Related papers: Nonlinear Dynamical Unbalanced Optimal Transport: …
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
In this article, we consider transport networks with uncertain demands. Network dynamics are given by linear hyperbolic partial differential equations and suitable coupling conditions, while demands are incorporated as solutions to…
We present a new framework for prioritized multi-task motion-force control of fully-actuated robots. This work is established on a careful review and comparison of the state of the art. Some control frameworks are not optimal, that is they…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
In this paper, we propose a novel trajectory optimization algorithm for mobile manipulators under end-effector path, collision avoidance and various kinematic constraints. Our key contribution lies in showing how this highly non-linear and…
This paper deals with a second-order primal-dual dynamical system with Hessian-driven damping and Tikhonov regularization terms in connection with a convex-concave bilinear saddle point problem. We first obtain a fast convergence rate of…
Designing optimal controllers for nonlinear dynamical systems often relies on reinforcement learning and adaptive dynamic programming (ADP) to approximate solutions of the Hamilton Jacobi Bellman (HJB) equation. However, these methods…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
We consider distributed optimization as motivated by machine learning in a multi-agent system: each agent holds local data and the goal is to minimize an aggregate loss function over a common model, via an interplay of local training and…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
We consider the numerical solution of the optimal transport problem between densities that are supported on sets of unequal dimension. Recent work by McCann and Pass reformulates this problem into a non-local Monge-Amp\`ere type equation.…
This paper is devoted to the study of the dynamic optimization of several controlled crowd motion models in the general planar settings, which is an application of a class of optimal control problems involving a general nonconvex sweeping…
Optimal transport (OT) and unbalanced optimal transport (UOT) are central in many machine learning, statistics and engineering applications. 1D OT is easily solved, with complexity O(n log n), but no efficient algorithm was known for 1D…
This paper studies two fundamental problems in power systems: the economic dispatch problem (EDP) and load shedding. For the EDP, an extension of the problem considering the transmission losses is presented. Because the optimization problem…