Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.
翻译:线性时间变化系统(LTV)由于其普遍性和简洁性,被广泛用于模拟现实世界动态系统。为LTV系统提供稳定性保障是控制理论中的一个中心问题。然而,保证稳定性的现有办法通常导致只有当前或短期系统信息的在线环境中的累积控制成本大大低于最佳水平。在这项工作中,我们提议一种高效的在线控制算法,即COVariance Contracted Online Lual Quadratic (CO-LQ) 控制,保证一大批LTV系统的投入到国家的稳定性,同时尽量减少控制成本。拟议方法将国家变量限制纳入半确定性LQ最佳控制器的编程中。我们在合成实验和电源系统频率控制示例中都以实验方式展示COCO-LQ的性能。