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首页> 外文期刊>IEEE Transactions on Automatic Control >Explicit Solution for Constrained Scalar-State Stochastic Linear-Quadratic Control With Multiplicative Noise
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Explicit Solution for Constrained Scalar-State Stochastic Linear-Quadratic Control With Multiplicative Noise

机译：具有乘法噪声的约束标量状态随机线性 - 二次控制的显式解决方案

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摘要

We study in this paper, a class of constrained linear-quadratic (LO) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper, the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piecewise affine function of the state and can be computed offline efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for an infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems.
机译：我们研究了本文，一类受约束的线性 - 二次（LO）的标量型随机系统具有乘法噪声的标量噪声，具有各种应用，特别是在金融风险管理中。我们模型中考虑的控制和状态变量的线性约束会破坏传统LQ制剂的优雅结构，并阻止了到目前为止在文献中达到了明确控制政策的推导。我们通过利用其结构诱导的状态分离特性，我们成功得出了这种问题的分析控制政策。我们揭示了最佳控制策略是状态的分段仿射函数，并且可以通过求解两个耦合的Riccati方程来高效地计算。在一些温和的条件下，我们还获得了无限时间范围的静止控制政策。我们通过一些说明性示例展示了我们的方法，并展示了如何校准我们的模型来解决动态约束的产品组合优化问题。

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