基于预测切换控制律的时滞离散切换仿射系统的鲁棒镇定
Robust stabilization of time-delay discrete switched affine systems via a predictive switching control law
中文总结 AI 辅助
本文针对受输入时滞的不确定离散切换仿射系统，提出基于各模态标称动力学的最小切换预测控制方法，给出鲁棒镇定条件并通过数值示例验证其有效性。
中文摘要 AI 辅助
本文研究受单个单位输入时滞影响的不确定离散切换仿射系统的鲁棒控制问题。这类系统的独特特征在于，控制输入为切换信号，其属于有限取值集合，因此闭环轨迹不会收敛到平衡点，而是收敛到极限环。为减轻输入时滞的影响，我们提出一种基于各模态已知标称动力学特性的最小切换预测控制方法。该方法旨在通过李雅普诺夫论证，利用该标称预测器确保不确定系统的鲁棒镇定。我们的主要结果提供了易于处理的鲁棒镇定条件，可保证在系统不确定性和切换时滞下收敛到鲁棒极限环。此外，还引入了优化程序以最小化吸引子的大小，吸引子是轨迹渐近收敛的区域。数值示例验证了所提方法的有效性。
英文摘要
This paper addresses the robust control of uncertain discrete-time switched affine systems subject to a single unitary input delay. The unique feature of this class of systems lies in the fact that the control input is the switching signal, which belongs to a finite set of values. Consequently, the closed-loop trajectories do not converge to an equilibrium point but rather to a limit cycle. To mitigate the impact of the input delay, we propose a min-switching predictive control approach, which is based on the known nominal dynamical characteristics of each mode. The objective of this approach is to ensure the robust stabilization of the uncertain system using this nominal predictor, employing a Lyapunov argument. Our main result provides tractable robust stabilization conditions that guarantee the convergence to a robust limit cycle under system uncertainties and delayed switching. Additionally, an optimization procedure has been incorporated to minimize the size of the attractor, which represents the region where the trajectories asymptotically converge. A numerical example validates the effectiveness of the proposed approach.
