Nonlinear model predictive control with Timed-Elastic-Bands

随着技术过程变得越来越复杂，对它们的控制和自动化的要求也增加了。因此，明确考虑过程约束(如控制和状态变量的限制)的控制概念在研究和应用中越来越重要。在这种背景下，预测控制器提供了一种重复地解决非线性动态过程的滚动最优控制问题的手段。在过去的十年里，人们对预测控制的数值高效实现的兴趣大大增加，以便使其能够被广泛应用，甚至对于具有快速动态的机电系统也是如此。到目前为止，预测控制中的大多数方法都局限于二次代价泛函的最小化，特别是控制误差和努力。然而，这些传统的公式不适合于时间最优的控制任务。考虑到这些目标，本研究项目致力于开发非线性预测控制的创新方法，并在状态表示和代价函数中明确考虑时间信息。本项目主要关注两个核心目标：第一，将模型预测控制推广到时间最优控制任务及其有效计算；第二，利用专用的有效数值解逼近一般控制任务的最优控制问题。研究计划包括基于所谓的时间弹性带的有效模型预测控制新方法的概念、发展、实现和评价。在仿真和实验中对新方法和已有方法进行了对比研究，分析了预测控制和闭环控制在干扰下的计算量、控制性能以及鲁棒性。

As technical processes become progressively more complex, the demands on their control and automation increase as well. Hence control concepts that explicity consider process constraints such as limitations of control and state variables gain importance in research and applications. In this context predictive controllers provide a means to repeatedly solve a receding horizon optimal control problem for nonlinear dynamic processes. Within the past decade the interest in numerical efficient realizations of predictive control has grown considerably in order to enable their widespread utilization even for mechatronic systems with fast dynamics. Until nowadays the majority of approaches in predictive control are restricted to the minimization of quadratic cost functionals, in particular control error and effort. However, these conventional formulations are not suited for time-optimal control tasks. With these objectives in mind, the research project devotes itself to the development of innovative methods for nonlinear predictive control with explicit consideration of temporal information in state representation and cost function. This project focusses on two central objectives: Firstly, extension of model predictive control to time-optimal control tasks and their efficient computation and secondly, approximation of the optimal control problem for general control tasks with dedicated efficient numeric solvers.The research programme involves the conception, development, realization and valuation of a new approach for efficient model predictive control that is based on so called Timed-Elastic-Bands. A comparative investigation among the novel approach and established methods is carried out in simulations and experiments including the analysis of computational effort, control performance as well as robustness of the prediction and closed-loop control under disturbances.