A max-plus method for the approximate solution of discrete time linear regulator problems with non-quadratic terminal payoff

Huan Zhang, P. Dower
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引用次数: 4

Abstract

Efficient Riccati equation based techniques for the approximate solution of discrete time linear regulator problems are restricted in their application to problems with quadratic terminal payoffs. Where non-quadratic terminal payoffs are required, these techniques fail due to the attendant nonquadratic value functions involved. In order to compute these non-quadratic value functions, it is often necessary to appeal directly to dynamic programming in the form of gridor element-based iterations for the value function. These iterations suffer from poor scalability with respect to problem dimension and time horizon. In this paper, a new max-plus based method is developed for the approximate solution of discrete time linear regulator problems with non-quadratic payoffs.
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具有非二次终端收益的离散时间线性调节器问题近似解的极大加法
基于Riccati方程的离散时间线性调节器问题近似解的有效方法在应用于具有二次型终端收益的问题时受到限制。在需要非二次终端收益的情况下,由于涉及到随之而来的非二次值函数,这些技术失败了。为了计算这些非二次值函数,通常需要以基于网格元素的值函数迭代的形式直接诉诸动态规划。这些迭代在问题维度和时间范围方面存在较差的可伸缩性。本文提出了一种新的基于max-plus的离散时间线性调节器问题近似解的方法。
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