Fully Automated and Correct-by-Construction Synthesis for Complex Control Problems

在许多应用领域的技术发展越来越多地提出了挑战，在越来越复杂的控制问题的形式，不能完全满足使用经典的控制器综合方法。基于抽象的综合是一种相对较新的方法，与经典方法相比具有明显的优势，例如能够以完全自动化的、按构造校正的方式解决非线性连续状态设备的控制问题，即使对于复杂的控制目标以及存在不确定性和干扰的情况也是如此。然而，目前一些尚未解决的问题妨碍了这一办法的例行应用。 申请人旨在推进基于抽象的控制器综合的理论和计算方法，以促进该方法的实用性。特别是，应该提供的方法，第一，能够解决更复杂的控制问题比现有的基于抽象的方法，第二，保证成功地合成一个控制器执行规范，只要这样的控制器存在，第三，产量控制器是正确的建设。为了实现这些目标，建立技术，以提高效率ofabstraction-based控制器综合，目前只适用于相当简单的控制目标，应扩展到涵盖一类控制目标的公式在线性时序逻辑。此外，这些技术应该与全新的方法相结合，在项目中进行探索，这些方法基于利用合成过程中计算的可达到集合的几何形状，在所有算法级别上调整计算精度，以及摊销验证数值的成本，以再次大幅提高效率。该项目的成功应该通过解决两个具有挑战性的控制问题来证明，这两个问题的处理超出了现有基于抽象的方法的能力。

The technological developments in numerous areas of application are increasingly posing challenges, in the form of more and more complex control problems, that cannot be fully met using classical controller synthesis methods. Abstraction-based synthesis is a relatively recent approach possessing distinct advantages over classical methods, such as the capability of solving control problems for nonlinear continuous-state plants in a fully automated, correct-by-construction fashion, even for complex control objectives and in the presence of uncertainties and disturbances. However, some unresolved issues currently prevent the approach from being routinely applied. The applicant aims at advancing the theory and computational methods for abstraction-based controller synthesis to facilitate the practical applicability of the approach. In particular, methods should be provided that, firstly, are capable of solving more complex control problems than existing abstraction-based methods, that, secondly, are guaranteed to successfully synthesize a controller enforcing the specification whenever such a controller exists, and that, thirdly, yield controllers that are correct by construction. To meet these goals, established techniques to improve the efficiency ofabstraction-based controller synthesis, which currently apply only to rather simple control objectives, should be extended to cover a class of control objectives given as formulas in Linear TemporalLogic. Additionally, these techniques should be combined with entirely new approaches, to be explored in the project, which are based on exploiting the geometry of attainable sets computed in the synthesis process, on the adaptation of the computational accuracy on all algorithmic levels, and on the amortization of the cost of validated numerics, to drastically increase efficiency once again. The success of the project should be demonstrated through the solution of two challenging control problems whose treatment is beyond the capacity of existing abstraction-based methods.