Related papers: Nonlinear Contraction Tools for Constrained Optimi…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
We show that many machine learning goals, such as improved fairness metrics, can be expressed as constraints on the model's predictions, which we call rate constraints. We study the problem of training non-convex models subject to these…
This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
Nonlinear constrained optimization problems are encountered in many scientific fields. To utilize the huge calculation power of current computers, many mathematic models are also rebuilt as optimization problems. Most of them have…
The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization (FL) -- a well-established…
The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from…
We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…
Constrained optimization problems exist in many domains of science, such as thermodynamics, mechanics, economics, etc. These problems are classically solved with the help of the Lagrange multipliers and the Lagrangian function. However, the…
In this article, we provide a novel and broadly-applicable contraction-theoretic approach to continuous-time time-varying convex optimization. For any parameter-dependent contracting dynamics, we show that the tracking error is…
We employ constraints to control the parameter space of deep neural networks throughout training. The use of customized, appropriately designed constraints can reduce the vanishing/exploding gradients problem, improve smoothness of…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
Contraction-Based Nonlinear Model Predictive Control (NMPC) formulations are attractive because of the generally short prediction horizons they require and the needless use of terminal set computation that are commonly necessary to…