针对观测受控制影响的系统，提出新型预测控制方法提升估计精度与决策可靠性。
Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Control
- 在状态估计中引入输入依赖的卡尔曼滤波，直接规划信念空间演化
- 实验显示新方法在特定场景下优于传统分离原理控制器和其MPC变体
- 能降低估计协方差，做出更考虑不确定性的动作选择，适合高不确定性环境
我们研究具有双线性观测的线性系统的有限时域二次控制问题，其中控制输入不仅影响状态动态，还影响状态的部分观测。在此设定下，由于控制输入影响未来状态估计质量，分离原理可能失效。状态估计需采用依赖输入的卡尔曼滤波器，其增益与误差协方差随控制输入变化。为此，我们提出信念空间模型预测控制（B-MPC）方法，直接在估计状态及其误差协方差上进行规划。B-MPC使用由输入依赖卡尔曼滤波器定义的信念演化的确定性代理模型进行规划。在两个合成设置的数值实验中，我们证明B-MPC在有利条件下可超越分离原理控制器及其MPC变体，且这些优势伴随着更低的估计协方差和更注重不确定性的动作选择。
原文摘要 · Abstract (English)
We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. In this setting, the separation principle can fail because control inputs influence the future quality of state estimates. State estimation requires an input-dependent Kalman filter whose gain and error covariance evolve as functions of the control inputs. To address this challenge, we propose a belief-space model predictive control ($\texttt{B-MPC}$) method that plans directly over both the estimated state and its error covariance. In particular, $\texttt{B-MPC}$ plans with a deterministic surrogate of the belief evolution defined by the input-dependent Kalman filter. Through numerical experiments in two synthetic settings, we show that $\texttt{B-MPC}$ can outperform both the separation-principle controller and its MPC variant in favorable regimes, and that these gains are accompanied by lower estimation covariance and more uncertainty-aware action choices.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。