Linear Parameter-Varying Control - Complexity of Analysis, Synthesis and Implementation

实际中遇到的系统往往只能用非线性或时变的微分方程组来准确地表示。线性变参数控制是建模和控制这类系统的一种有吸引力的框架，因为控制器综合工具可以保证在整个运行范围内的稳定性和性能。尽管这些工具已经支持了许多成功的应用程序，但它们的使用仅限于低复杂性的系统。我们解决了不同类型的复杂性带来的挑战：分析、综合和实现复杂性，每种复杂性都构成了在控制器设计的不同阶段需要克服的障碍。这将在四个工作包中完成。第一个涉及在使用不同类型的LPV表示时，在分析、综合和实施中遇到的问题的复杂性的评估。将提出基于到不同等价形式的变换或基于近似的用于减少调度参数的数量的方法。由于基于近似模型的综合控制器将使稳定性和性能保证失效，第二个工作包将开发一个后验分析工具，用于检查当控制器应用于原始对象时，保证是否仍然成立。这样做的一个重要好处是，在使用简单的综合方法获得低实现复杂性的控制器之后，可以以降低的保守性执行离线分析。将这一方法进一步推广，第三个工作包将致力于将这些分析结果转化为综合方法，从基于近似模型的初始控制器开始，并基于准确的对象模型在分析和综合之间迭代。更复杂的方法将包括组合的梯度-LMI算法，以有效地解决潜在的非线性优化问题。当稳定性和性能保证已经丧失，需要通过优化控制器参数来恢复时，这种综合技术也将被使用。对于更一般的LPV表示，我们建议研究已经为经典增益调度技术开发的分析方法。在第四个工作包中，所开发的方法将在汉堡理工大学提供的一些具有挑战性的植物上进行实验验证。

Systems encountered in practice can often only be accurately represented by nonlinear or time-varying sets of differential equations. The paradigm of linear parameter-varying control is an attractive framework for modelling and controlling such systems, due to the availability of controller synthesis tools that guarantee stability and performance in the whole operating range. Even though these tools have already enabled many successful applications, their use is limited to systems of low complexity. We address challenges imposed by different types of complexity: analysis, synthesis and implementation complexity, each posing obstacles to be overcome in different stages during controller design. This will be done in four work packages. The first deals with the assessment of complexity of problems encountered in analysis, synthesis and implementation when using different types of LPV representations. Methods for the reduction of the number of scheduling parameters will be proposed that are based either on a transformation into different equivalent forms or on an approximation. As synthesizing controllers based on approximated models will render stability and performance guarantees void, the second work package will develop a posteriori analysis tools for checking whether guarantees still hold when the controller is applied to the original plant. An important benefit of this will be that off-line analysis can be performed with reduced conservatism, after simple synthesis methods have been used to obtain controllers of low implementation complexity. Taking this approach further, the third work package will aim at turning these analysis results into synthesis methods, starting with initial controllers based on approximated models and iterating between analysis and synthesis based on an accurate plant model. More sophisticated approaches will include combined gradient-LMI algorithms for efficiently solving the underlying nonlinear optimization problem. Such synthesis techniques will also be used when stability and performance guarantees have been lost and need to be recovered by optimizing the controller parameters.For more general LPV representations, we propose to investigate analysis methods that have been developed for classical gain-scheduling techniques. In the fourth work package the developed methods will be validated experimentally on a number of challenging plants, which are available at the Hamburg University of Technology.