Efficient and guaranteed estimation of attainable sets of nonlinear systems

属性集是控制和系统理论中的一个重要概念。本申请人寻求开发算法以过度估计非线性连续时间系统的可达到集合。这些算法应特别适合于基于抽象的控制器综合的目的，并应区别于其他方法的三个属性：首先，在任何情况下，计算估计应该是正确的。保证了合成控制器实际上解决了控制问题，这允许它们在安全关键应用中使用。其次，算法应该是足够有效的，他们允许合成的控制器的植物更高的状态空间dimensionsthan竞争的方法。最后，合成的控制器应该足够简单，可以在廉价的硬件上实现。为此，申请人开发的面向集合的方法将被扩展以考虑到该方法的任何误差，使用先验和后验误差估计。在这样做时，将把适用于初始值大变化的方法与适用于小数值和舍入误差的方法结合起来。

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.