本文提出了一种无模型、数据驱动的控制合成方法，称为动态模式自适应控制（DMAC），用于数学模型不可用或不适合经典控制设计的系统。所提出的方法结合数据驱动的动力学近似与自适应控制合成，以实现在线控制器设计。DMAC包含两个主要模块：动力学近似模块和控制器合成模块。动力学近似模块使用带有遗忘因子的矩阵递推最小二乘算法，直接从测量数据估计系统的局部线性表示。估计的动力学随后用于计算具有全状态反馈和积分作用的在线稳定控制器。理论分析建立了递推动力学近似的收敛性以及在DMAC控制器下的闭环系统有界性。通过数值示例展示了所提出方法的性能，包括不稳定线性系统、Van der Pol振子和Burgers方程等代表性动态系统。灵敏度研究进一步展示了DMAC在算法超参数和系统参数变化方面的鲁棒性。
英文摘要：
This paper presents a model-free, data-driven control synthesis method called dynamic mode adaptive control (DMAC) for systems whose mathematical models are unavailable or unsuitable for classical control design. The proposed approach combines data-driven dynamics approximation with adaptive control synthesis to enable online controller design using measured system data. DMAC comprises two main components: a dynamics-approximation module and a controller-synthesis module. The dynamics approximation module estimates a local linear representation of the system dynamics directly from measurements using a matrix recursive least-squares algorithm with a forgetting factor. The estimated dynamics are then used to compute an online stabilizing controller with full-state feedback and integral action. Theoretical analysis establishes convergence properties of the recursive dynamics approximation and boundedness of the closed-loop system under the DMAC controller. The performance of the proposed method is demonstrated through numerical examples involving representative dynamical systems, including an unstable linear system, the Van der Pol oscillator, and the Burgers' equation. Sensitivity studies further demonstrate the robustness of DMAC with respect to both algorithm hyperparameters and variations in system parameters.
Adaptive Meshing for CPA Lyapunov Function Synthesis
Thomas Lord Department of Mechanical Engineering and Materials Science, Duke University（杜克大学托马斯·劳德机械与材料工程系）；Department of Aeronautics and Astronautics, Stanford University（斯坦福大学航空与航天工程系）
