论文标题
基于时间分配优化的线性模型预测控制的闭环稳定性分析
An Analysis of Closed-Loop Stability for Linear Model Predictive Control Based on Time-Distributed Optimization
论文作者
论文摘要
时间分配优化（TDO）是减少模型预测控制（MPC）的计算负担的一种方法。使用TDO时，通过维护运行解决方案估算并在每个采样瞬间更新它来分配优化迭代。在本文中，详细研究了将TDO应用于输入约束线性MPC，并针对系统增益进行了分析表达式，并绑定了确保闭环稳定性所需的每个采样即时的优化迭代次数。此外，可以证明，可以使用多种机制来保证基于TDO的MPC的闭环稳定性，包括增加求解器迭代的数量，预处理最佳控制问题，调整MPC成本矩阵以及减少回收视野的长度。这些结果在线性系统设置中还提供了可能更广泛适用的见解和准则，例如非线性MPC。
Time-distributed Optimization (TDO) is an approach for reducing the computational burden of Model Predictive Control (MPC). When using TDO, optimization iterations are distributed over time by maintaining a running solution estimate and updating it at each sampling instant. In this paper, TDO applied to input constrained linear MPC is studied in detail, and analytic expressions for the system gains and a bound on the number of optimization iterations per sampling instant required to guarantee closed-loop stability is derived. Further, it is shown that the closed-loop stability of TDO-based MPC can be guaranteed using multiple mechanisms including increasing the number of solver iterations, preconditioning the optimal control problem, adjusting the MPC cost matrices, and reducing the length of the receding horizon. These results in a linear system setting also provide insights and guidelines that could be more broadly applicable, e.g., to nonlinear MPC.
