Pyuyi Chufeng Huang, Zikang Song
Horizon-Uniform Sensitivity and Decay of Terminal Reward Perturbations in Discrete-Time Pontryagin Systems
We study local stationary solutions of finite-horizon discrete-time Pontryagin systems near a steady extremal. Under regular stationarity, hyperbolicity of the reduced state-costate map, and scaled transversality of the endpoint conditions, the linearized boundary-value problem has a horizon-uniform Green estimate. A weighted-norm contraction argument gives existence, uniqueness, uniform Lipschitz estimates, and pointwise quadratic remainders. For graph boundary conditions, terminal reward perturbations have exponentially small effects on the initial control and the stationary objective gradient; the linear-quadratic case yields exponential convergence of Riccati matrices and initial feedback gains.
Optimal controlPontryagin systemsSensitivity analysisExponential dichotomiesDynamic programmingSymplectic methods
