基于零和微分博弈的仿射非线性系统预设时间容错控制

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

  • 摘要: 针对一类带有执行器故障的仿射非线性系统,本文提出了一种基于零和微分博弈的预设时间最优容错控制策略。该方法通过辅助函数构建具有时间以及空间约束性能的状态方程。基于此状态方程,我们将控制信号以及偏置故障作为博弈双方,构建微分博弈模型。结合纳什-庞特里亚金最大最小原理,系统地推导了Hamilton-Jacobi-Isaacs(HJI)方程,以求解鞍点平衡,从而获得最优控制策略和偏差故障的边界值。为了解决求解高阶偏微分方程时固有的“维数灾难”,基于神经网络技术提出了自适应动态规划算法。设计的最优容错控制策略可以保证系统在执行器故障的情况下具有预设时间稳定性以及最优性能,并且该预设时间是显性的,可以由用户进行自行调整。仿真结果表明了本文设计算法的可行性与有效性。

     

    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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