Semi-Global Exponential Stability of Augmented Primal-Dual Gradient Dynamics for Constrained Convex Optimization

Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD) to incorporate general convex and nonlinear inequality constraints, and we establish its semi-global exponential stability when the objective function is strongly convex. We also provide an example of a strongly convex quadratic program of which the Aug-PDGD fails to achieve global exponential stability. Numerical simulation also suggests that the exponential convergence rate could depend on the initial distance to the KKT point

Stability and Regret bounds on Distributed Truncated Predictive Control for Networked Dynamical Systems

This work is primarily concerned about the distributed control of networked linear timeinvariant (LTI) systems. In particular, we propose a truncated predictive control algorithm based on $\kappa$-hop neighbourhoods of the agents of the networked system. We establish stability and regret bounds for the proposed algorithm, which shows that the regret decays exponentially when the temporal prediction horizon $k$ and the spatial radius $\kappa$ increases.Comment: 25 pages, 2 figures, submitted to ACC 202

Finite-Time Analysis of Asynchronous Stochastic Approximation and Q-Learning

We consider a general asynchronous Stochastic Approximation (SA) scheme featuring a weighted infinity-norm contractive operator, and prove a bound on its finite-time convergence rate on a single trajectory. Additionally, we specialize the result to asynchronou