Efficient and guaranteed estimation of attainable sets of nonlinear systems

可得集是控制与系统理论中的一个重要概念。申请人寻求开发算法来高估非线性连续时间系统的可实现集。这些算法应该特别适合于基于抽象的控制器综合的目的，并且应该通过三个属性将自己与其他方法区分开来：首先，在任何情况下，计算估计都应该是正确的。保证合成控制器实际解决了控制问题，从而允许它们在安全关键应用程序中使用。其次，算法应该足够有效，以允许对比竞争方法更高状态空间维的植物合成控制器。最后，合成控制器应该足够简单，可以在便宜的硬件上实现。为此，申请人开发的面向集合的方法将被扩展，以考虑方法的任何误差，使用先验和后验误差估计。在这样做时，适合于初始值大变化的方法将与适合于小数值和舍入误差的方法相结合。

Attainable sets are an important concept of control and systems theory. The applicant seeks to develop algorithms to over-estimate attainable sets for nonlinear continuous-time systems. These algorithms should be suitable particularly for the purpose of abstraction-based controller synthesis and should distinguish themselves from other approaches by three properties: Firstly, in any circumstance, the computes estimates should be correct. The guarantees that the synthesized controllers actually solve the control problems, which permits their use in safety-critical applications. Secondly, the algorithms should be sufficiently efficient that they permit the synthesis of controllers for plants of higher state space dimensionsthan competing methods. Finally, the synthesized controllers should be simple enough to be implementable on inexpensice hardware. To this end, set-oriented methods developed by the applicant will be extendedto take into account any error of the method, using both a-priori and a-posteriori error estimates. In doing so, methods appropiate for large variations in initial values will be combined with methods suitable for small numerical and rounding errors.