Near-optimal controls of random-switching LQ problems with indefinite control weight costs
Near-optimal controls of random-switching LQ problems with indefinite control weight costs
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DOI：
10.1016/j.automatica.2005.01.002
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发表时间：
2005-06
期刊：
影响因子：
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通讯作者：
Yuanjin Liu;G. Yin;X. Zhou
中科院分区：
文献类型：
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作者：
Yuanjin Liu;G. Yin;X. Zhou
本文研究了一类具有白色噪声扰动和马尔可夫状态切换的线性二次型问题的混合控制问题，其中状态切换由具有大状态空间的连续时间马尔可夫链建模，控制权是不确定的.大状态空间的使用使我们能够考虑不确定环境中的各种因素，但它会产生计算开销并增加难度。为了降低复杂性，我们演示了如何构造近最优控制。首先，在模型中，我们引入了一个小参数来突出弱相互作用和强相互作用以及快运动和慢运动的对比。这导致两个时间尺度的制剂。鉴于具有不定控制权和双时间尺度马尔可夫链的LQ问题的最新进展，我们建立了与混合LQ问题相关的Riccati方程组的收敛性.基于最优反馈控制的极限系统得到的Riccati方程系统，我们构造控制原问题，并表明，这种控制是近最优的。这里给出一个简单系统的数值演示。
In this paper, we consider hybrid controls for a class of linear quadratic problems with white noise perturbation and Markov regime switching, where the regime switching is modeled by a continuous-time Markov chain with a large state space and the control weights are indefinite. The use of large state space enables us to take various factors of uncertain environment into consideration, yet it creates computational overhead and adds difficulties. Aiming at reduction of complexity, we demonstrate how to construct near-optimal controls. First, in the model, we introduce a small parameter to highlight the contrast of the weak and strong interactions and fast and slow motions. This results in a two-time-scale formulation. In view of the recent developments on LQ problems with indefinite control weights and two-time-scale Markov chains, we then establish the convergence of the system of Riccati equations associated with the hybrid LQ problem. Based on the optimal feedback control of the limit system obtained using the system of Riccati equations, we construct controls for the original problem and show that such controls are near-optimal. A numerical demonstration of a simple system is presented here.