Distributed Resource Allocation Algorithm for Second-order Multi-agent Systems in Continuous-time
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摘要:
针对二阶多智能体系统中的分布式资源分配问题, 本文设计两种连续时间算法. 基于KKT (Karush−Kuhn−Tucker, 卡罗需−库恩−塔克)优化条件, 第一种控制算法利用节点局部不等式及其梯度信息来约束节点状态. 与上述梯度方法不同, 第二种控制算法包括一致性梯度下降法和固定时间收敛映射算子, 其中固定时间收敛映射算子确保算法的节点状态在固定时间收敛到局部约束集, 一致性梯度下降法目的是确保节点迭代到资源分配问题最优解. 两种控制算法都对状态无初始值约束, 且控制参数都是常数. 利用凸优化理论和固定时间李雅普诺夫方法, 分别分析了上述控制策略在有向平衡网络条件下的渐近和指数收敛性. 最后通过数值仿真验证了所设计算法在一维和高维资源分配问题的有效性.
Abstract:For the distributed resource allocation problem in second-order multi-agent systems (MASs), this paper proposes two continuous-time distributed algorithms. Based on the KKT (Karush-Kuhn-Tucker) optimal condition, the constrained state of each agent is ensured by applying the information of the local inequality constraints and its gradient in the first proposed control algorithm. Different from the previous gradient method, the second proposed algorithm consists of two parts: a consensus-based gradient descent algorithm and a fixed-time convergent projection operator, in which the projection operator plays a key role in ensuring local inequality constraints and the optimal solution of the distributed resource allocation problem is guaranteed by the gradient descent iteration. The above two proposed algorithms with constant control parameters is initialization-free. Based on convex optimization theory and fixed-time Lyapunov analysis, the asymptotic and exponential convergence results are given for weight-balanced directed network, respectively. Finally, the effectiveness of our proposed algorithm in one-dimensional and high-dimensional resource allocation problems is validated by several simulations.
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图 1 案例1中算法(8)的各发电机曲线图
Fig. 1 The trajectories of each generator by algorithm (8) in case 1
图 2 案例1中算法(9)的各发电机曲线图
Fig. 2 The trajectories of each generator by algorithm (9) in case 1
图 3 基于案例1数据的算法性能对比
Fig. 3 The comparison between the existence algorithms and ours based on case 1
图 4 案例2中算法 (8)的各节点仿真结果轨迹
Fig. 4 The trajectories of each agent by algorithm (8) in case 2
图 5 案例2中算法 (9)各节点仿真结果轨迹
Fig. 5 The trajectories of each agent by algorithm (9) in case 2
图 6 基于案例2数据的算法性能对比
Fig. 6 The comparison between the existence algorithms and ours based on case 2
图 8 案例3中算法 (8)的各节点仿真结果轨迹
Fig. 8 The trajectories of each agent by algorithm (8) in case 3
图 9 案例3中算法 (9)各节点仿真结果轨迹
Fig. 9 The trajectories of each agent by algorithm (9) in case 3
图 10 案例3中算法 (8)和 (9)的收敛速度比较
Fig. 10 The convergence rate comparison between algorithms (8) and (9) in case 3
表 1 案例1各节点参数
Table 1 System parameters in case 1
Agent $a_{i1}$ $a_{i2}$ $a_{i3}$ 功率约束 $d_i$ $x_i(0)$ 1 2 3 0.5 $[20,40]$ 45 40 2 1 4 1.5 $[25,35]$ 40 24 3 0.5 5 3 $[35,50]$ $25$ 35 4 1.5 2 1 $[25,45]$ 35 45 5 1 3.5 2.5 $[30,47]$ 30 28 6 1.5 4.5 2 $[28,42]$ 40 50 
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