OPTIMALITY, STABILITY, AND CONVERGENCE IN NONLINEAR CONTROL

Sufficient optimality conditions for infinite-dimensional optimization problems are derived in a setting that is applicable to optimal contr ol with endpoint constraints and with equality and inequality constrai nts on the controls. These conditions involve controllability of the s ystem dynamics, independence of the gradients of active control constr aints, and a relatively weak coercivity assumption for the integral co st functional. Under these hypotheses, we show that the solution to an optimal control problem is Lipschitz stable relative to problem pertu rbations. As an application of this stability result, we establish con vergence results for the sequential quadratic programming algorithm an d for penalty and multiplier approximations applied to optimal control problems.