Optimal finite-precision state-estimate feedback controller realizations of discrete-time systems

Investigates the stability issue of a discrete-time control system, where a state-estimate feedback controller (SEFC), digitally implemented with a fixed-point format, is used. A tractable closed-loop stability related measure is derived with finite-word-length implementation consideration of the controller. The optimal realizations of the SEFC are defined as those that maximize this measure and can be shown as the solutions of a nonlinear programming problem. A sophisticated optimization strategy is presented to provide an efficient method for solving this problem, and a numerical example is given to illustrate the design procedure.

[1]  Bing Lam Luk,et al.  Adaptive simulated annealing for optimization in signal processing applications , 1999, Signal Process..

[2]  Thomas Kailath,et al.  Linear Systems , 1980 .

[3]  Gordon S. G. Beveridge,et al.  Optimization: theory and practice , 1970 .

[4]  Gang Li,et al.  On the structure of digital controllers with finite word length consideration , 1998, IEEE Trans. Autom. Control..

[5]  J. Wu,et al.  Analysis of sensitivity measures of finite-precision digital controller structures with closed-loop stability bounds , 1998 .

[6]  Sheng Chen,et al.  Optimizing stability bounds of finite-precision PID controller structures , 1999, IEEE Trans. Autom. Control..

[7]  M. Gevers,et al.  Optimal finite precision implementation of a state-estimate feedback controller , 1990 .

[8]  M. Gevers,et al.  Parametrizations in control problems , 1993 .

[9]  M. Gevers,et al.  Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects , 1993 .

[10]  Lester Ingber,et al.  Simulated annealing: Practice versus theory , 1993 .

[11]  Tryphon T. Georgiou,et al.  On stability and performance of sampled-data systems subject to wordlength constraint , 1994 .

[12]  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.

[13]  James F. Whidborne,et al.  Finite word length stability issues of a teleoperation motion-scaling control system , 1998 .

[14]  Tryphon T. Georgiou.  On stability and performance of sampled-data systems , 1993 .