A well-established method for finding the optimal control policy for a given dynamical system is to solve the problem iteratively going from its terminal state "backwards" in time, known as Dynamic Programming Algorithm. For a generic problem with discrete state/action space, the algorithm has computational complexity of O(NM) for N states and M actions. In this thesis, we propose a novel numerical algorithm that approaches this problem in the conjugate domain, using the so-called Legendre-Fenchel Transform. In essence, the proposed approach is analogous to, and was inspired by Fast Fourier Transform, and how it can be beneficial to do computations/analysis in the frequency domain. In particular, this approach allows us to exploit the structure of the problem (e.g., in LQ control) to drastically reduce the computational complexity to O(N+M). Of course, this computational gain comes with a cost of introducing error. ... Read more

Nowadays, localization of cars is mostly done using GPS. Some major disadvantages of this method are that it is not very accurate and that it cannot be used indoors. These disadvantages do not form a major problem when an active human driver is controlling the car, but will become more critical when the autonomy of vehicles increases. The goal of this project is to use Synthetic Aperture Radar techniques to overcome the problems of GPS. To achieve this, different imaging algorithms have been implemented, and a single method has been extended to directly accommodate the road-mapping application. Different measurements were done to test the algorithms and the results were promising. It is hoped that the use of this technology will become wide-spread and that it can help with creating a safer and more efficient world of traffic, where increased self-driving capabilities are facilitated. ... Read more