This paper presents a new approach to Model Predictive Control for environments where essential, discrete variables are partially observed. Under this assumption, the belief state is a probability distribution over a finite number of states. We optimize a \textit{control-tree} where each branch assumes a given state-hypothesis. The control-tree optimization uses the probabilistic belief state information. This leads to policies more optimized with respect to likely states than unlikely ones, while still guaranteeing robust constraint satisfaction at all times. We apply the method to both linear and non-linear MPC with constraints. The optimization of the \textit{control-tree} is decomposed into optimization subproblems that are solved in parallel leading to good scalability for high number of state-hypotheses. We demonstrate the real-time feasibility of the algorithm on two examples and show the benefits compared to a classical MPC scheme optimizing w.r.t. one single hypothesis.

翻译：本文针对环境中关键离散变量部分可观测的情况，提出了一种模型预测控制的新方法。在此假设下，信念状态是有限状态上的概率分布。我们优化一棵"控制树"，其中每个分支对应一个给定的状态假设。该控制树优化利用了概率信念状态信息，从而得到更倾向于对高概率状态进行优化、同时对低概率状态仍保证全程鲁棒约束满足的策略。我们将该方法应用于带约束的线性和非线性MPC。控制树的优化被分解为若干子优化问题，通过并行求解实现了对大量状态假设的良好可扩展性。通过两个算例验证了该算法的实时可行性，并展示了与基于单一假设进行优化的经典MPC方案相比的优势。