2019/12/13 by N. Garcı́a, Garcia, Nicolas, Christoph Kawan +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Gene Regulatory Network Analysis #Optimization and Control (math.OC) #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.1912.06351
openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a stochastic nonlinear system controlled over a possibly noisy\ncommunication channel. An important problem is to characterize the largest\nclass of channels for which there exist coding and control policies so that the\nclosed-loop system is stochastically stable. In this paper, we consider the\nstability notion of (asymptotic) ergodicity. We prove lower bounds on the\nchannel capacity necessary to achieve the stability criterion. Under mild\ntechnical assumptions, we obtain that the necessary channel capacity is lower\nbounded by the log-determinant of the linearization, double-averaged over the\nstate and noise space. We prove this bound by introducing a modified version of\ninvariance entropy and utilizing the almost sure convergence of sample paths\nguaranteed by the pointwise ergodic theorem. The fundamental bounds obtained\ngeneralize well-known formulas for linear systems, and are in some cases more\nrefined than those obtained for nonlinear systems via information-theoretic\nmethods.\n