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Publications of Eduardo D. Sontag jointly with Z.P. Jiang
Articles in journal or book chapters
and E. D. Sontag.
Small-disturbance input-to-state stability of perturbed gradient flows: Applications to LQR problem.
Note: Submitted. Preprint in arXiv arxiv.org/abs/2310.02930.
This paper studies the effect of perturbations on the gradient flow of a general constrained nonlinear programming problem, where the perturbation may arise from inaccurate gradient estimation in the setting of data-driven optimization. Under suitable conditions on the objective function, the perturbed gradient flow is shown to be small-disturbance input-to-state stable (ISS), which implies that, in the presence of a small-enough perturbation, the trajectory of the perturbed gradient flow must eventually enter a small neighborhood of the optimum. This work was motivated by the question of robustness of direct methods for the linear quadratic regulator problem, and specifically the analysis of the effect of perturbations caused by gradient estimation or round-off errors in policy optimization. Interestingly, we show small-disturbance ISS for three of the most common optimization algorithms: standard gradient flow, natural gradient flow, and Newton gradient flow.
and Y. Wang.
Input-to-state stability for discrete-time nonlinear systems.
In Proc. 14th IFAC World Congress, Vol E (Beijing),
Keyword(s): input to state stability,
input to state stability,
This paper studies the input-to-state stability (ISS) property for discrete-time nonlinear systems. We show that many standard ISS results may be extended to the discrete-time case. More precisely, we provide a Lyapunov-like sufficient condition for ISS, and we show the equivalence between the ISS property and various other properties, as well as provide a small gain theorem.
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