Consensus Synthesis of Robust Cooperative Control for Homogeneous Leader-Follower Multi-Agent Systems Subject to Parametric Uncertainty

This paper presents a design of robust consensus for homogeneous leader-follower multiagent systems (MAS). Each agent of MAS is described by a linear time-invariant dynamic model subject to parametric uncertainty. The agents are interconnected through a static interconnection matrix over an undirected graph to cooperate and share information with their neighbours. The consensus design of MAS can be transformed to stability analysis by using decomposition technique. We apply Lyapunov theorem to derive the sufficient condition to ensure the consensus of all independent subsystems. In addition, we design a robust distributed state feedback gain based on linear quadratic regulator (LQR) setting. Controller gain is computed via solving a linear matrix inequality. As a result, we provide a robust design procedure of a cooperative LQR control to achieve consensus objective and maximize the admissible bound of the uncertainty. Finally, we give numerical examples to illustrate the effectiveness of the proposed consensus design. The results show that the response for MAS in presence of uncertainty using robust consensus design follows the response of the leader and is better than that of the existingnominal consensus design

Distributed linear quadratic tracking control for leader-follower multi-agent systems:A suboptimality approach

In this paper, we extend the results from Jiao et al. (2019) on distributed linear quadratic control for leaderless multi-agent systems to the case of distributed linear quadratic tracking control for leader-follower multi-agent systems. Given one autonomous leader and a number of homogeneous followers, we introduce an associated global quadratic cost functional. We assume that the leader shares its state information with at least one of the followers and the communication between the followers is represented by a connected simple undirected graph. Our objective is to design distributed control laws such that the controlled network reaches tracking consensus and, moreover, the associated cost is smaller than a given tolerance for all initial states bounded in norm by a given radius. We establish a centralized design method for computing such suboptimal control laws, involving the solution of a single Riccati inequality of dimension equal to the dimension of the local agent dynamics, and the smallest and the largest eigenvalue of a given positive definite matrix involving the underlying graph. The proposed design method is illustrated by a simulation example.Comment: 7 pages, 3 figures, submitted to a conference. arXiv admin note: text overlap with arXiv:1803.0268

Distributed Control with Low-Rank Coordination

A common approach to distributed control design is to impose sparsity constraints on the controller structure. Such constraints, however, may greatly complicate the control design procedure. This paper puts forward an alternative structure, which is not sparse yet might nevertheless be well suited for distributed control purposes. The structure appears as the optimal solution to a class of coordination problems arising in multi-agent applications. The controller comprises a diagonal (decentralized) part, complemented by a rank-one coordination term. Although this term relies on information about all subsystems, its implementation only requires a simple averaging operation

A Suboptimality Approach to Distributed Linear Quadratic Optimal Control

This paper is concerned with the distributed linear quadratic optimal control problem. In particular, we consider a suboptimal version of the distributed optimal control problem for undirected multi-agent networks. Given a multi-agent system with identical agent dynamics and an associated global quadratic cost functional, our objective is to design suboptimal distributed control laws that guarantee the controlled network to reach consensus and the associated cost to be smaller than an a priori given upper bound. We first analyze the suboptimality for a given linear system and then apply the results to linear multiagent systems. Two design methods are then provided to compute such suboptimal distributed controllers, involving the solution of a single Riccati inequality of dimension equal to the dimension of the agent dynamics, and the smallest nonzero and the largest eigenvalue of the graph Laplacian. Furthermore, we relax the requirement of exact knowledge of the smallest nonzero and largest eigenvalue of the graph Laplacian by using only lower and upper bounds on these eigenvalues. Finally, a simulation example is provided to illustrate our design method.Comment: 11 pages, 2 figure

Distributed Linear Quadratic Optimal Control: Compute Locally and Act Globally

In this paper we consider the distributed linear quadratic control problem for networks of agents with single integrator dynamics. We first establish a general formulation of the distributed LQ problem and show that the optimal control gain depends on global information on the network. Thus, the optimal protocol can only be computed in a centralized fashion. In order to overcome this drawback, we propose the design of protocols that are computed in a decentralized way. We will write the global cost functional as a sum of local cost functionals, each associated with one of the agents. In order to achieve 'good' performance of the controlled network, each agent then computes its own local gain, using sampled information of its neighboring agents. This decentralized computation will only lead to suboptimal global network behavior. However, we will show that the resulting network will reach consensus. A simulation example is provided to illustrate the performance of the proposed protocol.Comment: 7 pages, 2 figure