Algebraic approach to nonlinear finite-horizon optimal control problems with terminal constraints
Algebraic approach to nonlinear finite-horizon optimal control problems with terminal constraints
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DOI：
10.1109/ascc.2017.8287093
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发表时间：
2017-12
期刊：
影响因子：
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通讯作者：
Tomoyuki Iori;Y. Kawano;T. Ohtsuka
中科院分区：
文献类型：
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作者：
Tomoyuki Iori;Y. Kawano;T. Ohtsuka
通过将一类非线性函数约束为有理函数或代数函数，提出了一种求解具有终端约束的非线性有限时域最优控制问题的代数方法。所提出的方法递归地将欧拉-拉格朗日方程组分解为代数方程组，其中每组方程组仅包含同一时刻的变量。通过求解每个集合得到每个时刻的最优解的候选。这种结构的方法适用于非线性模型预测控制，因为我们可以得到初始的最优控制律，只需在初始时刻求解一组代数方程组。理论和实际的例子来说明所提出的方法，并显示该方法的效率。
This paper proposes an algebraic method to solve nonlinear finite-horizon optimal control problems with terminal constraints by restricting a class of nonlinear functions to rational or algebraic functions. The proposed method recursively decouples the Euler-Lagrange equations into sets of algebraic equations, where each set of equations contains only the variables of the same time instance. The candidates of the optimal solution at each time instance are obtained by solving each set. This structure of the method is suitable for nonlinear model predictive control because we can obtain the initial optimal control law by only solving a set of algebraic equations at the initial time instance. Academic and practical examples are provided to illustrate the proposed methodology and to show the efficiency of the method.