on the initial value of the state x sub 0 is obtained. However, using the principle of receding horizon control, the control can be applied as if it were always starting at an optimizing interval of T seconds; x sub 0 can be replaced by x(t) and T allowed to depend on the state to obtain a nonlinear feedback control. The details are the same as with linear systems.