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In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…
Motivated by perception-based control problems in autonomous systems, this paper addresses the problem of developing feedback controllers to regulate the inputs and the states of a dynamical system to optimal solutions of an optimization…
The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs…
The dual challenges of prohibitive communication overhead and the impracticality of gradient computation due to data privacy or black-box constraints in distributed systems motivate this work on communication-constrained gradient-free…
In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…
We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…
We propose a distributed accelerated primal-dual method with backtracking (D-APDB) for cooperative multi-agent constrained consensus optimization problems over an undirected network of agents, where only those agents connected by an edge…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
A class of distributed optimization problem with a globally coupled equality constraint and local constrained sets is studied in this paper. For its special case where local constrained sets are absent, an augmented primal-dual gradient…
An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…
This paper considers the problem of controlling inverter-interfaced distributed energy resources (DERs) in a distribution grid to solve an AC optimal power flow (OPF) problem in real time. The AC OPF includes voltage constraints, and seeks…
Aggregative cooperative optimization problems arise in distributed decision-making settings where each agent's objective depends on its own decision as well as on an aggregate variable capturing global system behavior. Motivated by…
We address an optimal control problem for linear stochastic systems with unknown noise distributions and joint chance constraints using conformal prediction. Our approach involves designing a feedback controller to maintain an error system…
This paper investigates the data-driven predictive control problems for a class of continuous-time industrial processes with completely unknown dynamics. The proposed approach employs the data-driven technique to get the system matrices…
This paper investigates how to accelerate the convergence of distributed optimization algorithms on nonconvex problems with zeroth-order information available only. We propose a zeroth-order (ZO) distributed primal-dual stochastic…
Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…
This paper presents a concise overview of sensitivity-based methods for solving large-scale optimization problems in distributed fashion. The approach relies on sensitivities and primal decomposition to achieve coordination between the…
This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…
Systems involving Partial Differential Equations (PDEs) have recently become more popular among the machine learning community. However prior methods usually treat infinite dimensional problems in finite dimensions with Reduced Order…
We study the sequential decision making problem of maximizing the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon…