Numerical simulation of power systems for real-time simulation applications: This report concerns to the study of FPGA-based electromagnetic transient simulations of power systems. Along its content, the discretization of electric circuits concerning power systems will be treated for RLC circuits and transmission lines. Our goal is to be able to de ne a program that, by reading a text le with the information of a certain network, computes the nodal admittance matrix for the Fixed Admittance Matrix Nodal Method. Several examples will be shown with the comparison between the values obtained from the EMTP-RV simulator software and the ones obtained from our solver in order to validate the model. Finally, the nodal admittance matrix (NAM) will be used in the code programmed for the CompactRIO and its FPGA for real-time simulations. Collision avoidance control design: This semester project has been developed at the Automatic Control Laboratory, at the Swiss Federal Institute of Technology in Lausanne. It is oriented at the implementation of obstacle avoidance algorithms, more concretely at the development of three of the most common algorithms using a user-friendly interface to allow third-party consumers to use them, either for simulation or implementation on real systems. In the paper attached to this report, the disadvantages of one of the implemented algo- rithms will be discussed in detail, and the model predictive control method (MPC) will be described and used to improve its performance to a great extent.