Aachen Dynamic Optimization Environment (ADE): Modeling and numerical methods for higher-order sensitivity analysis of differential-algebraic equation systems with optimization criteria

ADE项目的目标是开发具有最优性准则的微分-代数方程组(DAEO)的建模和新的数值方法。在第一个资助期，DAEO数值模拟的关键方法是用其关联的Karush-Kuhn-Tucker(KKT)最优性必要条件代替DAEO的嵌入的非线性程序。该方法将DAEO转化为特殊的非光滑微分-代数方程(DAE)系统。特别是，AVT.SVT部分的任务是针对DAEO采用非光滑DAE系统的仿真/灵敏度分析方法，而STCE部分则专注于模型残差的高阶导数和McCormick松弛的自动生成。后者是后续申请可能涵盖的第二个资助期的基础。在第一个资助期，开发了模拟和敏感性分析的数值方法。在第二阶段，我们的目标是解决最优控制、参数估计或基于模型的试验设计问题。为了求解上层NLP，我们打算使用基于梯度的数值优化算法，如序列二次规划(SQP)或内点法。如果需要，应将较低级别的嵌入NLP求解到全局最优，例如，通过分支定界方法。

The objective of the ADE project is to develop modeling and novel numerical methods for differential-algebraic equations systems with optimality criteria (DAEO). In the first funding period, the key methodology for the numerical simulation of DAEOs was the substitution of the embedded nonlinear program of the DAEO by its associated Karush-Kuhn-Tucker (KKT) necessary conditions of optimality. This approach transforms DAEOs into special nonsmooth differential-algebraic equation (DAE) systems. In particular, the task of AVT.SVT part was to adapt methods for simulation/sensitivity analysis of nonsmooth DAE systems for DAEOs, while the STCE part focused on the automatic generation of higher-order derivatives and McCormick relaxations of the model residuals. The latter form the basis for a potential second funding period covered by the follow-up application at hand.In the first funding period, numerical methods for the simulation and sensitivity analysis of DAEOs were developed. In the second period we aim to solve optimal control, parameter estimation or model-based experimental design problems. To solve the upper level NLP, we intent to use gradient-based numerical optimization algorithms such as sequential quadratic programming (SQP) or interior point methods. If required, the lower level embedded NLP shall be solved to global optimality, e. g. by means of Branch & Bound methods.