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We propose a hybrid control algorithm that guarantees fast convergence and uniform global asymptotic stability of the unique minimizer of a continuously differentiable, convex objective function. The algorithm, developed using hybrid system…
We study the instability properties of Nesterov's ODE in non-conservative settings, where the driving term is not necessarily the gradient of a potential function. While convergence properties under Nesterov's ODE are well-characterized for…
High order momentum-based parameter update algorithms have seen widespread applications in training machine learning models. Recently, connections with variational approaches have led to the derivation of new learning algorithms with…
We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed…
We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…
We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…
In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
We study the algorithmic stability of Nesterov's accelerated gradient method. For convex quadratic objectives, Chen et al. (2018) proved that the uniform stability of the method grows quadratically with the number of optimization steps, and…
In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations…
In convex optimization, continuous-time counterparts have been a fruitful tool for analyzing momentum algorithms. Fewer such examples are available when the function to minimize is non-convex. In several cases, discrepancies arise between…
This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as…
Algorithms having uniform convergence with respect to their initial condition (i.e., with fixed-time stability) are receiving increasing attention for solving control and observer design problems under time constraints. However, we still…
There is a growing interest in using robust control theory to analyze and design optimization and machine learning algorithms. This paper studies a class of nonconvex optimization problems whose cost functions satisfy the so-called…
This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by…
In this paper, a proof of asymptotic stability for the combined system-optimizer dynamics associated with a class of real-time methods for equality constrained nonlinear model predictive control is presented. General Q-linearly convergent…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
This paper deals with the development and analysis of novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do not maintain…
This work addresses the instability in asynchronous data parallel optimization. It does so by introducing a novel distributed optimizer which is able to efficiently optimize a centralized model under communication constraints. The optimizer…