基于管道的鲁棒模型预测控制用于以多面体LPV建模的分布式参数系统（扩展版）
Tube-based Robust Model Predictive Control for a Distributed Parameter System Modeled as a Polytopic LPV (extended version)
AI总结：
本文针对分布式参数系统，提出将非线性嵌入LPV系统，采用鲁棒管道MPC处理不确定性，离线计算大部分，在线仅求解简单QP，仿真验证了良好性能与稳定性。
摘要：
分布式参数系统（DPS）以偏微分方程（PDE）形式表述。尤其是在时变边界条件下，偏微分方程引入了力耦合。在柔性堆垛起重机（STC）的情况下，引入了非线性耦合。因此，在线轨迹规划与跟踪可通过非线性模型预测控制（NMPC）来解决。然而，由于NMPC计算需求高，本文探讨了将非线性嵌入线性参数变化（LPV）系统，从而利用计算需求低的线性MPC的可能性。由此产生的失配在鲁棒管道MPC（TMPC）框架下被视为参数性和加性不确定性。对于所提出的方法，大部分计算在离线完成，仅一个简单的凸二次规划（QP）在线进行。此外，简要提出了软约束扩展。仿真结果用于说明所提方法在存在不确定性情况下仍具有良好的性能、闭环稳定性和递归可行性。
英文摘要：
Distributed parameter systems (DPS) are formulated as partial differential equations (PDE). Especially, under time-varying boundary conditions, PDE introduce force coupling. In the case of the flexible stacker crane (STC), nonlinear coupling is introduced. Accordingly, online trajectory planning and tracking can be addressed using a nonlinear model predictive control (NMPC). However, due to the high computational demands of a NMPC, this paper discusses a possibility of embedding nonlinearities inside a linear parameter varying (LPV) system and thus make a use of a numerically low-demanding linear MPC. The resulting mismatches are treated as parametric and additive uncertainties in the context of robust tube-based MPC (TMPC). For the proposed approach, most of the computations are carried out offline. Only a simple convex quadratic program (QP) is conducted online. Additionally a soft-constrained extension was briefly proposed. Simulation results are used to illustrate the good performance, closed-loop stability and recursive feasibility of the proposed approach despite uncertainties.
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