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An alternative approach for non-linear optimal control problems based on the method of moments

机译:基于矩量法的非线性最优控制问题的一种替代方法

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We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.
机译:我们提出了一种替代方法,当以Lagrange,Bolza或Mayer形式给出时,可以有效地计算非线性,固定终端时间的最优控制问题的解决方案。当控制变量中的非线性可以表示为多项式时,此方法效果很好。该建议的实质是将非线性,非凸的最优控制问题转化为具有线性和凸结构的等效最优控制问题。该方法基于采用矩量法的多项式的全局优化。通过这种方法,我们可以确定是否存在最小化器。此外,当原始问题缺少极小值时,我们可以计算广义解。我们还提出了数值方案来解决科学技术中出现的几个例子。

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