Nonlinear Basis Pursuit

In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit. In contrast to the existing nonlinear compressive sensing methods, the new algorithm that solves the nonlinear basis pursuit problem is convex and not greedy. The novel algorithm enables the compressive sensing approach to be used for a broader range of applications where there are nonlinear relationships between the measurements and the unknowns

Model Predictive Control for Integrated Lateral Stability

This paper studies the design of a Model Predictive Controller (MPC) for integrated lateral stability, traction/braking control, and rollover prevention of electric vehicles intended for very high speed (VHS) racing applications. We first identify the advantages of a state-of-the-art dynamic model in that it includes rollover prevention into the MPC (a total of 8 states) and also linearizes the tire model prior to solving the MPC problem to save computation time. Then the design of a novel model predictive controller for lateral stability control is proposed aimed for achieving stable control at top speed significantly greater than typical highway speed limits. We have tested the new solution in simulation environments associated with the Indy Autonomous Challenge, where its real-world racing conditions include significant road banking angles, lateral position tracking, and a different suspension model of its Dallara Indy Lights chassis. The results are very promising with a low solver time in Python, as low as 50 Hz, and a lateral error of 30 cm at speeds of 45 m/s. Our open source code is available at: https: //github.com/jadyahya/Roll-Yaw-and-Lateral-Velocity-MPC/.Comment: 8 Pages, 10 figure