  This paper considers the problem of regulating a dynamical system to
equilibria that are defined as solutions of an input- and state-constrained
optimization problem. To solve this regulation task, we design a state feedback
controller based on a continuous approximation of the projected gradient flow.
We first show that the equilibria of the interconnection between the plant and
the proposed controller correspond to critical points of the constrained
optimization problem. We then derive sufficient conditions to ensure that, for
the closed-loop system, isolated locally optimal solutions of the optimization
problem are locally exponentially stable and show that input constraints are
satisfied at all times by identifying an appropriate forward-invariant set.
