| Abstract: | This paper studies the formulation of the constrained infinite horizon linear quadratic regulator control law (CIHLQR). Results from recent studies in this area are extended to show that conditions used in the standard formulation of the CIHLQR law are not necessary, but merely sufficient. Through the use of a novel proof it is shown that for a general SISO system with input constraints and certain conditions imposed, saturated LQR provides the same control sequence as CIHLQR. It is further shown that saturated LQR is equivalent to the CIHLQR in the case of first-order systems, subject to both state and control constraints. Finally, the region of constrained stabilisability is characterised for the case of open-loop unstable first-order systems. |
