A semi-infinite programming approach to continuously constrained LQ optimal control problems

SICE '99. Proceedings of the 38th SICE Annual Conference. International Session Papers (IEEE Cat. No.99TH8456) Pub Date : 1999-07-28 DOI:10.1109/SICE.1999.788714

Y. Liu, S. Ito, K. Teo

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引用次数: 4

Abstract

Consider the class of LQ optimal control problems with continuous linear state constraints, that is, constraints imposed on every instant of the time horizon. This class of problems are known to be difficult to solve numerically. In this paper, a computational method based on a semi-infinite programming approach is given. The LQ optimal control problem is formulated as a positive quadratic infinite programming problem. This can be done by considering the control as the decision variable while taking the state as a function of the control. After parameterizing the decision variable, an approximate quadratic semi-infinite programming problem is obtained. It is shown that as we refine the parameterization, the solution sequence of the approximate problems converge to the solution of the infinite programming problem (hence to the solution of the original optimal control problem). Numerically, the semi-infinite programming problems obtained above can be efficiently solved using an algorithm based on a dual parameterization method.

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连续约束LQ最优控制问题的半无限规划方法

考虑一类具有连续线性状态约束的LQ最优控制问题，即在时间范围的每个瞬间施加约束。众所周知，这类问题很难用数值方法来解决。本文给出了一种基于半无限规划方法的计算方法。将LQ最优控制问题表述为一个正二次无限规划问题。这可以通过将控制作为决策变量，同时将状态作为控制的函数来实现。将决策变量参数化后，得到了一个近似二次半无限规划问题。结果表明，随着参数化的细化，近似问题的解序列收敛于无限规划问题的解(从而收敛于原最优控制问题的解)。数值上，利用基于对偶参数化方法的算法可以有效地求解上述半无限规划问题。

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SICE '99. Proceedings of the 38th SICE Annual Conference. International Session Papers (IEEE Cat. No.99TH8456)

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