Prof. Nacim Ramdani

Interval methods are computational methods that can perform, in a natural way, nonlinear computations with sets of real numbers. They are at the core of guaranteed system solving methods that can prove the existence of a solution and, if the latter is not unique, compute the set of all solutions while taking into account all sources of uncertainty. Interval methods have been successfully used to solve diverse engineering and control issues. Quite interestingly, they can also address reachability analysis for uncertain complex dynamical systems. In this talk, I will briefly overview theories and algorithms underlying interval methods among which interval analysis, constraint programming and reliable numerical solving of differential equations. Then, I will illustrate and emphasize these interval methods on two challenging applications. (i) I will show how one can plan and fast re-plan safe motions for a humanoid robot while ensuring its safety, balance, and integrity over the whole motion duration [S.Lengagne, N.Ramdani & P.Fraisse. Planning and fast re-planning safe motions for humanoid robots, IEEE Transactions on Robotics 27(6): 1095-1106, 2011]. (ii) Then, I will show how one can compute the set reachable by a nonlinear hybrid dynamical system in presence of uncertainty [N.Ramdani &N.S.Nedialkov, Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint propagation techniques, Nonlinear Analysis: Hybrid Systems, 5(2): 149-162, 2011].