Distributed Adaptive Convex Optimization on Directed Graphs via Continuous-Time Algorithms

Abstract

Abstract-This note considers the distributed optimization problem on directed graphs with nonconvex local objective functions and the unknown network connectivity. A new adaptive algorithm is proposed to minimize a differentiable global objective function. By introducing dynamic coupling gains and updating the coupling gains using relative information of system states, the nonconvexity of local objective functions, unknown network connectivity and the uncertain dynamics caused by locally Lipschitz gradients are tackled concurrently. Consequently, the global asymptotic convergence is established when the global objective function is strongly convex and the gradients of local objective functions are only locally Lipschitz. When the communication graph is strongly connected and weight-balanced, the algorithm is independent of any global information. Then, the algorithm is naturally extended to unbalanced directed graphs by using the left eigenvector of the Laplacian matrix associated with the zero eigenvalue. Several numerical simulations are presented to verify the results.

Adaptive consensus control for stochastic nonlinear multiagent systems with full state constraints

“…Theorem 1. Consider the nonstrict-feedback stochastic nonlinear MASs (2) with Assumptions 1-4, if the the distributed controllers are chosen as (12), (16), and (19), RBF NNS parameter update laws are chosen as (13), (17) and (20), for bounded initial conditions, we have the following results.…”

“…[5][6][7] Based on fixed or switching topologies, preliminary results for the consensus problem were presented in previous works. [8][9][10][11][12] Among them, the leaderless problem was discussed by Xi et al 9 and leader-following problem was studied by Liu and Yang, 8 Olfati-saber et al, 10 and Liang et al 12 To address the consensus control problem, some discussions have been reported on this issue with the combination of finite-time synchronization, 13,14 event-triggered control, [15][16][17][18] adaptive optimal control, 19,20 and adaptive fault-tolerant control. [21][22][23] However, the aforementioned consensus methods were employed under the assumption that there are no stochastic disturbance and time delays in the controlled system.…”

Distributed Continuous-Time Optimization With Scalable Adaptive Event-Based Mechanisms

“…The DOP for multiagent system with high-order linear model is analyzed in [18]. The adaptive algorithms in [19] successfully solve DOP with This paper intends to solve the continuous-time DOP by proposing a fully distributed consensus-based algorithm with event-triggered communication mechanisms. Since only sampled local information between neighboring agents is available, the adaptive algorithm with continuous communications in [19] is not applicable.…”

“…The adaptive algorithms in [19] successfully solve DOP with This paper intends to solve the continuous-time DOP by proposing a fully distributed consensus-based algorithm with event-triggered communication mechanisms. Since only sampled local information between neighboring agents is available, the adaptive algorithm with continuous communications in [19] is not applicable. The design of adaptive DOP algorithms with event-triggered mechanisms faces new challenges, such as the nonlinearity of local gradient, the coupling among the real-time states, sampled states at the communication moment, and the internal states.…”

Distributed Adaptive Optimization for Generalized Linear Multiagent Systems

“…To face this challenge, some well-performing adaptive algorithms have been proposed, where the adaptive gain updating laws rely on local information of the agents. For example, in [16,17], the adaptive algorithms of the finite time convergence have been established upon integrator multiagent systems. In [18], the adaptive algorithms have been proposed upon general linear multiagent systems from the edge-based and node-based design.…”