王鼎, 范文倩, 刘奥. 未知不匹配互联系统的非对称约束分散控制器设计[J]. 工程科学学报. DOI: 10.13374/j.issn2095-9389.2024.02.08.001
引用本文: 王鼎, 范文倩, 刘奥. 未知不匹配互联系统的非对称约束分散控制器设计[J]. 工程科学学报. DOI: 10.13374/j.issn2095-9389.2024.02.08.001
Decentralized controller design with asymmetric input constraints for unknown unmatched interconnected systems[J]. Chinese Journal of Engineering. DOI: 10.13374/j.issn2095-9389.2024.02.08.001
Citation: Decentralized controller design with asymmetric input constraints for unknown unmatched interconnected systems[J]. Chinese Journal of Engineering. DOI: 10.13374/j.issn2095-9389.2024.02.08.001

未知不匹配互联系统的非对称约束分散控制器设计

Decentralized controller design with asymmetric input constraints for unknown unmatched interconnected systems

  • 摘要: 本文基于自适应动态规划算法研究了具有未知不匹配互联和非对称输入约束的连续时间非线性系统分散控制问题。首先,根据孤立子系统的局部状态和耦合子系统的参考状态,采用径向基函数神经网络近似未知互连项,从而消除了互联项满足匹配条件且存在上界的常见假设。基于自适应评判框架,本文将分散系统的稳定问题转化为设计一系列非对称约束条件下的局部最优控制器,同时也证明了非对称控制策略可以镇定大规模系统。然后,通过引入状态观测器以估计互联子系统的状态并保证了观测误差是一致最终有界的。另外, 通过评判神经网络近似最优代价函数,从而近似求解Hamilton–Jacobi–Bellman方程, 以得到满足非对称输入约束的最优分散控制策略。与此同时,基于评判网络权值更新规则,保证了权值近似误差是一致最终有界的。最后,通过仿真实例验证了该算法的有效性,并通过与未改进代价函数的传统方法对比,体现了该方法的先进性。

     

    Abstract: In this paper, the decentralized control problem is investigated based on adaptive dynamic programming for continuous-time nonlinear systems with unknown mismatched interconnections and asymmetric input constraints. First, the unknown interconnection term is approximated by the radial basis function neural network based on the local state of the isolated subsystem and the reference state of the coupled subsystem. As a result, common assumptions are eliminated that interconnections are matched and upper bounded. Then, by using the framework of adaptive critic networks, the stability problem of decentralized systems is transformed into the design of a series of local optimal controllers under asymmetric constraints, and it is also proved that asymmetric control strategies can stabilize large-scale systems. Then, a state observer is introduced to estimate the state of the interconnected subsystems and ensure that the observed errors are uniformly ultimately bounded. In addition, the optimal cost function can be approximated by the critic neural network, and then the Hamilton-Jacobi-Bellman equation can be approximatively solved, so as to obtain the optimal decentralized control strategy satisfying the asymmetric input constraints. At the same time, based on the weight updating rule of the critic neural network, it guarantees that the weight approximation errors are uniformly ultimately bounded. Finally, the effectiveness of the algorithm is verified by a simulation example, and the progressiveness of the developed method is reflected by comparing with the traditional method without improved cost function.

     

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