CapitalistImperialistPig

To a man with a hammer, it is said, everything looks like a nail. For a man (I have one particular man in mind here) with a little knowledge of control theory, a number of things start looking like hybrid autonomous systems. Like people, for example. Such systems have some key weaknesses, which can be traced back to their switching hybrid character. In particular, while a whole bunch of individual behaviors may be well regulated, when the switching character of the hybrid system is accounted for, instabilities can develop. I trace a number of our characteristic human failings to the fact that the some of our control systems are being driven outside their design parameters. More on this later perhaps. I had addiction in mind. Interestingly enough, some of these problems can be ameliorated with a procedure based on computing Lie Derivatives of the appropriate function at some critical control points. So do you suppose that our brains have built in Lie derivators somewhere?

Via Alex Tabbarok at Marginal Revolution , this nice video of two quadcopters playing catch with an inverted pendulum. The inverted pendulum is a classic problem in elementary control theory (a fact I recently learned in my Coursera " Control of Mobile Robots " class).  Juggling an inverted pendulum with flying robots is a classic case of hybrid control - in effect, various separate control algorithms cooperatively managing the overall control problem of catch and balance while managing not to collide with each other or anything sol id.  This sort of hybrid automaton is exemplified by robots (or people, or animals)with complex behaviors.

I think it was Banerjee who asked me to write something about engineering, so that the engineers could beat me up. Here is my first try. It stems from the class in Control of Mobile Robots that I am taking from Coursera and Georgia Tech. One of the most common control strategies for simple systems is so-called PID control, where the P stands for proportional, the I for integrating, and the D for derivative. The essence of the strategy is that you measure an error in your system behavior, and generate a correction control signal that is proportional to the error, its integral over time, and its derivative. My quasi-philosophical question is this: does the value of this strategy have anything to do with the fact that so many laws of physics take the form of second order differential equations? UPDATE: Second question. Suppose we replaced the Fed's Open Market Committee with a PID control robot which attempted to maintain a 2% inflation rate. What do think would happen?