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.

该项目的总体目的是为广泛的模型预测控制问题（尤其是经济非线性模型预测性控制问题（NMPC））开发有效的算法，并确保基于无限地平线策略的闭环稳定性。经济NMPC基于非线性目标函数，该目标函数由过程运营的收入和成本组成，因此不一定是正常功能。因此，由于目标函数不能用作Lyapunov函数，因此无法应用监管NMPC的标准稳定性证明。此外，有限的移动视野概念仍在计算上涉及，并且不完全令人满意。在该项目的头三年中，我们探索了一种依靠无限范围方法的替代配方。通过应用Bellman的最优原则，这种方法自然意味着可以计算出足够准确的数值解决方案，以进行调节和经济NMPC。首先，研究了时间轴的转换，导致有限的地平线问题和有限成本。为了应用非线性编程的解决方案技术，转换有限的地平线问题被离散化。随后，研究了减少计算负荷的几种可能性，同时研究了足够的解决方案准确性，例如新型的控制网格适应策略和相邻的超级更新。最后，将无限地平线配方的闭环性能与有限的地平线配方进行了比较。可以表明，无限 - 摩尼子公式是连续操作的过程的有前途的替代方法，不存在预先指定的最终时间。尽管如此，关于算法以及方法论细节仍然存在开放问题，这些细节应在第四年进行调查。首先，对于具有离散时间控制移动的连续时间过程，闭环稳定性将得出。其次，新颖的控制网格适应策略将扩展到路径约束的多阶段问题，以确保在地平线的瞬态部分中也有足够的良好分辨率。第三，我们将使用有限的奖励研究无限 - 马配方的数值解。最后，借助相邻的超级控制器将进一步缩短计算时间。