论文标题
学习减少的非线性状态空间模型：基于输出的规范方法
Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach
论文作者
论文摘要
非线性动态模型的识别是控制理论中的一个开放主题，尤其是从稀疏输入输出测量中。这个问题的一个基本挑战是，在州和非线性系统模型上都可以提供很少至零的先验知识。为了应对这一挑战，我们通过提倡一种依赖三种主要成分的方法来研究深度学习在具有非线性行为的动态系统建模中的有效性：（i）我们表明，在某些结构性条件下，对已确定的模型的某些结构条件，状态可以在过去的输入和输出序列和输出的序列中表达； （ii）我们称之为状态图的这种关系可以通过诉诸深度神经网络的近似近似能力来建模； （iii）利用现有的学习方案的优势，最终可以确定一个状态空间模型。在对该方法进行配方和分析之后，我们显示了其识别三种不同非线性系统的能力。根据模拟中生成的测试数据以及无人驾驶飞行飞行测量的现实世界数据集，对表演进行了评估。
The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the state and the nonlinear system model. To cope with this challenge, we investigate the effectiveness of deep learning in the modeling of dynamic systems with nonlinear behavior by advocating an approach which relies on three main ingredients: (i) we show that under some structural conditions on the to-be-identified model, the state can be expressed in function of a sequence of the past inputs and outputs; (ii) this relation which we call the state map can be modelled by resorting to the well-documented approximation power of deep neural networks; (iii) taking then advantage of existing learning schemes, a state-space model can be finally identified. After the formulation and analysis of the approach, we show its ability to identify three different nonlinear systems. The performances are evaluated in terms of open-loop prediction on test data generated in simulation as well as a real world data-set of unmanned aerial vehicle flight measurements.
