Its worth noting that Least Squares is a form of statistical estimation; as we recall from lecture, the idea is to define a criteria for matching a model to some data and then minimize the squared error. Thus, we find a Least-Squared estimator for the given problem. There are, however, two key points […]

The traditional approach to controlling systems with many degrees of freedom (e.g., aircraft, submarines, etc) is to assume that each degree of freedom is more or less independent and then use a standard single-input single-output such as PID.  While there are cases where this is generally true– an airplane, for example, almost always has a […]

With all this talk of approximating derivatives, we take it for granted that derivatives work.  Somewhat surprisingly perhaps, this hasn’t always been the case.  Derivatives present some odd philosophical issues.  Newton’s original method of differential calculus required dividing by a number that’s zero in all but name; no doubt many of us remember how well that worked […]