论文标题
LQG用于约束线性系统：与Kalman过滤的间接反馈随机MPC
LQG for Constrained Linear Systems: Indirect Feedback Stochastic MPC with Kalman Filtering
论文作者
论文摘要
我们为线性系统提供了一种输出反馈随机模型预测控制（SMPC）方法，但在系统状态和输入上受到高斯干扰和测量噪声和概率约束的约束。提出的方法将线性卡尔曼过滤器与间接反馈SMPC结合在一起，该滤波器以预测的名义状态初始化，而当前状态估计值的反馈通过SMPC问题的目的进入。对于此组合，由于选择的初始化，我们建立了SMPC问题的递归可行性，并且由于对状态估计不确定性的限制也适当地拧紧了SMPC问题中的约束，因此闭环的机会约束满意度。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，则恢复了无约束的线性界面高斯（LQG）解决方案。我们在数值示例中证明了这一事实，并证明所得的输出反馈控制器可以提供非保守的约束满意度。
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.
