论文标题
模型预测控制中约束违规概率的最小化
Minimization of Constraint Violation Probability in Model Predictive Control
论文作者
论文摘要
尽管强大的模型预测控制考虑了最坏情况系统的不确定性，但随机模型预测控制使用机会约束，通过允许根据预定义的风险参数允许某些约束违规概率来提供较不保守的解决方案。但是，对于安全至关重要的系统，不仅要限制约束违规概率，而且要尽可能降低这种概率。因此，必须采用一种方法，以最大程度地减少约束违规概率，同时确保模型预测控制优化问题仍然可行。我们提出了一种新型的模型预测控制方案，该方案在不确定性的环境中产生对规范约束的违反概率的解决方案。确保最小的约束违规行为后，还针对其他控制目标进行了优化解决方案。此外，可以考虑随着不确定性支持的时间的变化。我们首先提出一种通用方法，然后提供一种具有对称，单峰概率密度函数的不确定性的方法。证明了该方法的递归可行性和收敛性。一个模拟示例证明了所提出的方法的有效性。
While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability depending on a predefined risk parameter. However, for safety-critical systems it is not only important to bound the constraint violation probability but to reduce this probability as much as possible. Therefore, an approach is necessary that minimizes the constraint violation probability while ensuring that the Model Predictive Control optimization problem remains feasible. We propose a novel Model Predictive Control scheme that yields a solution with minimal constraint violation probability for a norm constraint in an environment with uncertainty. After minimal constraint violation is guaranteed the solution is then also optimized with respect to other control objectives. Further, it is possible to account for changes over time of the support of the uncertainty. We first present a general method and then provide an approach for uncertainties with symmetric, unimodal probability density function. Recursive feasibility and convergence of the method are proved. A simulation example demonstrates the effectiveness of the proposed method.
