Stabilization of networked multi-input systems with channel resource allocation

In this paper, we study the problem of stabilizing a linear time-invariant discrete-time system with information constraints in the input channels. The information constraint in each input channel is modeled as a sector uncertainty. Equivalently, the transmission error of an input channel is modeled as an additive system uncertainty with a bound in the induced norm.We attempt to find the least information required, or equivalently the largest allowable uncertainty bound, in each input channel which renders the stabilization possible. The solution for the single-input case, which gives a typical Hinfin optimal control problem, is available in the literature and is given analytically in terms of the Mahler measure or topological entropy of the plant. The main purpose of this paper is to address the multi-input case. In the multi-input case, if the information constraint in each input channel is given a priori, then our stabilization problem turns out to be a so-called mu synthesis problem, a notoriously hard problem. In this paper, we assume that the information constraints in the input channels are determined by the network resources assigned to the channels and they can be allocated subject to a total recourse constraint. With this assumption, the resource allocation becomes part of the design problem and a modified mu synthesis problem arises. Surprisingly, this modified mu-synthesis problem can be solved analytically and the solution is also given in terms of the Mahler measure or topological entropy as in the single-input case.

[1]  Chung-Yao Kao,et al.  Stabilization of linear systems with limited information multiple input case , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  Guoxiang Gu,et al.  Robust stabilization of multiplicative/relative uncertain systems and networked feedback control , 2009, 2009 IEEE International Conference on Control and Automation.

[3]  K. Mahler An application of Jensen's formula to polynomials , 1960 .

[4]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[5]  W. Wonham,et al.  On pole assignment in multi-input controllable linear systems , 1967, IEEE Transactions on Automatic Control.

[6]  Julio H. Braslavsky,et al.  Stabilization with disturbance attenuation over a Gaussian channel , 2007, 2007 46th IEEE Conference on Decision and Control.

[7]  D.E. Quevedo,et al.  A brief introduction to the analysis and design of Networked Control Systems , 2008, 2008 Chinese Control and Decision Conference.

[8]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[9]  Special Issue on Networked Control Systems , .

[10]  Nicola Elia,et al.  Remote stabilization over fading channels , 2005, Syst. Control. Lett..

[11]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[12]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[13]  L. Qiu,et al.  Networked Stabilization of Multi-Input Systems with Channel Resource Allocation ⋆ , 2008 .

[14]  Peter J Seiler,et al.  Analysis of communication losses in vehicle control problems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[15]  Graham C. Goodwin,et al.  Combining switching, over-saturation and scaling to optimise control performance in the presence of model uncertainty and input saturation , 2002, Autom..

[16]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

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

[18]  Huijun Gao,et al.  A new approach to quantized feedback control systems , 2008, Autom..

[19]  J. Shamma Robust stability with time-varying structured uncertainty , 1994, IEEE Trans. Autom. Control..

[20]  J. Baillieul Feedback coding for information-based control: operating near the data-rate limit , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[21]  Andrey V. Savkin,et al.  Analysis and synthesis of networked control systems: Topological entropy, observability, robustness and optimal control , 2005, Autom..

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

[23]  H. Haimovich,et al.  On Infimum Quantization Density for Multiple-input Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[24]  John C. Doyle Analysis of Feedback Systems with Structured Uncertainty , 1982 .

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

[26]  Panos J. Antsaklis,et al.  Special Issue on Technology of Networked Control Systems , 2007 .

[27]  Koji Tsumura,et al.  Tradeoffs between quantization and packet loss in networked control of linear systems , 2009, Autom..

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

[29]  Bruno Sinopoli,et al.  Kalman filtering with intermittent observations , 2004, IEEE Transactions on Automatic Control.

[30]  Anant Sahai,et al.  The Necessity and Sufficiency of Anytime Capacity for Stabilization of a Linear System Over a Noisy Communication Link—Part I: Scalar Systems , 2006, IEEE Transactions on Information Theory.

[31]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[32]  Richard M. Murray,et al.  Introduction to Networked Control Systems , 2018, Optimal Networked Control Systems with MATLAB.

[33]  Richard H. Middleton,et al.  Feedback stabilization over signal-to-noise ratio constrained channels , 2007, Proceedings of the 2004 American Control Conference.

[34]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[35]  Ertem Tuncel,et al.  Optimal tracking performance of discrete-time systems over an additive white noise channel , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.