Traditional control methods for nonlinear dynamical systems are predicated on verification of complex mathematical conditions related to the existence of a positive-definite Lyapunov function whose value must strictly decrease with time. Rigorous verification of Lyapunov conditions can be extremely difficult in real-world systems with high-dimensional and complex dynamics. In this paper, we present a novel control logic that can be readily applied to a general class of nonlinear systems irrespective of the complexities in their dynamics. The Iterative Control Framework (ICF) is designed to guarantee the convergence of the closed-loop system state to zero without a priori verification of Lyapunov-like conditions. The underlying computational routine runs in the background in real time and reconfigures the control vector at each time step in such a way that when the control input is applied to the system, the system trajectory reaches closer to the desired state. The technique is applicable to a broad class of complex nonlinear systems but is particularly suitable for systems inherently admitting control action of short duration such as missiles, rockets, satellites, and space vehicles. In this work, we focus on the application of ICF to guidance and attitude control of rockets and missiles where actuation is provided via single-use thrusters.

中文翻译：

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应用于火箭制导和姿态控制的迭代控制框架


非线性动力学系统的传统控制方法基于对与正定 Lyapunov 函数的存在相关的复杂数学条件的验证，该函数的值必须随时间严格减小。在具有高维和复杂动力学的现实世界系统中，严格验证李雅普诺夫条件可能非常困难。在本文中，我们提出了一种新的控制逻辑，它可以很容易地应用于一般类别的非线性系统，而不管其动力学的复杂性如何。迭代控制框架 （ICF） 旨在保证闭环系统状态收敛为零，而无需对类似 Lyapunov 的条件进行先验验证。底层计算例程在后台实时运行，并在每个时间步重新配置控制向量，这样当控制输入施加到系统时，系统轨迹更接近所需状态。该技术适用于一大类复杂的非线性系统，但特别适用于本身就接受短时控制动作的系统，例如导弹、火箭、卫星和航天器。在这项工作中，我们专注于将 ICF 应用于火箭和导弹的制导和姿态控制，其中通过一次性推进器提供驱动。