An LMI approach to optimal consensus seeking in multi-agent systems

Abstract

Abstract-In this paper an optimal control design strategy to guarantee consensus achievement in a multi-agent network is developed. Minimization of a global cost function for the entire network guarantees a stable consensus with an optimal control effort. In solving the optimization problem it is shown that the solution of the Riccati equation cannot guarantee the consensus achievement. Therefore, the linear matrix inequality (LMI) formulation is used to solve the corresponding optimization problem and simultaneously to address the consensus achievement constraint. Moreover, using the LMI formulation a controller specific structure based on the neighboring sets can be imposed as an additional LMI constraint. Therefore, the only information each controller needs is the one it receives from its associated neighbors in its neighboring set. The global cost function formulation provides more insight into the optimal performance of the entire network and would result in a "global" optimal (or suboptimal) solution. Simulation results are presented to illustrate the performance of the multi-agent team in achieving consensus.

Multi-AUV Control Method Based on Inverse Optimal Control of Integrated Obstacle Avoidance Algorithm

“…It is assumed that the obstacle appears at (14,17,20) and that it does not appear on the trajectory of any AUV. Assume that the collision zone (obstacle radius) is r 1 = 0.5 and the radius of the diagnostic zone is R 1 = 1.…”

“…Assume that the first obstacle appears in the trajectory of AUV 2 (23,24,22), the radius of the obstacle is r 1 = 0.7, and the diagnostic zone is R 1 = 1.5. The second obstacle at (14,17,20) does not exist in the trajectory of any AUV. The final obstacle is assumed to appear in the trajectory of AUV 1 at (7,7,7).…”

“…Furthermore, the average consensus problem was realized by developing an optimal interaction graph [16]. In another study, the consensus problem was expressed as an optimization problem using the linear matrix inequality method [17]. An optimal linear consensus algorithm based on the linear quadratic adjuster has also been proposed [18].…”

Multi-agent consensus algorithm with obstacle avoidance via optimal control approach

“…From the optimization perspective, consensus algorithms have been developed along two lines: 1) fastest convergence time: the algorithms were designed to achieve the fastest convergence time by finding an optimal weighting matrix [5], constructing a proper configuration that maximizes the second smallest eigenvalue of the Laplacian [6], and exploring an optimal interaction graph for the average consensus problem [7]; 2) Optimal control design: the consensus problem was formulated as an optimal control problem and solved using a linear matrix inequality (LMI) approach [8], a LQR-based optimal linear consensus algorithm [9], a distributed subgradient method for multiagent optimization [10], and a locally optimal nonlinear consensus strategy by imposing individual objectives [11].…”

Autonomy and machine intelligence in complex systems: A tutorial

“…Thus it is better to fight adversaries in the networks than guard against them. Most of the cooperative algorithms proposed in the literature either are not optimizing some performance criteria [49] or they optimize global ones and solve the problem offline with complicated Riccati matrix equations [71], [72]. The authors in [13] have evaluated the cost of every agent by considering constant states for the other agents.…”