Bode-Like Fundamental Performance Limitations in Control of Nonlinear Systems

This paper is concerned with entropy based fundamental limitation results for the nonlinear disturbance rejection problem. We propose a hidden Markov model (HMM) framework for entropy calculations. We obtain explicit entropy bounds for both the classical Bode problem (with linear dynamics) as well as certain cases of nonlinear dynamics. An important message of this paper is that the limitations arise due to fundamental issues pertaining to estimation as opposed to the stabilization control problem.