Distributed Consensus of Linear Multi-Agent Systems with Switching Directed Topologies

This paper addresses the distributed consensus problem for a linear multi-agent system with switching directed communication topologies. By appropriately introducing a linear transformation, the consensus problem is equivalently converted to a stabilization problem for a class of switched linear systems. Some sufficient consensus conditions are then derived by using tools from the matrix theory and stability analysis of switched systems. It is proved that consensus in such a multi-agent system can be ensured if each agent is stabilizable and each possible directed topology contains a directed spanning tree. Finally, a numerical simulation is given for illustration.Comment: The paper will be presented at the 2014 Australian Control Conference (AUCC 2014), Canberra, Australi

Guaranteed Cost Tracking for Uncertain Coupled Multi-agent Systems Using Consensus over a Directed Graph

This paper considers the leader-follower control problem for a linear multi-agent system with directed communication topology and linear nonidentical uncertain coupling subject to integral quadratic constraints (IQCs). A consensus-type control protocol is proposed based on each agent's states relative to its neighbors and leader's state relative to agents which observe the leader. A sufficient condition is obtained by overbounding the cost function. Based on this sufficient condition, a computational algorithm is introduced to minimize the proposed guaranteed bound on tracking performance, which yields a suboptimal bound on the system consensus control and tracking performance. The effectiveness of the proposed method is demonstrated using a simulation example.Comment: Accepted for presentation at the 2013 Australian Control conferenc

Designing Fully Distributed Consensus Protocols for Linear Multi-agent Systems with Directed Graphs

This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this paper, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.Comment: 16 page, 3 figures. To appear in IEEE Transactions on Automatic Contro

Solving specified-time distributed optimization problem via sampled-data-based algorithm

Despite significant advances on distributed continuous-time optimization of multi-agent networks, there is still lack of an efficient algorithm to achieve the goal of distributed optimization at a pre-specified time. Herein, we design a specified-time distributed optimization algorithm for connected agents with directed topologies to collectively minimize the sum of individual objective functions subject to an equality constraint. With the designed algorithm, the settling time of distributed optimization can be exactly predefined. The specified selection of such a settling time is independent of not only the initial conditions of agents, but also the algorithm parameters and the communication topologies. Furthermore, the proposed algorithm can realize specified-time optimization by exchanging information among neighbours only at discrete sampling instants and thus reduces the communication burden. In addition, the equality constraint is always satisfied during the whole process, which makes the proposed algorithm applicable to online solving distributed optimization problems such as economic dispatch. For the special case of undirected communication topologies, a reduced-order algorithm is also designed. Finally, the effectiveness of the theoretical analysis is justified by numerical simulations

Finite-Time Convergent Algorithms for Time-Varying Distributed Optimization

This paper focuses on finite-time (FT) convergent distributed algorithms for solving time-varying distributed optimization (TVDO). The objective is to minimize the sum of local time-varying cost functions subject to the possible time-varying constraints by the coordination of multiple agents in finite time. We first provide a unified approach for designing finite/fixed-time convergent algorithms to solve centralized time-varying optimization, where an auxiliary dynamics is introduced to achieve prescribed performance. Then, two classes of TVDO are investigated included unconstrained distributed consensus optimization and distributed optimal resource allocation problems (DORAP) with both time-varying cost functions and coupled equation constraints. For the previous one, based on nonsmooth analysis, a continuous-time distributed discontinuous dynamics with FT convergence is proposed based on an extended zero-gradient-sum method with a local auxiliary subsystem. Different from the existing methods, the proposed algorithm does not require the initial state of each agent to be the optimizer of the local cost function. Moreover, the provided algorithm has a simpler structure without estimating the global information and can be used for TVDO with nonidentical Hessians. Then, an FT convergent distributed dynamics is further obtained for time-varying DORAP by dual transformation. Particularly, the inverse of Hessians is not required from a dual perspective, which reduces the computation complexity significantly. Finally, two numerical examples are conducted to verify the proposed algorithms

A Novel Dynamic Event-triggered Mechanism for Dynamic Average Consensus

This paper studies a challenging issue introduced in a recent survey, namely designing a distributed event-based scheme to solve the dynamic average consensus (DAC) problem. First, a robust adaptive distributed event-based DAC algorithm is designed without imposing specific initialization criteria to perform estimation task under intermittent communication. Second, a novel adaptive distributed dynamic event-triggered mechanism is proposed to determine the triggering time when neighboring agents broadcast information to each other. Compared to the existing event-triggered mechanisms, the novelty of the proposed dynamic event-triggered mechanism lies in that it guarantees the existence of a positive and uniform minimum inter-event interval without sacrificing any accuracy of the estimation, which is much more practical than only ensuring the exclusion of the Zeno behavior or the boundedness of the estimation error. Third, a composite adaptive law is developed to update the adaptive gain employed in the distributed event-based DAC algorithm and dynamic event-triggered mechanism. Using the composite adaptive update law, the distributed event-based solution proposed in our work is implemented without requiring any global information. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.Comment: 9 pages, 8 figure

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs). First, a general class of nonlinear functions in designing FxTGFs is provided. A unified method for designing first-order FxTGFs is shown under PolyakL jasiewicz inequality assumption, a weaker condition than strong convexity. When there exist both bounded and vanishing disturbances in the gradient flow, a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented. Under the strict convexity assumption, Newton-based FxTGFs is given and further extended to solve time-varying optimization. Besides, the proposed FxTGFs are further used for solving equation-constrained optimization. Moreover, an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization. To show the effectiveness of various FxTGFs, the static regret analysis for several typical FxTGFs are also provided in detail. Finally, the proposed FxTGFs are applied to solve two network problems, i.e., the network consensus problem and solving a system linear equations, respectively, from the respective of optimization. Particularly, by choosing component-wisely sign-preserving functions, these problems can be solved in a distributed way, which extends the existing results. The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications

A Framework on Fully Distributed State Estimation and Cooperative Stabilization of LTI Plants

How to realize high-level autonomy of individuals is one of key technical issues to promote swarm intelligence of multi-agent (node) systems with collective tasks, while the fully distributed design is a potential way to achieve this goal. This paper works on the fully distributed state estimation and cooperative stabilization problem of linear time-invariant (LTI) plants with multiple nodes communicating over general directed graphs, and is aimed to provide a fully distributed framework for each node to perform cooperative stabilization tasks. First, by incorporating a novel adaptive law, a consensus-based estimator is designed for each node to obtain the plant state based on its local measurement and local interaction with neighbors, without using any global information of the communication topology. Subsequently, a local controller is developed for each node to stabilize the plant collaboratively with performance guaranteed under mild conditions. Specifically, the proposed method only requires that the communication graph be strongly connected, and the plant be collectively controllable and observable. Further, the proposed method can be applied to pure fully distributed state estimation scenarios and modified for noise-bounded LTI plants. Finally, two numerical examples are provided to show the effectiveness of the theoretical results

Cooperative Control of Multi-Channel Linear Systems with Self-Organizing Private Agents

Cooperative behavior design for multi-agent systems with collective tasks is a critical issue to promote swarm intelligence. This paper investigates cooperative control for a multi-channel system, where each channel is managed by an agent that can communicate with neighbors in a network. Each agent is expected to self-organize a controller based only on local information and local interaction to stabilize the multi-channel system collaboratively. A novel cooperative control strategy is designed for each agent by leveraging a decomposing technique and a fusion approach. Then, a privacy-preserving mechanism is incorporated into this strategy to shield all private information from eavesdropping. Moreover, a fully distributed designing method for the strategy parameters is developed. As a result, agents can self-design and self-perform their controllers with private information preserved. It is proved that the multi-channel system stability can be ensured by the proposed strategy with finite fusion steps during each control interval. In addition, the cost of introducing the privacy-preserving mechanism and the effect of adding more channels on the system performance are quantitatively analyzed, which benefits mechanism design and channel placement. Finally, several comparative simulation examples are provided to demonstrate the effectiveness of the theoretical results