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

该项目的总体目标是为广泛的模型预测控制问题，特别是经济非线性模型预测控制问题（NMPC），开发有效的算法，保证闭环稳定性的基础上的无限时域策略。经济NMPC是基于一个非线性的目标函数，包括收入和成本的过程操作，这是不一定是一个正定函数。因此，标准的稳定性证明监管NMPC不能应用的目标函数不能作为一个李雅普诺夫函数。此外，有限移动地平线的概念仍然涉及计算，并不完全令人满意。在这个项目的前三年，我们探索了一种替代配方依赖于无限地平线的方法。通过应用贝尔曼的最优性原理，这种方法自然意味着稳定的监管以及经济NMPC -提供了一个足够准确的数值解可以计算。首先，时间轴的转换导致有限的时间范围内的问题，有界的成本进行了调查。为了应用非线性规划的求解技巧，将变换后的有限时域问题离散化。随后，几种可能性，以减少计算负荷，同时保持足够的解决方案的精度进行了研究，如一种新的控制网格自适应策略和相邻极值更新。最后，闭环性能的无限地平线配方进行了比较，有限地平线配方。它可以表明，无限时域配方是一个有前途的替代连续操作的过程，没有预先指定的最终时间存在。尽管如此，在算法和方法细节方面仍然存在悬而未决的问题，这些问题将在第四年进行调查。首先，闭环稳定性将推导出连续时间过程的离散时间控制动作。其次，新的控制网格自适应策略将被扩展为路径约束的多阶段问题，以保证足够好的分辨率也在地平线的瞬态部分。第三，我们将研究具有有限回报的无限时域公式的数值解。最后，计算时间将进一步减少与相邻极值控制器的帮助下。

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.