Relatively optimal control with characteristic polynomial assignment

A relatively optimal control is a stabilizing controller such that, if initialized at its zero state, produces the optimal (constrained) behavior for the nominal initial condition of the plant (without feedforwarding and tracking the optimal trajectory). In a previous work we have shown that one of such controllers is linear, dead-beat, and its order is equal to the length of the horizon minus the plant order, thus of complexity which is known a-priori. In this work we remove the assumption of zero terminal state and we show how to assign an arbitrary closed-loop characteristic stable polynomial to the plant (an explicit solution is provided.) We also show how to choose the characteristic polynomial in such a way that the constraints (which are enforced on a finite horizon) can be globally or ultimately satisfied.