Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality reduction introduces model uncertainty which can potentially compromise the stability and safety of the original high-dimensional system. In this work, we propose a novel reduced-order model predictive control (ROMPC) scheme to solve constrained optimal control problems for nonlinear, high-dimensional systems. To address the challenges of using ROMs in predictive control schemes, we derive an error bounding system that dynamically accounts for model reduction error. Using these bounds, we design a robust MPC scheme that ensures robust constraint satisfaction, recursive feasibility, and asymptotic stability. We demonstrate the effectiveness of our proposed method in simulations on a high-dimensional soft robot with nearly 10,000 states.

翻译：实际系统通常具有高维非线性动力学特性，这使得其实时控制极具挑战性。虽然降阶模型（ROM）常被用于基于模型的控制方案中，但维度降低会引入模型不确定性，可能危及原高维系统的稳定性与安全性。本研究提出一种新颖的降阶模型预测控制（ROMPC）方案，用于求解非线性高维系统的约束最优控制问题。为应对在预测控制方案中使用ROM的挑战，我们推导了一个能动态反映模型降阶误差的误差边界系统。基于这些边界，我们设计了鲁棒MPC方案，确保鲁棒约束满足性、递推可行性与渐近稳定性。通过在具有近10,000个状态的高维软体机器人仿真中，我们验证了所提方法的有效性。