Abstract Models are of great importance for many purposes, including control design. However, most real systems are complex, frequently nonlinear and first principle models tend to be too complicated, or even unknown, for control-oriented modeling. Therefore, data-based models are often used; however, since most likely the true system is not an element of any assumed model class, the available model is an approximation of the real system. To identify nonlinear systems, universal approximations are often used, e.g., polynomial nonlinear models whose number of parameters rapidly increases with model complexity. Because of the high number of parameters to be identified and the presence of nonlinearity, the accurate choice of an appropriate excitation becomes essential and not trivial. The aim of the present paper is to analyze classical design of experiment (DOE) and present its limits in terms of prediction error, for the static polynomial setup under investigation. First, when the system belongs to the assumed model class, we suggest the use of a more suitable optimization criterion that we prove to be a generalization of the well-known V-optimality. Second, we show that if we design the excitation input based on a higher degree model than the one to be identified, it gives rise to a more efficient approximation.

中文翻译：

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非线性系统静态多项式逼近实验的优化设计

摘要 模型对于许多目的都非常重要，包括控制设计。然而，大多数真实系统是复杂的，经常是非线性的，第一原理模型对于面向控制的建模来说往往过于复杂，甚至是未知的。因此，经常使用基于数据的模型；然而，由于真实系统很可能不是任何假定模型类的元素，因此可用模型是真实系统的近似值。为了识别非线性系统，通常使用通用逼近，例如多项式非线性模型，其参数数量随着模型复杂性而迅速增加。由于需要识别的参数数量众多且存在非线性，因此准确选择合适的激励变得至关重要且并非微不足道。本文的目的是分析经典实验设计 (DOE) 并展示其在预测误差方面的限制，用于研究中的静态多项式设置。首先，当系统属于假定的模型类时，我们建议使用更合适的优化标准，我们证明它是众所周知的 V 最优性的推广。其次，我们表明，如果我们基于比待识别模型更高阶的模型来设计激励输入，则会产生更有效的近似。