Modified Dynamic Programming Algorithms for GLOSA Systems with Stochastic Signal Switching Times

A discrete-time stochastic optimal control problem was recently proposed to address the GLOSA (Green Light Optimal Speed Advisory) problem in cases where the next signal switching time is decided in real time and is therefore uncertain in advance. The corresponding numerical solution via SDP (Stochastic Dynamic Programming) calls for substantial computation time, which excludes problem solution in the vehicle's on-board computer in real time. To overcome the computation time bottleneck, as a first attempt, a modified version of Dynamic Programming, known as Discrete Differential Dynamic Programming (DDDP) was recently employed for the numerical solution of the stochastic optimal control problem. The DDDP algorithm was demonstrated to achieve results equivalent to those obtained with the ordinary SDP algorithm, albeit with significantly reduced computation times. The present work considers a different modified version of Dynamic Programming, known as Differential Dynamic Programming (DDP). For the stochastic GLOSA problem, it is demonstrated that DDP achieves quasi-instantaneous (extremely fast) solutions in terms of CPU times, which allows for the proposed approach to be readily executable online, in an MPC (Model Predictive Control) framework, in the vehicle's on-board computer. The approach is demonstrated by use of realistic examples. It should be noted that DDP does not require discretization of variables, hence the obtained solutions may be slightly superior to the standard SDP solutions

Global Exponential Stabilization of Freeway Models

This work is devoted to the construction of feedback laws which guarantee the robust global exponential stability of the uncongested equilibrium point for general discrete-time freeway models. The feedback construction is based on a control Lyapunov function approach and exploits certain important properties of freeway models. The developed feedback laws are tested in simulation and a detailed comparison is made with existing feedback laws in the literature. The robustness properties of the corresponding closed-loop system with respect to measurement errors are also studied.Comment: Generalization of previous versions. 32 pages, 9 figures, submitted to the International Journal of Robust and Nonlinear Control for possible publicatio

Forward Completeness and Applications to Control of Automated Vehicles

Forward complete systems are guaranteed to have solutions that exist globally for all positive time. In this paper, a relaxed Lyapunov-like condition for forward completeness is presented for finite-dimensional systems defined on open sets that does not require boundedness of the Lyapunov-like function along the solutions of the system. The corresponding condition is then exploited for the design of autonomous two-dimensional movement, with focus on lane-free cruise controllers for automated vehicles described by the bicycle kinematic model. The derived feedback laws (cruise controllers) are decentralized and can account for collision avoidance, roads of variable width, on-ramps and off-ramps as well as different desired speed for each vehicle.Comment: 30 pages, 9 figure