Functional approaches to designing the discrete side of hybrid systems

Question

I'm working on developing controllers for hybrid systems in Haskell.

FRP libraries (right now I'm using netwire, but there are several good ones and a lot of interesting research on future ones) provide a great solution for the continuous-time side of the problem. Augmenting them with signal names, dimensions, preferred units, and so forth gets you a system that has modularity, is self-describing, and has a straightforward path to confidence in correctness.

I'm looking for information, folklore, or papers that provide similar properties for the discrete-time side. In some sense the problem is much easier, state machines are well-studied and simple. In other senses it's more difficult, I'll briefly explain how.

Correctness is obviously the most important thing, and thankfully it's also straightforward.

Self-description is more of a problem. You'd like the controller not just to be in the correct state, but to be capable of telling you what state it's in. Also how it got there. And where it might go next. So you can tack names on to everything, and it works, but it conflicts somewhat with modularity. You'd also like to be able to build complex discrete time behaviors from simpler ones. But when you ask the system what state it's in, generally the high-level answer is more interesting (or at least, as interesting) as the low level answer. How do you get this cleanly? I've tried a few naive approaches and have wrapped myself in spaghetti a few different ways, but it seems like there must be elegant solutions?

Another problem I've had with self-description is that I'd like to have a list of self-describing conditions (generally comparisons: has it been 10 seconds? am I within 3 feet of the next waypoint? has the battery power fallen below 15%? etc) that are being monitored which might trigger the next state transition. There are tricky questions of what even are the desirable semantics here, since it seems like some of these events are better handled "from the bottom up" (e.g. expected termination conditions of whatever low level step you are performing) and some "from the top down" (e.g. equipment failure detection, geofencing, ...). This can lead to spaghetti of its own even if you relax the goal of self-description.

In addition to diagnostics, accurate self-description information here could also be very useful for abstract interpretation, projecting the state of the system into the future by guessing which events are likely to occur when. Many of the event conditions lead themselves to fairly simple guesses (e.g. using velocity made good, fuel consumption rate, timers). Others are more complicated but might still be worth the effort to develop projections for some applications (e.g. expected orders from operators, weather forecasts, projected tracks for moving objects of interest). It would be nice to find a design that annotates conditions not only with names, but also with functions for this sort of stuff.

Does anyone have experience with this that they are willing to share?

Answer 1

Okay, so I would say the "real" answer to your question is that some of things that you are asking for are open areas of research --- in particular I think some of the self-describing features you desire may necessitate some degree of "spaghetti" simply because the problem you are trying to solve is inherently complicated.

That being said, your focus on modularity is exactly the right approach. I would say, take a look at Keymaera as I believe it has the features you are looking for despite being in Java. I would also recommend looking at the publications page on the Keymaera website as this should provide you valuable insight to the problem in general.

If you do not like Keymaera's approach you can also look into using Timed Automata which is another direction modeling-wise that should be sufficient for your problem description.