Stability of solutions for controlled nonlinear systems under perturbation of state constraints

This paper tackles the problem of unbounded nonlinear systems under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring one that lies in the interior of the constraints, and which can be made arbitrarily close to the reference trajectory both in L∞-distance and L2-control cost. This result is an important tool to ference trajectory both in L-distance and L2-control cost. This result is an important tool to prove the convergence of approximation schemes of state constraints based on interior solutions.