Flat Hybrid Automata for Automation and Control of Hybrid Systems

Differential flatness and hybrid systems are established concepts in the automation and control of dynamic systems. The system property of differential flatness allows for greatly simplified control of linear and non-linear systems. Hybrid systems, on the other hand, are a highly expressive modeling approach due to the combination of discrete and continuous variables. Within this area, Hybrid Automata (HA) are considered the most fundamental model class, as they can represent almost all other hybrid system models. However, the combination of the expressiveness of HA with the simplification offered by differential flatness has not yet been studied and formalized. In this thesis, we therefore address the questions of how the concept of flatness can be applied to HA and what possibilities and limitations this approach entails.
In the first part of the thesis, we present the fundamental theory and define the relevant objects and concepts. First, we extend the concept of differential flatness to apply it to finite automata. To this end, we use the definition of flatness from behavioral system theory, which is based on equivalence relations of trajectories. ... mehrFundamental to the flatness of automata are a strongly connected automaton graph and the controllability of events. Based on these considerations, we propose a definition of flatness for HA, which we refer to as flat hybrid automata (FHA). The definition comprises three fundamental properties: flatness of continuous dynamics, a strongly connected automaton graph, and the reachability of guard sets. These properties ensure that all paths through the automaton can be realized.
The reachability of guard sets is a property that is not easy to demonstrate. We therefore investigate both theoretical properties and numerical methods to determine the reachability of switching conditions. We use the linearized representation of flat dynamics to derive sufficient conditions for reachability. We use optimization algorithms for the numerical determination of reachability.
In the last part of the thesis, we apply the results to a total of four example systems. We present examples of hybrid system models from electrical engineering, mechatronics, and process engineering. For these systems, we demonstrate the modeling as FHA in detail and check their flatness properties. We then apply feedforward control and optimized trajectory planning to these systems. In doing so, we examine the specific properties and possibilities of the presented FHA model with respect to these control approaches.