Assisting saturated control for a linear system with saturating actuators

For a linear system with saturating actuators, a new control scheme, AS (Assisting Saturated) control is proposed. The AS control has a modified form of an ARE (Algebraic Riccati Equation) based saturating control in the case of some control input channels are not saturated. The AS control is given by the least square solution to minimize the exceeding amounts of saturated inputs which are initially obtained by LQR (Linear Quadratic Regulating) optimal control. If the conventional LQR control law is applied to a linear system with saturating actuators, control efforts must be decreased so to remain within the saturation limits. This is obtainable by adjusting input weighting matrix in the cost function. However the AS control gives better performance than the conventional LQR which gives unnecessarily small control efforts. Also, the AS control enlarges the stabilizable region of an unstable system. A simulation example is provided to verify the features of the proposed AS control.