论文标题
高斯推断非线性系统的数据驱动状态反馈设计
Gaussian inference for data-driven state-feedback design of nonlinear systems
论文作者
论文摘要
具有严格保证的非线性系统的数据驱动控制是一个具有挑战性的问题，因为它通常需要进行非凸优化，并且通常需要了解系统动力学的真实基础功能。为了解决这些缺点，这项工作基于利用泰勒多项式的一般非线性系统的数据驱动的多项式表示。因此，我们设计了状态反馈定律，该定律在相对于所需的二次性能标准时，在操作时，在全球范围内均匀稳定了一个已知的平衡点。多项式状态反馈的计算归结为单个平方之和优化问题，从而归功于计算可牵引的线性矩阵不平等。此外，我们通过贝叶斯推论在存在高斯噪声的情况下检查了状态输入数据，以克服从最近的数据驱动的高斯噪声控制方法中对确定性噪声表征的保守性。
Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these drawbacks, this work is based on a data-driven polynomial representation of general nonlinear systems exploiting Taylor polynomials. Thereby, we design state-feedback laws that render a known equilibrium point globally asymptotically stable while operating with respect to a desired quadratic performance criterion. The calculation of the polynomial state feedback boils down to a single sum-ofsquares optimization problem, and hence to computationally tractable linear matrix inequalities. Moreover, we examine state-input data in presence of Gaussian noise by Bayesian inference to overcome the conservatism of deterministic noise characterizations from recent data-driven control approaches for Gaussian noise.
