Distributed Optimization of Multiagent Systems With Preserved Network Connectivity

Decentralized Robust Portfolio Optimization Based on Cooperative-Competitive Multiagent Systems

This article addresses decentralized robust portfolio optimization based on multiagent systems. Decentralized robust portfolio optimization is first formulated as two distributed minimax optimization problems in a Markowitz return-risk framework. Cooperative-competitive multiagent systems are developed and applied for solving the formulated problems. The multiagent systems are shown to be able to reach consensuses in the expected stock prices and convergence in investment allocations through both intergroup and intragroup interactions. Experimental results of the multiagent systems with stock data from four major markets are elaborated to substantiate the efficacy of multiagent systems for decentralized robust portfolio optimization.

Distributed Time-Varying Optimization of Second-Order Multiagent Systems Under Limited Interaction Ranges

This article investigates the distributed time-varying optimization problem for second-order multiagent systems (MASs) under limited interaction ranges. The goal is to seek the minimum of the sum of local time-varying cost functions (CFs), where each CF is only available to the corresponding agent. Limited communication range refers to the scenario where the agents have limited sensing and communication capabilities, that is, a pair of agents can communicate with each other only if their distance is within a certain range. To handle such a problem, a new continuous connectivity-preserving mechanism is presented to preserve the connectivity of the considered network. Then, two distributed optimization algorithms are presented to solve the optimization problem with time-varying CFs and time-invariant CFs, respectively. Theoretical analysis and two numerical examples are provided to verify the effectiveness of the methods.

Adaptive Finite-Time Tracking Control of Nonholonomic Multirobot Formation Systems With Limited Field-of-View Sensors

This article studies the vision-based tracking control problem for a nonholonomic multirobot formation system with uncertain dynamic models and visibility constraints. A fixed onboard vision sensor that provides the relative distance and bearing angle is subject to limited range and angle of view due to limited sensing capability. The constraint resulting from collision avoidance is also taken into account for safe operations of the formation system. Furthermore, the preselected specifications on transient and steady-state performance are provided by considering the time-varying and asymmetric constraint requirements on formation tracking errors for each robot. To address the constraint problems, we incorporate a novel barrier Lyapunov function into controller design and analysis. Based on the recursive adaptive backstepping procedure and neural-network approximation, we develop a vision-based formation tracking control protocol such that formation tracking errors can converge into a small neighborhood of the origin in finite time while meeting the requirements of visibility and performance constraints. The proposed protocol is decentralized in the sense that the control action on each robot only depends on the local relative information, without the need for explicit network communication. Moreover, the control protocol could extend to an unconstrained multirobot system. Both simulation and experimental results show the effectiveness of the control protocol.

Privacy Masking Stochastic Subgradient-Push Algorithm for Distributed Online Optimization

This article investigates the problem of distributed online optimization for a group of units communicating on time-varying unbalanced directed networks. The main target of the set of units is to cooperatively minimize the sum of all locally known convex cost functions (global cost function) while pursuing the privacy of their local cost functions being well masked. To address such optimization problems in a collaborative and distributed fashion, a differentially private-distributed stochastic subgradient-push algorithm, called DP-DSSP, is proposed, which ensures that units interact with in-neighbors and collectively optimize the global cost function. Unlike most of the existing distributed algorithms which do not consider privacy issues, DP-DSSP via differential privacy strategy successfully masks the privacy of participating units, which is more practical in applications involving sensitive messages, such as military affairs or medical treatment. An important feature of DP-DSSP is tackling distributed online optimization problems under the circumstance of time-varying unbalanced directed networks. Theoretical analysis indicates that DP-DSSP can effectively mask differential privacy as well as can achieve sublinear regrets. A compromise between the privacy levels and the accuracy of DP-DSSP is also revealed. Furthermore, DP-DSSP is capable of handling arbitrarily large but uniformly bounded delays in the communication links. Finally, simulation experiments confirm the practicability of DP-DSSP and the findings in this article.