Chance-Constrained Model Predictive Control based on Deterministic Density Approximation and Homotopy Continuation

基于确定性密度逼近和同伦延拓的机会约束模型预测控制

基本信息

批准号：
267437392
负责人：
Professor Dr.-Ing. Uwe D. Hanebeck
金额：
--
依托单位：
Lehrstuhl für Intelligente Sensor-Aktor-Systeme (ISAS)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2014
资助国家：
德国
起止时间：
2013-12-31 至 2017-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/267437392?language=en
关键词：
Chance Constrained Model Predictive Control

项目摘要

In Model Predictive Control (MPC), control inputs are obtained by online solving an optimization problem. In order to be applicable in real-world applications, MPC has to provide closed-loop stability and robustness to endogenous and exogenous disturbances. For this purpose, constraints are introduced into the MPC problem. In standard MPC, the constraints are hard, because the disturbances are assumed to be bounded, i.e., they are contained within some closed set. Thus, constraint satisfaction is guaranteed for the worst case scenario ignoring probably available statistical properties of the disturbances. The desire to incorporate statistical properties of disturbances in order to achieve better performance and the additional desire to consider unbounded disturbances modeled as stochastic processes led to the development of chance-constrained MPC. In chance-constrained MPC, hard deterministic constraints are replaced by soft constraints that require that the constraints are satisfied with a specified probability. Chance-constrained MPC can be applied in chemical engineering, robotically-assisted surgery, tracking control, energy-efficient temperature control, etc.The main challenge of chance-constrained MPC is the tractability of the MPC solution process. This process consists of an optimization procedure that generally has to be evaluated numerically using iterative methods. For this purpose, in order to check the constraints at each iteration step, multivariate integrals of probability densities have to be computed. State-of-the-art methods therefore approximate these densities, either by means of conservative deterministic approximations or stochastic sample-based approximations. Both these approaches have their advantages and disadvantages. Conservative deterministic approximations yield low computational burden but they do not find optimal control policies due to their conservatism. Sample-based approximation methods on the other hand are far less conservative but they are not applicable in real-time applications due to their computational burden.In this proposal, we investigate a new MPC approach that combines the advantages of the conservative approximation methods and the stochastic sampling methods. For this purpose, we approximate the occurring densities using a deterministic sample-based method. This approximation method allows to tune the conservatism level by adapting the number of samples. In order to solve the MPC optimization problem, we will apply homotopy continuation methods. These methods first solve the unconstrained control problem for which analytical solutions are available if process and measurement dynamics are linear. Then, the constraints are introduced progressively into the control problem and search algorithms can be applied. We expect the proposed method to be computationally faster than state-of-the-art methods based on stochastic sampling yielding optimization results with the same quality.

在模型预测控制（MPC）中，通过在线解决优化问题获得控制输入。为了适用于现实世界应用，MPC必须为内源性和外源性干扰提供闭环稳定性和鲁棒性。为此，将约束引入到MPC问题中。在标准MPC中，限制很难，因为假定干扰是有界的，即它们包含在某些封闭的集合中。因此，在最坏情况下，保证了限制满意度，忽略了干扰可能可用的统计属性。为了实现更好的性能，以及考虑以随机过程为模型的无界干扰的愿望，渴望纳入干扰的统计特性，从而导致了机会约束的MPC的发展。在偶然受限的MPC中，硬确定性约束被软约束所取代，这些约束要求约束对指定概率满意。偶然受限的MPC可以应用于化学工程，机器人辅助手术，跟踪控制，节能温度控制等。被机会约束的MPC的主要挑战是MPC解决方案工艺的障碍。此过程由一个优化过程组成，通常必须使用迭代方法对数字进行数字评估。为此，为了检查每个迭代步骤的约束，必须计算概率密度的多元积分。因此，最新的方法通过保守的确定性近似值或基于随机样本的近似值近似这些密度。这两种方法都有其优势和缺点。保守的确定性近似值会产生较低的计算负担，但由于保守主义，他们找不到最佳的控制政策。另一方面，基于样本的近似方法的保守程度要差得多，但由于其计算负担，它们不适用于实时应用。在此提案中，我们研究了一种新的MPC方法，该方法结合了保守近似方法和该方法的优势。随机抽样方法。为此，我们使用基于确定性样本的方法近似发生的密度。这种近似方法允许通过调整样本数来调整保守主义水平。为了解决MPC优化问题，我们将采用同型延续方法。这些方法首先解决了不受约束的控制问题，如果过程和测量动态是线性的，则可以为其提供分析解决方案。然后，将约束逐渐引入控制问题，并可以应用搜索算法。我们期望提出的方法比基于随机抽样的最先进方法更快地计算方法，从而得出具有相同质量的优化结果。