Minimal Bit Rates and Entropy for Exponential Stabilization

Minimal bit rates and entropy are studied for exponential stabilization of control systems in continuous time. Upper and lower bounds for the stabilization entropy are derived. In particular, for linear systems, a formula is given in terms of the real parts of eigenvalues. Then the minimal bit rate is related to the stabilization entropy.

[1]  Jean-Charles Delvenne,et al.  An optimal quantized feedback strategy for scalar linear systems , 2006, IEEE Transactions on Automatic Control.

[2]  D. Delchamps.  Stabilizing a linear system with quantized state feedback , 1990 .

[3]  Robin J. Evans,et al.  Feedback Control Under Data Rate Constraints: An Overview , 2007, Proceedings of the IEEE.

[4]  A. Matveev,et al.  Estimation and Control over Communication Networks , 2008 .

[5]  C. Robinson.  Dynamical Systems: Stability, Symbolic Dynamics, and Chaos , 1994 .

[6]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[7]  T. Morrison,et al.  Dynamical Systems , 2021, Nature.

[8]  M. Mirzakhani,et al.  Introduction to Ergodic theory , 2010 .

[9]  J. Zukas.  Introduction to the Modern Theory of Dynamical Systems , 1998 .

[10]  Matteo Turilli,et al.  Dynamics of Control , 2007, First Joint IEEE/IFIP Symposium on Theoretical Aspects of Software Engineering (TASE '07).

[11]  Li Xie.  TOPOLOGICAL ENTROPY AND DATA RATE FOR PRACTICAL STABILITY : A SCALAR CASE , 2009 .

[12]  P. Walters.  Introduction to Ergodic Theory , 1977 .

[13]  Sandro Zampieri,et al.  A Symbolic Approach to Performance Analysis of Quantized Feedback Systems: The Scalar Case , 2005, SIAM J. Control. Optim..

[14]  C. Kawan.  Upper and lower estimates for invariance entropy , 2011 .

[15]  R. Bowen.  Entropy for group endomorphisms and homogeneous spaces , 1971 .

[16]  Robin J. Evans,et al.  Topological feedback entropy and Nonlinear stabilization , 2004, IEEE Transactions on Automatic Control.

[17]  Christoph Kawan,et al.  Invariance Entropy of Control Sets , 2011, SIAM J. Control. Optim..

[18]  Wing Shing Wong,et al.  Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback , 1999, IEEE Trans. Autom. Control..

[19]  Christoph Kawan,et al.  Invariance Entropy for Control Systems , 2009, SIAM J. Control. Optim..

[20]  Claudio De Persis,et al.  n-bit stabilization of n-dimensional nonlinear systems in feedforward form , 2004, IEEE Transactions on Automatic Control.

[21]  Sekhar Tatikonda,et al.  Control under communication constraints , 2004, IEEE Transactions on Automatic Control.

[22]  Christoph Kawan,et al.  Invariance entropy for outputs , 2011, Math. Control. Signals Syst..