ROUHLING , Damien

In this thesis, we put a library for analysis in the Coq proof assistant to the test through a case study in control theory. We formalise a proof of stability for the inverted pendulum, a standard example in control theory. Controlling the inverted pendulum is challenging because of its non-linearity, so that this system is often used as a...

Control theory provides techniques to design controllers, or control functions, for dynamical systems with inputs, so as to grant a particular behaviour of such a system. The inverted pendulum is a classic system in control theory: it is used as a benchmark for nonlinear control techniques and is a model for several other systems with various...

Large scale reflection tactics are often implemented with ad-hoc data-structures and in a way which is specific to the problematic. This makes it hard to add improvements and to implement variations without writing an extensive theory of the specific data-structures involved. We suggest to replace the core of such tactics with procedures that...

Stability analysis of dynamical systems plays an important role in the study of control techniques. LaSalle's invariance principle is a result about the asymptotic stability of the solutions to a nonlinear system of differential equations and several extensions of this principle have been designed to fit different particular kinds of system. In...

Formalizing analysis on a computer involves a lot of "epsilon-delta" reasoning, while informal reasoning may use some asymptotical hand-waving. Whether or not the arithmetic details are hidden using some abstraction like filters, a human user eventually has to break it down for the proof assistant anyway, and provide a witness for the...

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