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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广泛的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），具有基于无限视界策略的保证闭环稳定性。经济NMPC是建立在一个非线性目标函数的基础上的，该目标函数由过程运行的收入和成本组成，因此不一定是一个正定函数。因此，由于目标函数不能作为Lyapunov函数，因此不能应用规范NMPC的标准稳定性证明。此外，有限移动视界的概念仍然涉及计算，并不是完全令人满意。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Bellman的最优性原理，该方法自然意味着监管和经济NMPC的稳定性——只要可以计算出足够精确的数值解。首先，研究了时间轴的变换导致有限代价的有限视界问题。为了应用非线性规划中的求解技术，将变换后的有限水平问题离散化。在此基础上，研究了一种新的控制网格自适应策略和邻极值更新等降低计算量的方法。最后，比较了无限视界公式与有限视界公式的闭环性能。可以证明，无限视界公式是一个有希望的替代连续操作过程，没有预先规定的最终时间存在。尽管如此，在算法和方法细节方面仍有悬而未决的问题，将在第四年进行调查。首先，导出具有离散控制动作的连续过程的闭环稳定性。其次，将新的控制网格自适应策略扩展到路径约束的多阶段问题，以保证在视界的暂态部分也有足够好的分辨率。第三，我们将研究具有有限报酬的无限视界公式的数值解。最后，利用邻极值控制器进一步减少了计算时间。