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Numerical Optimization Methods for the Falsification of Hybrid Dynamical Systems
Kuřátko, Jan ; Ratschan, Stefan (advisor) ; Bergamaschi, Luca (referee) ; Lukšan, Ladislav (referee)
Title: Numerical Optimization Methods for the Falsification of Hybrid Dynamical Systems Author: Jan Kuřátko Department: Department of Numerical Mathematics Supervisor: Stefan Ratschan, Institute of Computer Science, The Czech Academy of Sciences Abstract: This thesis consists of three published papers that contribute to the finding of error trajectories of hybrid dynamical systems. A hybrid dynamical system is a dynamical system that has both discrete and continuous state. For example, one can use it as a model for a thermostat in a room: Such a thermostat may have two discrete states, one where the heating is off, and another one, where the heating is on. Its continuous state is the temperature in the room. For such a model one may be interested in finding an error trajectory, that is, an evolution of the system that reaches an unsafe state that is to be avoided. Industry is in need of methods for automatized testing and verification of safety conditions in order to identify flaws in the design of systems. The thesis contains several contributions to finding error trajectories that are based on numerical optimization. Keywords: optimization, dynamical systems, saddle-point matrix
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