Logiciels, Prototypes et Démonstrateurs

SOFTWARE

  • Validated Computing Software - We propose efficient numerical routines together with sure and reasonably tight error bounds. Applications: computer aided proofs, certification of numerical results in safety-critical control systems (e.g., cyber-physical systems):
    • RealCertify:  Maple package to tackle the problem of deciding the non-negativity of rational polynomials over semi-algebraic domains defined by polynomial constraints with rational coefficients. This is done by computing sum of squares certificates of non-negativity for inputs where such certificates hold over the rational numbers. It can be applied to numerous problems coming from engineering sciences, program verification and cyber-physical systems. It is based on hybrid symbolic-numeric algorithms relying on semi-definite programming. Developed by/with the help of: Victor Magron, Mohab Safey El Din. Freely available.  
  • SATAW-Tool - Matlab Toolbox for analysis and controller design in presence of saturation elements in the control loop. LMI based functionalities are provided, where sector conditions are used for the saturation modeling. It is entirely written in Matlab and uses YALMIP for parsing LMIs, the optimization problems being solved using any SDP free solvers supported by YALMIP ou using LMILAB (not recommended for relatively high dimension problems). Can be freely downloaded and used. Developed by Isabelle Queinnec and Sophie Tarbouriech
  • GloptiPoly 3 - Moments, optimization and semidefinite programming. Matlab parser for generalized problems of moments. Allows to build and solve convex linear matrix inequality (LMI) relaxations of the (generally non-convex) global optimization problem of minimizing a multivariable polynomial function subject to polynomial inequality, equality or integer constraints.  Can be freely downloaded and used. Developed by Didier Henrion, Jean-Bernard Lasserre and Johan Lofberg (ETH, Zurich). 
  • R-RoMulOC - Randomized and robust multi-objective control toolbox for Matlab. Modeling and robustness analysis based on LMI techniques. Works with parser YALMIP, all control problems are solved by SDP solvers such as SeDuMi, CSDP, DSDP, SDPT3... Can be freely downloaded and used. Main developer: Dimitri Peaucelle.
  • HIFOO - A Matlab package for fixed-order controller design and H-infinity optimization, using a hybrid algorithm for nonsmooth, nonconvex optimization based on quasi-Newton updating, bundling and gradient sampling. Can be freely downloaded and used. Main developer: Michael L. Overton (Courant Institute, NY).
  • TSSOS - This is a new open source Julia library developed for large-scale polynomial optimization, based on the sparsity adapted moment-SOS hierarchies. Related modules can perform complex polynomial optimization, eigenvalue/trace optimization of noncommutative polynomials, compute joint spectral radii for stability analysis, approximate attractors and invariants of sparse dynamical systems. Developed by/with the help of: Victor Magron, Jie Wang. Freely available.

 

HELICOPTER BENCHMARK

The Helicopter setup consists of a base on which a long arm is mounted. The arm carries the helicopter body on one end and a counterweight on the other end. The arm can tilt on an elevation axis as well as swivel on a vertical (travel) axis. Quadrature optical encoders mounted on these axes measure the elevation and travel of the arm. The helicopter body, which is mounted at the end of the arm, is free to pitch about the pitch axis. The pitch angle is measured via a third encoder. Two motors with propellers mounted on the helicopter body can generate a force proportional to the voltage applied to them. The force, generated by the propellers, causes the helicopter body to lift off the ground and/or to rotate about the pitch axis. All electrical signals to and from the arm are transmitted via a slipping with eight contacts. The system is also equipped with a motorized lead screw that can drive a mass along the main arm in order to impose known controllable disturbances (the so-called Active Disturbance Option, ADO). 

This Helicopter is a Quanser product.