标题： 受约束线性系统的LQG：基于卡尔曼滤波的间接反馈随机MPC 显示英文标题

标题： LQG for Constrained Linear Systems: Indirect Feedback Stochastic MPC with Kalman Filtering

摘要： 我们提出了一种输出反馈随机模型预测控制（SMPC）方法，适用于受高斯扰动和测量噪声影响以及系统状态和输入概率约束的线性系统。 该方法结合了用于状态估计的线性卡尔曼滤波器与间接反馈SMPC，其中间接反馈SMPC以预测的标称状态为初始值，而当前状态估计的反馈通过SMPC问题的目标函数进入。 对于这种组合，由于选择的初始化，我们证明了SMPC问题的递归可行性，并通过适当收紧SMPC问题中的约束条件（同时考虑状态估计不确定性），保证闭环机会约束满足。 此外，我们表明，对于SMPC问题中的特定设计选择，如果对于给定的初始条件和所考虑的约束是可行的，则可以恢复无约束线性二次高斯（LQG）解。 我们通过数值例子验证了这一事实，并展示了由此产生的输出反馈控制器可以提供非保守的约束满足。 显示英文摘要

摘要： We present an output feedback stochastic model predictive control (SMPC) approach for linear systems subject to Gaussian disturbances and measurement noise and probabilistic constraints on system states and inputs. The presented approach combines a linear Kalman filter for state estimation with an indirect feedback SMPC, which is initialized with a predicted nominal state, while feedback of the current state estimate enters through the objective of the SMPC problem. For this combination, we establish recursive feasibility of the SMPC problem due to the chosen initialization, and closed-loop chance constraint satisfaction thanks to an appropriate tightening of the constraints in the SMPC problem also considering the state estimation uncertainty. Additionally, we show that for specific design choices in the SMPC problem, the unconstrained linear-quadratic-Gaussian (LQG) solution is recovered if it is feasible for a given initial condition and the considered constraints. We demonstrate this fact for a numerical example, and show that the resulting output feedback controller can provide non-conservative constraint satisfaction.