Efficient and guaranteed estimation of attainable sets of nonlinear systems

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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.