![]() the progress is maximized when the distance between the cars is minimized. In order to guarantee maximal progress Ego should follow Front as close as possible, i.e. Ego may choose to stay home or even drive backwards without any progress. An emediate remark follows that even though the distance is safe it can still be arbitrary large, i.e. Apart from being safe, the strategy also exhibits rich (non-deterministic) behavior saying that there are many ways to stay safe. Previous section showed some properties of the safe strategy. ![]() Maximizing Progress by Minimizing Distance ![]() Front is approaching towards Ego) and it is a bit more complicated when Front is moving away. The plot shows that the distance has a quadratic dependency on velocity when the velocity is negative (i.e. The plot shows that discrete variables have exactly the same values as continuous ones at integer time points: simulate 1 We validate the discrete approximation by inspecting both discrete and continuous trajectories. In this case all variables are ignored as noise except the process locations. The RESET location provides special hint for statistical learning (the syntax is going to change in the future): the looping edge resets the variables which should not influence the strategy. Likewise, the stochastic features become plain non-deterministic under symbolic model checking queries. ![]() The hybrid clocks here are special: they do not influence the behavior of the model but rather monitor the “cost” of a simulation run, consequently they are abstracted away under symbolic model checking queries and enabled in statistical queries. !(cruise-monitor.svg "Dynamical monitor with reset for learning") hybrid clock rVelocityEgo, rVelocityFront // continuous "real" velocities hybrid clock rDistance // continuous "real" distance between cars hybrid clock D // "cost" to be minimized: integral over distance double _distanceRate_( double velFront, double velEgo, double dist) Given our model, we can inspect sample trip trajectories via SMC simulate query where the locations are encoded as different levels: simulate 1 [ Kim.Sydney) // probability of reaching Sydney within 60 minutes is about 0.97 (not certain, thus not safe)Į (max: trip) // mean trip is about 28 minutes There is also a small risk (1 out of 11) that the train is canceled and we end up in Wait, where we would have to decide either to switch to another train or GoBack home and in Aalborg make a decision again.
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