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Distributed Cooperative Adaptive Identification and Control for a Group of Continuous-Time Systems With a Cooperative PE Condition via Consensus

机译:具有共识性PE条件的一组连续时间系统的分布式协作自适应辨识与控制

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摘要

In this paper, we first address the uniformly exponential stability (UES) problem of a group of distributed cooperative adaptive systems in a general framework. Inspired by consensus theory, distributed cooperative adaptive laws are proposed to estimate the unknown parameters of these systems. It is shown that not only is the entire closed-loop system stable, but also both the identification/tracking error and the parameter estimation error converge to zero uniformly exponentially under a cooperative persistent excitation (PE) condition of a regressor matrix in each system which is weaker than the traditionally defined PE condition. The effects of network topology on UES of the closed-loop system are also explored. If the topology is time-invariant, it needs to be undirected and connected. However, when the topology is time-varying, it is just required that the integration of the topology over an interval with fixed length is undirected and connected. The established results are then employed to identify and control several classes of linearly parameterized systems. Simulation examples are also provided to demonstrate the effectiveness and applications of the proposed distributed cooperative adaptive laws.
机译:在本文中,我们首先在一个通用框架中解决一组分布式协作自适应系统的均匀指数稳定性(UES)问题。受共识理论的启发,提出了分布式协作自适应定律来估计这些系统的未知参数。结果表明,不仅闭环系统稳定,而且在每个系统的回归矩阵的协同持续激励(PE)条件下,识别/跟踪误差和参数估计误差均均匀地收敛于零。比传统定义的PE条件要弱。还探讨了网络拓扑对闭环系统UES的影响。如果拓扑是时不变的,则它必须是无方向的并已连接。但是,当拓扑结构随时间变化时,仅要求拓扑结构在固定长度的时间间隔内不定向并连接。然后将建立的结果用于识别和控制几类线性参数化系统。还提供了仿真示例,以证明所提出的分布式协作自适应律的有效性和应用。

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