Nonlinear model-predictive control and dynamic real-time optimization on infinite horizons

无限范围内的非线性模型预测控制和动态实时优化

基本信息

批准号：
152353704
负责人：
Professor Dr.-Ing. Wolfgang Marquardt
金额：
--
依托单位：
Forschungszentrum Jülich
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2009
资助国家：
德国
起止时间：
2008-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/152353704?language=en
关键词：
Nonlinear model predictive control dynamic

项目摘要

The overall objective of this project is to develop efficient algorithms for a wide range of model-predictive control problems, in particular economic nonlinear model-predictive control problems (NMPC), with guaranteed closed-loop stability based on an infinite horizon strategy. Economic NMPC is based on a nonlinear objective function consisting of revenues and costs for process operation, which is thus not necessarily a positive-definite function. Consequently, standard stability proofs for regulatory NMPC cannot be applied as the objective function cannot serve as a Lyapunov function. Furthermore, finite moving horizon concepts are still computationally involved and not completely satisfactory.In the first three years of this project, we explored an alternative formulation relying on an infinite horizon approach. By applying Bellman's principle of optimality, this method naturally implies stability for regulatory as well as economic NMPC - provided a sufficiently accurate numerical solution can be computed. First, a transformation of the time axis was investigated leading to a finite horizon problem with bounded costs. In order to apply solution techniques from nonlinear programming, the transformed finite horizon problem was discretized. Subsequently, several possibilities to reduce computational load while maintaining sufficient solution accuracy were investigated such as a novel control grid adaptation strategy and neighboring-extremal updates. Finally, the closed-loop performance of the infinite horizon formulation was compared to a finite horizon formulation. It could be shown that the infinite-horizon formulation is a promising alternative for continuously operated processes for which no prespecified final time exists. Nonetheless, there remain open issues regarding algorithmic as well as methodological details which shall be investigated in the fourth year. First, closed-loop stability will be derived for continuous-time processes with discrete-time control moves. Second, the novel control grid adaptation strategy will be extended for path-constrained multi-stage problems in order to guarantee a sufficiently good resolution also in the transient parts of the horizon. Third, we will investigate the numerical solution of the infinite-horizon formulation with finite rewards. Finally, computational time will be further reduced with the help of a neighboring-extremal controller.

该项目的总体目标是为各种模型预测控制问题开发有效的算法，特别是经济非线性模型预测控制问题（NMPC），并基于无限视野策略保证闭环稳定性。经济 NMPC 基于由过程操作的收入和成本组成的非线性目标函数，因此不一定是正定函数。因此，监管 NMPC 的标准稳定性证明不能应用，因为目标函数不能充当 Lyapunov 函数。此外，有限移动视界概念仍然涉及计算，并不完全令人满意。在这个项目的前三年，我们探索了一种依赖于无限视界方法的替代公式。通过应用贝尔曼的最优性原理，该方法自然意味着监管和经济 NMPC 的稳定性 - 前提是可以计算出足够准确的数值解。首先，研究了时间轴的变换，导致了具有有限成本的有限范围问题。为了应用非线性规划的求解技术，将变换后的有限层问题离散化。随后，研究了在保持足够的解精度的同时减少计算负载的几种可能性，例如新颖的控制网格自适应策略和邻近极值更新。最后，将无限水平公式与有限水平公式的闭环性能进行了比较。可以证明，对于不存在预先指定的最终时间的连续运行过程，无限视野公式是一种有前途的替代方案。尽管如此，关于算法和方法细节仍然存在悬而未决的问题，应在第四年进行调查。首先，将针对具有离散时间控制运动的连续时间过程导出闭环稳定性。其次，新颖的控制网格自适应策略将扩展到路径约束的多阶段问题，以保证在视野的瞬态部分也有足够好的分辨率。第三，我们将研究具有有限奖励的无限范围公式的数值解。最后，在邻近极值控制器的帮助下，计算时间将进一步减少。