未知不匹配互联系统的非对称输入约束分散控制器设计

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

  • 摘要: 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. 然后,基于自适应评判框架,将分散最优控制器设计问题转化为一系列子系统非对称约束下局部最优控制器设计问题. 利用Lyapunov稳定性定理,证明了不对称输入约束控制器能够迅速地镇定大规模分散系统. 其中,引入状态观测器估计大规模非线性互联子系统状态并保证了观测误差满足一致最终有界. 另外,利用评判神经网络近似改进后的代价函数,以近似求解Hamilton–Jacobi–Bellman方程,获得满足非对称输入约束的最优分散控制策略. 基于评判网络权值更新规则,通过选择合适的Lyapunov函数保证了权值近似误差满足一致最终有界. 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, we explore the decentralized control problem through the lens of adaptive dynamic programming for continuous-time nonlinear systems, particularly those with unknown mismatched interconnections and asymmetric input constraints. First, the unknown interconnection term is addressed by approximating it with a radial basis function neural network. This approximation relies on the local states of isolated subsystems and the reference states of coupled subsystems, thus sidestepping the common assumption that interconnections are matched and upper bounded. Following this, the challenge of designing a decentralized optimal controller design is reframed as a series of local optimal controller design problems. This reframing is facilitated by adaptive critic networks and considers the asymmetric constraints of subsystems. The application of the Lyapunov stability theorem demonstrates that controllers, even with asymmetric input constraints, can rapidly stabilize the large-scale system. More importantly, we conclude that the control laws designed here serve as the decentralized control strategies for large-scale nonlinear systems. Our methodology employs the radial basis function neural network and the critic neural network. The former approximates interconnection terms, while the latter deals with cost functions, enabling to derive optimal decentralized control strategies under asymmetric constraints. The uniform ultimate boundedness of observation error and weight approximation error are assured by using the Lyapunov theorem. This is further supported by the introduction of a state observer to estimate the state of the interconnected subsystems and the use of the critic neural network to approximate an improved cost function. This approach allows for an approximate solution to the Hamilton–Jacobi–Bellman equation, resulting in optimal decentralized control strategies satisfying the asymmetric input constraints. At the same time, based on the weight updating rules of the critic neural network, we can guarantee that weight approximation errors are uniformly ultimately bounded by selecting the suitable Lyapunov function. The selection of neural networks in this study is driven by considerations of convergence speed and computational burden, leading to the choice of two specific types of networks. The effectiveness of the developed control method is then rigorously tested through simulation and comparative experiments implemented in a MATLAB environment. Comparative experiments underscore the advancements made by the algorithm developed in this paper, especially under asymmetric control constraints. Contrasting our approach with unimproved cost functions and strategies lacking control constraints, we showcase significant improvements. The simulation results are shown in Figs. 19, which fully verify the effectiveness of our established scheme. We can derive that the developed control method significantly enhances stabilization speed and performance.

     

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