An Optimal Dynamic Quantization Scheme for Control With Discrete-Valued Input

This paper presents optimal dynamic quantizers for controlling linear time-invariant systems with the discrete- valued input. The quantizers considered here are in the form of a difference equation, for which we find a quantizer such that the system composed of a given linear plant and the quantizer is an optimal approximation of the given linear plant in the sense of the input-output relation. First, we derive a closed form expression for the performance (the degree of the approximation) of a class of dynamic quantizers. Next, based on this, an optimal dynamic quantizer and its performance, corresponding to the performance limitation of the dynamic quantizers, are provided. Finally, the validity of the proposed quantizer is shown by numerical simulations.

[1]  Jörg Raisch,et al.  Control of Continuous Plants by Symbolic Output Feedback , 1994, Hybrid Systems.

[2]  Nicola Elia,et al.  Stabilization of linear systems with limited information , 2001, IEEE Trans. Autom. Control..

[3]  Daniel Liberzon,et al.  Quantized control via locational optimization , 2002, IEEE Transactions on Automatic Control.

[4]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[5]  G. Goodwin,et al.  Finite constraint set receding horizon quadratic control , 2004 .

[6]  Jan M. Maciejowski,et al.  Optimal quantization of signals for system identification , 2003, ECC.

[7]  G. Goodwin,et al.  Audio quantization from a receding horizon control perspective , 2003, Proceedings of the 2003 American Control Conference, 2003..

[8]  Vassilis Anastassopoulos,et al.  Delta-Sigma Modulators: Modeling, Design and Applications , 2003 .

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

[10]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[11]  Robin J. Evans,et al.  Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates , 2004, SIAM J. Control. Optim..

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

[13]  Lihua Xie,et al.  The sector bound approach to quantized feedback control , 2005, IEEE Transactions on Automatic Control.

[14]  C. Canudas-de-Wit,et al.  Differential coding in networked controlled linear systems , 2006, 2006 American Control Conference.

[15]  Masato Ishikawa,et al.  Quantized Controller Design Using Feedback Modulators , 2007 .