Approximation of reachable sets using optimal control and support vector machines

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of a function chosen in a reproducing kernel Hilbert space. In some sense, the method can be considered as an extension to the optimal control algorithm approach recently developed by Baier, Gerdts and Xausa. The convergence of the method is illustrated numerically for selected examples

Towards optimal space-time discretization for reachable sets of nonlinear control systems

Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial discretizations of Euler's method for reachable set computation in a non-uniform way to improve the performance of the method

Some perspectives on the analysis and control of complementarity systems

International audienceThis paper is devoted to presenting controllability and stabilizability issues associated to a class of nonsmooth dynamical systems, namely complementarity dynamical systems. The main existing results are summarized, and some possible research directions are provided. Convex analysis and complementarity problems are claimed to be the main analysis tools for control related studies. This paper mainly focuses on mechanical applications