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求解最优控制问题的微分变换方法
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O232

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国家自然科学基金资助项目(60871027)


The Differential Transform Method for Solving Optimal Control Problems
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    摘要:

    针对无约束最优控制问题,建立求其近似解析解的微分变换法。对哈密顿正则方程组中状态方程、协态方程和控制方程构造基于初值的微分变换形式或基于终端的微分变换形式,将最优性条件化为相应的代数方程,得到最优控制问题的近似解析解。在特定条件下,对结构复杂的非线性最优控制问题,依据插值逼近原理,结合微分变换法,可构建离散型代数方程组得到其近似解析解。利用微分变换法将微分方程初边值问题和泛函优化问题构成的复杂系统化为易于求解的代数方程形式,简单可行,易于实现。最后,通过算例验证方法的有效性。

    Abstract:

    The differential transform method used for solving the approximation analytic solution of the unconstrained optimal control problem is established. According to the state equation, costate equation and governing equation in the set of Hamilton regular equations, we first construct the differential transform form based on initial value or terminal station, by which the optimality condition is transformed into a corresponding algebraic equation, furthermore, the approximation analytic solution of the optimal control problem is obtained. In addition, to the nonlinear optimal control problem which is complex in structure, in particular condition, the discreteness set of algebraic equations can be constructed in light of the principle of approximation by interpolation and the differential transform method to obtain its approximation analytic solution. By using this method, the initial-boundary value problem of the differential equation and the complex system of the functional optimization problems are converted into algebraic equations which facilitate getting the solution, also are simple, feasible and easy to realize. Finally, the effectiveness of this method is verified by numerical examples.

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李炳杰,张国华,吕园.求解最优控制问题的微分变换方法[J].空军工程大学学报,2011,(1):90-94

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  • 在线发布日期: 2015-11-24
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