Active probing for information in control systems with quantized state measurements: a minimum entropy approach

In this paper the effect of state quantization in scaler discrete-time linear control systems is studied by analyzing the system as a partially observed stochastic system. The problem of optimal state information gathering and filtering is investigated using information theoretic measures and formulating the state estimation problem as an entropy optimization problem. The active probing effect of the feedback control is thoroughly studied. Optimal feedback controls which minimize various types of entropy costs are determined, and it is shown that this problem is equivalent to an optimal control problem for a controlled Markov chain.

[1]  J. Doob.  Stochastic processes , 1953 .

[2]  D. Naidu,et al.  Optimal Control Systems , 2018 .

[3]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[4]  Henry L. Weidemann.  Entropy Analysis of Feedback Control Systems1 1The research for this paper was supported in part by funds from the United States Air Force Office of Scientific Research under AFOSR Grant 699-67. , 1969 .

[5]  Edwin B. Stear,et al.  Entropy analysis of estimating systems , 1970, IEEE Trans. Inf. Theory.

[6]  R. Curry.  Estimation and Control with Quantized Measurements , 1970 .

[7]  Sigeru Omatu,et al.  An application of the information theory to filtering problems , 1976, Inf. Sci..

[8]  Clifford T. Mullis,et al.  Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[9]  Richard S. Bucy,et al.  Information and filtering , 1979, Inf. Sci..

[10]  Paul Kalata,et al.  Linear prediction, filtering, and smoothing: An information-theoretic approach , 1979, Inf. Sci..

[11]  Paul Moroney,et al.  The digital implementation of control compensators: The coefficient wordlength issue , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[12]  Sigeru Omatu,et al.  Information-theoretical optimal smoothing estimators , 1980, Inf. Sci..

[13]  D. Williamson.  Finite wordlength design of digital Kalman filters for state estimation , 1985 .

[14]  Toshimitsu Ushio,et al.  Chaotic behavior in piecewise-linear sampled-data control systems , 1985 .

[15]  Barry E. Griffiths,et al.  Optimal control of jump-linear gaussian systems† , 1985 .

[16]  Pravin Varaiya,et al.  Stochastic Systems: Estimation, Identification, and Adaptive Control , 1986 .

[17]  Toshimitsu Ushio,et al.  Chaotic rounding error in digital control systems , 1987 .

[18]  Robert M. Gray,et al.  Oversampled Sigma-Delta Modulation , 1987, IEEE Trans. Commun..

[19]  David F. Delchamps.  The 'stabilization' of linear systems with quantized feedback , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[20]  G. Saridis.  Entropy formulation of optimal and adaptive control , 1988 .

[21]  D. Delchamps.  Controlling the flow of information in feedback systems with measurement quantization , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[22]  Kenneth A. Loparo,et al.  Optimal policies for passive learning controllers , 1989, Autom..

[23]  J. Farrell,et al.  Quantizer effects on steady-state error specifications of digital feedback control systems , 1989 .

[24]  O. Hernández-Lerma.  Adaptive Markov Control Processes , 1989 .

[25]  D. F. Delchamps.  Some chaotic consequences of quantization in digital filters and digital control systems , 1989, IEEE International Symposium on Circuits and Systems,.

[26]  Peter J. Ramadge,et al.  On the periodicity of symbolic observations of piecewise smooth discrete-time systems , 1990 .

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

[28]  D. Delchamps.  Extracting state information form a quantized output record , 1990 .

[29]  K. Loparo,et al.  On the Design of Active Learning Controllers for Linear Systems with Quantized State Measurements , 1992, 1992 American Control Conference.

[30]  A study of chaos in discrete-time linear systems with quantized state feedback , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[31]  K. Loparo,et al.  Optimal state estimation for stochastic systems: an information theoretic approach , 1997, IEEE Trans. Autom. Control..