Analysis of Time-Distributed Model Predictive Control When Using a Regularized Primal–Dual Gradient Optimizer
Analysis of Time-Distributed Model Predictive Control When Using a Regularized Primal–Dual Gradient Optimizer
复制标题
使用正则化原始双梯度优化器时的时间分布模型预测控制分析
DOI：
10.1109/lcsys.2022.3186631
复制
发表时间：
2023
影响因子：
3
通讯作者：
Nicotra, Marco M.
中科院分区：
文献类型：
--
作者：
Skibik, Terrence;Nicotra, Marco M.
时间分布优化（Time-distributed Optimization，TDO）是一种用于降低模型预测控制（Model Predictive Control，MPC）的计算成本的方法，其中优化迭代通过维持在每个采样时刻更新的运行解估计而随时间分布。在这封信中，TDO适用于线性MPC的状态和输入约束，使用正则化的原始-对偶梯度下降法作为优化。对收敛速度的详细分析显示了不同的设计选择，即，最大迭代次数、正则化项的值和预测时域长度影响TDO-MPC的稳定性。此外，它表明，显着的稳定性改善，可以实现通过使用闭环范例，以提高最优控制问题的条件数。开环不稳定系统的数值模拟表明，每个设计选择的稳定性和约束满足的整体影响。
Time-distributed Optimization (TDO) is a method for reducing the computational cost of Model Predictive Control (MPC) where optimization iterations are distributed over time by maintaining a running solution estimate that is updated at each sampling instant. In this letter, TDO is applied to linear MPC with state and input constraints using a regularized primal-dual gradient descent method as the optimizer. A detailed analysis of the rate of convergence shows how different design choices, i.e., maximum number of iterations, value of the regularization term, and prediction horizon length, affect the stability of TDO-MPC. Additionally, it is shown that significant stability improvements can be achieved by using the Closed-Loop Paradigm to improve the conditioning number of the optimal control problem. Numerical simulations on an open-loop unstable system demonstrate the overall impact on stability and constraint satisfaction of each design choice.