Some impossibility theorems on feedback and uncertainty

Since feedback is a key principle in dealing with various kinds of uncertainties in control systems, the quantitative understanding of the maximum uncertainty that can be dealt with by the feedback mechanism is a fundamental issue in control theory. In this talk, we will present some impossibility theorems on the maximum capability of feedback mechanism in dealing with uncertainties for some general classes of dynamical systems to be controlled. We will show how the structural uncertainty coupled with the nonlinearity of the discrete-time or sampled-data control systems give rise to fundamental limits to the capability of feedback, we will also show how the well-known Cramer-Rao Inequality in mathematical statistics and the Heisenberg Uncertainty Principle in quantum mechanics will result in the fundamental limits on the performance of feedback.