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基于零和微分博弈的仿射非線性系統預設時間容錯控制

Prescribed-time fault-tolerant control for affine nonlinear systems based on zero-sum differential games

  • 摘要: 針對一類帶有執行器故障的仿射非線性系統,本文提出了一種基于零和微分博弈的預設時間最優容錯控制策略。該方法通過輔助函數構建具有時間以及空間約束性能的狀態方程。基于此狀態方程,我們將控制信號以及偏置故障作為博弈雙方,構建微分博弈模型。結合納什-龐特里亞金最大最小原理,系統地推導了Hamilton-Jacobi-Isaacs(HJI)方程,以求解鞍點平衡,從而獲得最優控制策略和偏差故障的邊界值。為了解決求解高階偏微分方程時固有的“維數災難”,基于神經網絡技術提出了自適應動態規劃算法。設計的最優容錯控制策略可以保證系統在執行器故障的情況下具有預設時間穩定性以及最優性能,并且該預設時間是顯性的,可以由用戶進行自行調整。仿真結果表明了本文設計算法的可行性與有效性。

     

    Abstract: For a class of affine nonlinear systems with actuator faults, this paper proposes a prescribed-time optimal fault-tolerant control strategy based on zero-sum differential games. The methodology constructs state equations with time and space constraint performance through auxiliary functions. Based on these state equations, we establish a differential game model by considering the control signal and bias fault as two game participants. The Hamilton-Jacobi-Isaacs (HJI) equation and Nash-Pontryagin maximin principle are employed to derive the optimal control strategy and boundary values of bias faults, while an adaptive dynamic programming algorithm is implemented to address the curse of dimensionality. The designed optimal fault-tolerant control strategy guarantees prescribed-time stability and optimal performance of the system under actuator faults. Furthermore, the prescribed-time parameter can be flexibly adjusted by users according to specific mission requirements without redesigning gain parameters or considering initial states. Simulation results demonstrate the evolution of system states and control torques under the proposed algorithm, along with comparative analyses of state variations under different initial conditions and prescribed times, which collectively validate the feasibility and effectiveness of the designed methodology.

     

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