AI 中文总结
本文提出一种针对差凸非线性系统的凸管模型预测控制方法，利用配置约束多胞形管和凸方向界，在单个凸规划中联合优化管几何与控制律，保证鲁棒性和收敛性。
AI 中文摘要
本文针对受约束非线性系统提出了一种凸管模型预测控制（Tube MPC）公式。我们考虑由离散时间状态空间模型描述的动力学，该模型包含参数不确定性和加性不确定性，并允许差凸（difference-of-convex）分解。将非线性动力学的凸方向界与配置约束的多胞形管（configuration-constrained polytopic tubes）相结合，其预定义的组合结构使得管顶点具有仿射参数化。由此产生的有限维充分条件保证了在参数不确定性和加性扰动下鲁棒的一步管传播，同时允许在单个凸规划中联合优化管几何形状和相关的顶点控制律。隐式终端条件保证了递归可行性和预测管收敛到目标鲁棒控制不变集。数值结果展示了闭环特性以及几何灵活性与计算复杂度之间的权衡。
英文摘要
This paper develops a convex tube model predictive control formulation for constrained nonlinear systems. We consider dynamics described by a discrete-time state-space model with parametric and additive uncertainty that admits a difference-of-convex decomposition. Convex directional bounds of the nonlinear dynamics are combined with configuration-constrained polytopic tubes, whose predefined combinatorial structure yields an affine parameterization of their vertices. The resulting finite-dimensional sufficient conditions certify robust one-step tube propagation under parametric uncertainty and additive disturbances, while allowing the tube geometry and an associated vertex control law to be optimized jointly in a single convex program. An implicit terminal condition guarantees recursive feasibility and convergence of the predicted tube to a target robust control invariant set. Numerical results illustrate the closed-loop properties and the trade-off between geometric flexibility and computational complexity.
Comments11 pages, 3 figures, submitted to Automatica
