The following technical report is available from http://aib.informatik.rwth-aachen.de:

Comparative Evaluation and Improvement of Computational Approaches to Reachability Analysis of Linear Hybrid Systems
Ibtissem Ben Makhlouf
AIB 2016-02

This thesis addresses the problem of reachability analysis with the
focus on linear hybrid systems. Hybrid systems are a mixture of
continuous and discrete behaviors. The Hybrid automaton consisting of a
graph, in which the locations describe the continuous and the
transitions the discrete behavior, represents the best formal model for
such kind of systems. It provides a formalism integrating differential equations and logic expressions in a same framework, thus opening new
horizons in research and development of new methods and novel
algorithms. Despite recent progress made in this field in the last
years, actual verification methods and available tools have exhibited
their shortcomings.

We started this work with the assessment of some verification tools
using a suite of benchmarks conceived specially for this task. The
benchmarks possess particular characteristics for testing of efficiency, applicability, scalability, capability and performances of these tools.

We offer a theoretical overview of existing methods for computing an overapproximation of reachable sets for linear time invariant hybrid
systems. This covers approaches for overapproximating reachable sets of
the continuous dynamics with and without invariants as well as methods
for solving the problem of guard intersection at transitions. We
furthermore propose new overapproximation techniques for treating the continuous part as well as the discrete part of the hybrid automaton. We suggest scalable, modular implementations of these diverse methods
allowing thereby possible combinations between them first using support functions and then with zonotopes. The implementations include different approaches for handling invariants, guards and transitions for the above-mentioned set representations. Two toolboxes are the results of
this implementation effort. Both tools integrate the methods described
above. They offer a GUI and allow for a user-configurable reachability analysis. We use both tools to carry out a performance comparison of
different methods. We note thereby that there is a correlation between
these performances and the complexity of the tested example. However, we
note during this survey using the proposed benchmark suite that the
difference in the performance with regards to the tightness of the over-approximation and the computation time is not so crucial for low dimensional systems.

We propose a networked platoon of vehicles to demonstrate different
context where reachability analysis can be useful. We first perform a reachability analysis to determine unsafe gaps between the vehicles
which are controlled using LMI-formalism. Reachability analysis can be
helpful for control design. The choice between controllers on the basis
of reachability results has led to controller ensuring the best
compromise between safe and small gaps when applying H2 or H<UTF16-221E> control
design techniques. Reachability can also be used to determine
time-critical conditions. As demonstration, we opt for a platoon
approaching an intersection.

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