A new method of controller design for systems with input constraints using interpolation functions

We present a LQ-based control law that increases the LQ gain as the system trajectory converges towards the origin in the presence of asymmetric input constraints. A gain interpolation function is used to ensure that gain increases occur in a continuous manner. This extends previous work of Wredenhagen and Belanger (1994) in which gain increases are piecewise-constant. A simulation is done for the linearized dynamics of the simple pendulum