FEANICSES 2018 Workshop

Inspired by Lockheed Martin 2017 S5 presentation we will outline some properties and see how these could be analyzed at code level.

In addition to some cool nonlinearities and positive invariance, it also has an interesting hybrid switch at zero velocity.

In this talk, we present a method to prove or disprove a property on a stable LTI discrete-time system. The method consists in safely replacing an infinite sequence of optimization problems by a finite number of them. This method is based on basic tools from matrix theory such as Rayleigh ratios, spectral analyses and matrix norms.

This talk concerns the computation of positively invariant sets for uncertain, discrete-time linear systems and the corresponding synthesis of invariance-inducing controllers. Positive invariance plays an important role in robust control to guarantee the satisfaction of safety constraints under "worst case uncertainty". To describe positively invariant sets, polytopes are used since they are simple enough to certify invariance through linear programming, yet expressive enough to be applicable to a wide range of problems. In our talk, a connection will be established between invariant polytope synthesis and lattice theory, providing a foundation for set-theoretic analysis using polytopes. We will provide a tutorial overview, along with examples, of methods used for the computation of minimal and maximal positively invariant sets on a polytopic subset of the state space. The applicability, and particularity the scalability with respect to the state space dimension, of these methods will be elucidated in view of practical systems. Finally, several invariance-inducing control strategies will be proposed.

This talk introduces the main concepts of DynIBEX library that can handle differential constraints in constraint programming framework. After some examples of use, a focus on the first elements of optimal control problem solving using DynIBEX will be given.