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首页> 外文期刊>IEEE Transactions on Aerospace and Electronic Systems >Multistage Linear Gauss Pseudospectral Method for Piecewise Continuous Nonlinear Optimal Control Problems
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Multistage Linear Gauss Pseudospectral Method for Piecewise Continuous Nonlinear Optimal Control Problems

机译：多级线性高斯假谱法分段连续非线性最优控制问题

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摘要

This article aims at proposing a multistage linear Gauss pseudospectral method (MS-LGPM) for solving the piecewise continuous nonlinear optimal control problem (OCP) with interior-point constraints and terminal constraints. First, the first-order necessary conditions for the multistage nonlinear OCP are derived, and a typical multipoint boundary value problem is obtained. Second, the original problem can be solved iteratively by integral prediction and quasi-linearization. Then Lagrange interpolation polynomials are used to approximate the state, control, and costate variables, to transfer those differential equations into a set of linear algebraic equations. Therefore, the control update coming closer to the optimal solution can be derived in an analytical manner. Additionally, those linear algebraic equations are formulated in regular banded matrix forms to make the code as concise as possible. Finally, the proposed method is applied to the midcourse guidance design for a dual-pulse missile to evaluate its performance. Simulation results show that the proposed method performs well in providing the optimal control with high accuracy and computational efficiency. Furthermore, a comparison with other typical guidance method and Monte Carlo simulations are also provided. Results demonstrate, even with some random uncertainties, the proposed method still has strong robustness and superior performance.
机译：本文旨在提出多级线性高斯假谱法（MS-LGPM），用于解决与内部点约束和终端约束的分段连续非线性最佳控制问题（OCP）。首先，导出多级非线性OCP的一阶必要条件，获得典型的多点边值问题。其次，通过积分预测和准线性化可以迭代地解决原始问题。然后，Lagrange插值多项式用于近似于状态，控制和成本速度变量，将这些微分方程转换为一组线性代数方程。因此，可以以分析方式导出更接近最佳解决方案的控制更新。另外，这些线性代数方程以规则的带状矩阵形式配制，以使代码尽可能简洁。最后，该方法应用于双脉冲导弹的中级指导设计，以评估其性能。仿真结果表明，该方法在提供高精度和计算效率的优化控制方面表现良好。此外，还提供了与其他典型引导方法和蒙特卡罗模拟的比较。结果表明，即使有一些随机的不确定性，所提出的方法仍然具有强大的鲁棒性和卓越的性能。

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