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首页> 外文期刊>IEEE Transactions on Automatic Control >Modeling and Control of Stochastic Systems With Poorly Known Dynamics
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Modeling and Control of Stochastic Systems With Poorly Known Dynamics

机译：动力学未知的随机系统的建模和控制

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This paper is concerned with controlling poorly known systems, for which only a simplified and rough model is available for control design. There are many systems that cannot be reasonably probed for the sake of identification, yet they are important for areas such as economy, populations, or medicine. The ideas are developed around an alternative way to account for the bare modeling in a stochastic-based setting, and to heighten the control features for such a modified model. The mathematical framework for the optimal control reveals important features such as the raising of a precautionary feedback policy of “keep the action unchanged” (inaction for short), on a certain state-space region. This feature is not seen in the robust approach, but has been pointed out and permeates part of the economics literature. The control problem relies on the viscosity solution for the Hamilton-Jacobi-Bellman equation, and the value of the problem is shown to be convex. When specialized to the quadratic problem with discounted cost, the exact solution inside the inaction region is given by a Lyapunov type of equation, and asymptotically, for large state values, by a Riccati-like equation. This scenario bridges to the stochastic stability analysis for the controlled model. The single control input is developed in full, part analytically, part numerically, for the scalar case, and an approximation is tested for the multidimensional case. The advantage of the precautionary policy is substantial in some situations.
机译：本文涉及控制鲜为人知的系统，对于这种系统，只有简化和粗糙的模型可用于控制设计。为了识别目的，有许多系统无法进行合理的探测，但是它们对于诸如经济，人口或医学等领域非常重要。这些想法是围绕一种替代方法提出的，该替代方法是在基于随机的设置中考虑裸露的建模，并提高这种修改后的模型的控制功能。最优控制的数学框架揭示了重要的特征，例如在特定的状态空间区域上提出了“保持动作不变”（简称“不动作”）的预防性反馈策略。在稳健的方法中看不到此功能，但已指出该功能，并渗入了经济学文献的一部分。控制问题依赖于Hamilton-Jacobi-Bellman方程的粘度解，并且问题的值显示为凸的。当专门研究具有折扣成本的二次问题时，不活动区域内的精确解由Lyapunov类型的方程式给出，对于大状态值，由Riccati式方程渐近给出。这种情况桥接了受控模型的随机稳定性分析。对于标量情况，将对单个控制输入进行完整，部分分析，部分数字化开发，并针对多维情况进行近似测试。在某些情况下，预防政策的优势是巨大的。

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