Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma.We derive robust practical stabilizability results by quantized and ternary controllers and apply them to a few control problems.

Dynamic modeling and control of dc-dc series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely contin...

In this paper we present the continuous and discontinuous Galerkin methods in a unified setting for the numerical approximation of the transport dominated advection-reaction equation. Both methods are stabilized by the interior penalty method, more precisely by the jump of the gradient in the continuous case whereas in the discontinuous case the stabilization of the jump of the solution and opt...

A tutorial on solutions, nonsmooth analysis, and stability Discontinuous dynamical systems arise in a large number of applications. In optimal control problems, open-loop bang-bang controllers switch discontinuously between extreme values of the inputs to generate minimum-time trajectories from the initial to the final states [1]. Thermostats implement on-off controllers to regulate room temper...

A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE’s is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions ...

We compare numerically the performance of a new continuous-discontinuous finite element method (CDFEM) for linear convection-diffusion equations with three well-known upwind finite element formulations, namely with the streamline upwind Petrov-Galerkin finite element method, the residualfree bubble method and the discontinuous Galerkin finite element method. The defining feature of the CDFEM is...

We introduce a new method for incremental shift-reduce parsing of discontinuous constituency trees, based on the fact that discontinuous trees can be transformed into continuous trees by changing the order of the terminal nodes. It allows for a clean formulation of different oracles, leads to faster parsers and provides better results. Our best system achieves an F1 of 80.02 on TIGER.