论文标题
两侧频率约束随机模型预测控制具有未知噪声分布的分布强大的优化方法
A distributionally robust optimization approach to two-sided chance constrained stochastic model predictive control with unknown noise distribution
论文作者
论文摘要
在这项工作中，我们提出了一个分布强大的随机模型预测性控制（DR-SMPC）算法，以解决两面机会约束的离散时间线性线性系统被添加剂噪声损坏的问题。应对双面机会限制的普遍机制是所谓的风险分配方法，该方法通过应用Boole的不平等，保守地近似具有两个单一机会限制的双面机会约束。在该提出的DR-SMPC框架中，采用了确切的可拖动二阶方法（SOC）方法来通过考虑噪声的第一和第二矩来抽象双面机会限制。提出的DR-SMPC算法能够确保违反安全限制的上限和下限的最坏情况概率在预先指定的最大概率（PSMP）之内。通过灵活调整此PSMP，对于SMPC问题，可以增加初始状态的可行区域。拟议的DR-SMPC的递归可行性和收敛性是通过引入名义状态的二进制初始化策略来严格建立的。进行了两种实际情况的模拟研究，以证明拟议的DR-SMPC算法的有效性。
In this work, we propose a distributionally robust stochastic model predictive control (DR-SMPC) algorithm to address the problem of two-sided chance constrained discrete-time linear system corrupted by additive noise. The prevalent mechanism to cope with two-sided chance constraints is the so-called risk allocation approach, which conservatively approximates the two-sided chance constraints with two single chance constraints by applying the Boole's inequality. In this proposed DR-SMPC framework, an exact tractable second-order cone (SOC) approach is adopted to abstract the two-sided chance constraints by considering the first and second moments of the noise. The proposed DR-SMPC algorithm is able to guarantee that the worst-case probability of violating both the upper and lower limits of safety constraints is within the pre-specified maximum probability (PsMP). By flexibly adjusting this PsMP, the feasible region of the initial states can be increased for the SMPC problem. The recursive feasibility and convergence of the proposed DR-SMPC are established rigorously by introducing binary initialization strategy of nominal state. Simulation studies of two practical cases are conducted to demonstrate the effectiveness of the proposed DR-SMPC algorithm.
