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未知不匹配互聯系統的非對稱輸入約束分散控制器設計

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

  • 摘要: 基于自適應動態規劃算法研究了具有未知不匹配互聯和非對稱輸入約束的連續時間非線性系統分散控制問題. 首先,根據孤立子系統的局部狀態和耦合子系統的參考狀態,采用徑向基函數神經網絡近似未知互連項,從而消除了互聯項滿足匹配條件且存在上界的常見假設. 然后,基于自適應評判框架,將分散最優控制器設計問題轉化為一系列子系統非對稱約束下局部最優控制器設計問題. 利用Lyapunov穩定性定理,證明了不對稱輸入約束控制器能夠迅速地鎮定大規模分散系統. 其中,引入狀態觀測器估計大規模非線性互聯子系統狀態并保證了觀測誤差滿足一致最終有界. 另外,利用評判神經網絡近似改進后的代價函數,以近似求解Hamilton–Jacobi–Bellman方程,獲得滿足非對稱輸入約束的最優分散控制策略. 基于評判網絡權值更新規則,通過選擇合適的Lyapunov函數保證了權值近似誤差滿足一致最終有界. 最后,通過仿真實例驗證了該算法的有效性,并通過與未改進代價函數的傳統方法對比,體現了該方法的先進性.

     

    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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