An H∞ control based receding horizon control scheme for linear systems subject to input saturation

This paper proposes an H_∞ control based receding horizon control design scheme for discrete-time linear systems subject input saturation and external ℒ₂ disturbances. Conditions are established under which the state trajectories of the closed-loop starting from an ellipsoid remain within another larger ellipsoid and the restricted ℒ₂ gain from the disturbance to the controlled output over a class of ℒ₂ disturbances with a given bound on their energies is no greater than a given number. These conditions allow the saturation to occur and reveal a clear trade-off between the sizes of the ellipsoids and the level of the restricted ℒ₂ gain, which motivates the adoption of the receding horizon control design approach. At each time instant, the control design is formulated as an LMI optimization problem. Both state feedback and output feedback are considered.