标题： LQG 用于约束线性系统：带有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，用于受高斯扰动和测量噪声影响的线性系统，并且系统状态和输入具有概率约束。 所提出的方法结合了一个用于状态估计的线性卡尔曼滤波器与一种间接反馈SMPC，该SMPC以预测的名义状态进行初始化，而当前状态估计的反馈则通过SMPC问题的目标函数引入。 对于这种组合，由于选择的初始化，我们建立了SMPC问题的递归可行性，并通过在SMPC问题中适当收紧约束（同时考虑状态估计不确定性）保证了闭环的概率约束满足性。 此外，我们证明了在SMPC问题中的特定设计选择下，如果对于给定的初始条件和所考虑的约束是可行的，则可以恢复无约束的线性二次高斯（LQG）解。 我们通过一个数值示例验证了这一事实，并表明所得的输出反馈控制器可以提供非保守的约束满足性。 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.