This article studies the distributed optimal output agreement problem for multiagent systems described by uncertain nonlinear models. By using the partial information of an objective function, the design aims to steer the outputs of the agents to an agreement on the optimal solution to the objective function. To solve this problem, this article introduces distributed coordinators to calculate the desired outputs, and designs reference-tracking controllers for the agents to follow the desired outputs. To deal with the nonlinear uncertain dynamics, the closed-loop multiagent system is considered as a dynamical network, and Sontag's input-to-state stability is employed to characterize the interconnections. It is shown that output agreement in multiagent nonlinear systems is achievable by means of distributed optimal controllers via a small-gain approach. The proposed design features a three-layer architecture, and the reference-tracking controllers can be implemented as successive nonlinear proportional-integral loops. A numerical example is employed to show the effectiveness of the design.

This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local multipliers and a nonsmooth penalty function. Then we construct a distributed continuous-time algorithm by virtue of a projected primal-dual subgradient dynamics. Based on the nonsmooth analysis and Lyapunov function, we obtain the existence of the solution to the nonsmooth algorithm and its convergence.

Single-cell data integration can provide a comprehensive molecular view of cells. However, how to integrate heterogeneous single-cell multi-omics as well as spatially resolved transcriptomic data remains a major challenge. Here we introduce uniPort, a unified single-cell data integration framework that combines a coupled variational autoencoder (coupled-VAE) and minibatch unbalanced optimal transport (Minibatch-UOT). It leverages both highly variable common and dataset-specific genes for integration to handle the heterogeneity across datasets, and it is scalable to large-scale datasets. uniPort jointly embeds heterogeneous single-cell multi-omics datasets into a shared latent space. It can further construct a reference atlas for gene imputation across datasets. Meanwhile, uniPort provides a flexible label transfer framework to deconvolute heterogeneous spatial transcriptomic data using an optimal transport plan, instead of embedding latent space. We demonstrate the capability of uniPort by applying it to integrate a variety of datasets, including single-cell transcriptomics, chromatin accessibility, and spatially resolved transcriptomic data.

This article proposes a new framework for distributed optimization, called distributed aggregative optimization, which allows local objective functions to be dependent not only on their own decision variables, but also on the sum of functions of decision variables of all the agents. To handle this problem, a distributed algorithm, called distributed aggregative gradient tracking, is proposed and analyzed, where the global objective function is strongly convex, and the communication graph is balanced and strongly connected. It is shown that the algorithm can converge to the optimal variable at a linear rate. A numerical example is provided to corroborate the theoretical result.