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Nonlinear Optimal Approach to Spacecraft Formation Flying Using Lorentz and Impulsive Actuation
Journal of Optimization Theory and Applications ( IF 1.9 ) Pub Date : 2021-07-18 , DOI: 10.1007/s10957-021-01892-1
Esmaeil Sharifi 1 , Christopher J. Damaren 1
Affiliation  

This paper proposes an optimal control design framework for hybrid nonlinear time-dependent dynamical systems involving an interacting mixture of continuous-time and discrete-time dynamics. Aiming to extend hybrid linear optimal control synthesis to nonlinear non-quadratic formulation, a hybrid version of the Hamilton–Jacobi–Bellman (HJB) equation with time-dependency is first presented. A hybrid computational framework, which alternates between continuous-time and discrete-time subsystems at an appropriate sequence of time instants, is then developed to solve the resultant set of the HJB equations in an interacting manner. The proposed control scheme is subsequently applied to spacecraft formation flying establishment with a hybrid source of actuation, namely Lorentz force and impulsive thrusting. By optimal combination of the Lorentz force and impulsive thrusting proposed in this paper, not only are the uncontrollability issues pertinent inherently to the Lorentz-actuated control systems effectively resolved, but use of both Lorentz and impulsive control inputs is also optimized. As a consequence, the expendable chemical fuels required to actuate thrusters are significantly reduced, thereby extending the duration of such space missions.



中文翻译:

使用洛伦兹和脉冲驱动的航天器编队飞行非线性优化方法

本文提出了一种用于混合非线性瞬态动态系统的最佳控制设计框架,该系统涉及连续时间和离散时间动态的相互作用混合。为了将混合线性最优控制综合扩展到非线性非二次公式,首先提出了具有时间依赖性的 Hamilton-Jacobi-Bellman (HJB) 方程的混合版本。然后开发了一个混合计算框架,它在连续时间和离散时间子系统之间以适当的时间序列交替,以交互方式求解 HJB 方程的结果集。所提出的控制方案随后被应用于具有混合驱动源(即洛伦兹力和脉冲推力)的航天器编队飞行设施。通过本文提出的洛伦兹力和脉冲推力的最佳组合,不仅有效解决了与洛伦兹驱动控制系统固有的不可控性问题,而且还优化了洛伦兹和脉冲控制输入的使用。因此,驱动推进器所需的消耗性化学燃料显着减少,从而延长了此类太空任务的持续时间。

更新日期:2021-07-19
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