State and input constraint satisfaction for nonlinear systems

Nonlinear systems with both state and input constraints are difficult to control. The complexity of such system is the problem of simultaneous satisfying the nominal control object and each of the individual constraints. In this report, a method is proposed to design state-feedback control laws that guarantee state-constraint satisfaction while the control input remains bounded. The main idea is to use a recursive procedure to construct a constraint feasible set that is positive invariant with bounded control. Constraint satisfaction is then achieved bymodifying the control input on the boundaries such that the solution of the system remains inside the feasible set for all time. The proposed method will be illustrated on two simple design examples at the end of this report