Sensitivity analysis in parametric multiobjective discrete-time control via Fréchet subdifferential calculus of the frontier map

This paper studies the first-order behavior of the frontier map of a vector parametric control problem with nonconvex objective functions, nonlinear state equations and control constraints. By establishing an abstract result on the Fréchet subdifferential of the frontier map of a vector parametric optimization problem, we derive a formula for computing the Fréchet subdifferential of the frontier map to a parametric multiobjective discrete-time control problem. Examples are given to illustrate the obtained results.