This article addresses the continuous-time distributed optimization of a strictly convex summation-separable cost function with possibly nonconvex local functions over strongly connected digraphs. Distributed optimization methods in the literature require convexity of local functions, or balanced weights, or vanishing step sizes, or algebraic information (eigenvalues or eigenvectors) of the Laplacian matrix. The solution proposed here covers both weight-balanced and unbalanced digraphs in a unified way, without any of the aforementioned requirements.

This paper addresses distributed and robust leaderless consensus control for a class of uncertain multiagent systems with matched unknown nonlinearities and disturbances. The problem is challenging due to the lack of a leader (reference signal), the large uncertainties in agent dynamics, and the asymmetric communications among the agents. A novel neural network embedded model reference adaptive consensus (NN-MRACon) framework is proposed, which bridges NN and MRACon by means of nonsmooth control. Asymptotic consensus is proved based on robust analysis and input-to-state stability theory. Numerical examples on networks of second-order integrators and two-mass-spring systems are included to validate the effectiveness of NN-MRACon.

In this article, the time-varying formation and time-varying formation tracking problems are solved for linear multiagent systems over digraphs without the knowledge of the eigenvalues of the Laplacian matrix associated with the digraph. The solution to these problems relies on an approach that generalizes the directed spanning tree (DST) adaptive method, which was originally limited to consensus problems. Necessary and sufficient conditions for the existence of solutions to the formation problems are derived. Asymptotic convergence of the formation errors is proved via graph theory and Lyapunov analysis.