论文标题
线性参数变化系统的直接数据驱动的状态反馈控制
Direct Data-Driven State-Feedback Control of Linear Parameter-Varying Systems
论文作者
论文摘要
线性参数变化（LPV）系统的框架已证明是使用线性工具为复杂非线性系统设计控制器的强大工具。在这项工作中，我们得出了新的方法，可以直接从单个数据序列中直接合成LPV状态反馈控制器，并保证闭环系统的稳定性和性能。我们表明，如果系统中测得的开环数据满足激发条件的持久性，则只能使用数据来表示完整的开环和闭环输入 - 安排安全状态行为。通过此表示，我们制定了数据驱动的分析和综合问题，后者产生的控制器可确保稳定性和性能，从无限的地平线二次成本，概括性$ \ Mathcal {h} _2 $ -Norm和$ \ ell_2 $ - 闭合系统的gain。通过求解半明确程序来合成控制器。此外，我们提供了一种合成方法来处理嘈杂的测量数据。拟议数据驱动的合成方法的竞争性能已证明W.R.T.在多个模拟研究中基于模型的合成，包括非线性不平衡盘系统。
The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV state-feedback controllers directly from only a single sequence of data and guarantee stability and performance of the closed-loop system. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation we formulate data-driven analysis and synthesis problems, where the latter yields controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\ell_2$-gain of the closed-loop system. The controllers are synthesized by solving a semi-definite program. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis in multiple simulation studies, including a nonlinear unbalanced disc system.
