【摘要】 研究了一般有向图上采暖、通风和空调系统的能源消耗问题。首先将所考虑的问题表述为一个纳什均衡寻求问题,然后提出了一种基于一致性的分布式纳什均衡寻求算法来解决该问题。为了解决一般有向图所带来的挑战,嵌入了一种分布式估计算法,从而避免了对拉普拉斯矩阵与特征值零相关的左特征向量的显式依赖。然后,在一个常见假设下,证明了所提出的分布式纳什均衡寻求算法的指数收敛性。最后通过数值算例验证了该算法的有效性。更多还原

【Abstract】 The energy consumption problem of heating, ventilation, and air conditioning systems over general directed graphs is investigated. The considered problem is firstly reformulated as a Nash equilibrium seeking problem, and a distributed consensus-based algorithm is then proposed to solve it. To address the challenge arising from general directed graphs, a distributed estimation algorithm is embedded such that the explicit dependence on the left eigenvector associated with the eigenvalue zero of the Laplacian matrix can be avoided. Then, the exponential convergence of the proposed distributed Nash equilibrium seeking algorithm is established under a standing assumption. A numerical example is finally provided to verify the effectiveness of the proposed algorithm.更多还原