Controllable set based saturation management using backstepping control

Physical systems are limited in how far or how fast they may move, while control actuators have a limited amount of effort they may put forth. The effects of these constraints must be considered when designing the controller for these systems since violation of these bounds could be harmful. Exactly how they are to be considered is a difficult issue to resolve. One approach is to define a priori a set of states at which the system may safely operate. That is, as long as the states are on or within the boundary of this set, they may be safely directed to the origin. This work uses the idea of ellipsoidal controllable sets to define this safe operating region of the state space. It combines this set with a controller designed via a modified backstepping technique to produce a control law that prevents the states from violating the constraints