Text Box:   Girish Nair's Web-Page Email: gnair (at) ee (dot) unimelb (dot) edu (dot) au

  Big Beer


Teaching 

  • 431-222 Electronic Circuit Design, part 1 of 2 (2006-7)
  • 431-658 Advanced Linear Systems & Control, part 2 of 3 (graduate course) (2003-4)
  • 431-460 Digital Communications, part 1 of 2 (2003-4)
  • 431-325 Stochastic Signals & Systems, part 2 of 2 (2003-4)
  • 431-102 Digital Systems 1 (2002)
  • 431-330 Design Laboratory supervision (2001-)
  • 431-400 Project Work supervision (2001-7)

Publications

Book Chapters

  • R. J. Evans, V. Krishnamurthy & G. Nair, ``Sensor adaptive target tracking over variable bandwidth networks'', Model Identification and Adaptive Control (ed. G. C. Goodwin), Springer,  pp.115-124, 2000.

Journal Articles

  1. A. Gurt & G. N. Nair, "Internal stability of dynamic quantised control for stochastic linear plants", Automatica, provisionally accepted as a regular paper, Aug. 2008 (11 pages).  Abstract: Existing analyses of ‘zooming’ quantisation schemes for bit-rate-limited control systems rely on the encoder and controller being initialised with identical internal states. Due to the quantiser discontinuity and the plant instability, it was not clear if closed-loop stability could be recovered if a channel error occurred or, equivalently, if the encoder and controller commenced from different initial conditions. In this paper, we consider the case of partially observed, unstable linear time-invariant plants with unbounded and possibly non-Gaussian noise. We propose a modified zooming-like quantised control scheme, with dynamic, finite-dimensional internal encoder and controller states that may not initially be identical. Using a stochastic pseudo-norm, we prove that this scheme yields mean-square stability in all closedloop state variables, not just the plant state, under a sufficient condition involving this initial error, the open-loop plant dynamics and the channel bit rate. With diminishing initial error, this criterion approaches the well-known Data Rate Theorem. Furthermore, we show that the scheme automatically corrects itself, in the sense that the errors between the internal states of the encoder and controller tend to zero stochastically with time. This suggests that the policy will still maintain mean square internal stability in the presence of channel errors, for sufficiently low bit error rates. We support these conclusions with simulations.
  2. P. Minero, M. Franceschetti, S. Dey & G.N. Nair, "Data rate theorem for stabilization over time-varying feedback channels", IEEE Trans. Automat. Contr., accepted July 2008 (32 pages). Abstract: A data rate theorem for stabilisation of a linear, discrete-time, dynamical system with arbitrarily large disturbances over a communication channel with randomly time-varying rate is presented. Necessary and sufficient conditions for stabilisation are derived, their implications and relationships with related results in the literature are discussed. The proof techniques rely on both information-theoretic and control-theoretic tools.
  3. G. N. Nair, F. Fagnani, S. Zampieri, R. J. Evans, "Feedback control under data rate constraints: an overview", Proceedings of the IEEE, Institute of Electrical & Electronics Engineers, USA, vol. 95, no. 1, pp. 108-37, Jan. 2007.

  4. R. Evans, V. Krishnamurthy, G. Nair, L. Sciacca, "Networked sensor management and data rate control for tracking maneuvering targets", IEEE Transactions on Signal Processing, Institute of Electrical & Electronics Engineers, USA, vol. 53, no. 6, pp. 1979-91, June 2005. 

  5.  I. Mareels, E. Weyer, S. K. Ooi, M. Cantoni, Y. Li, G. Nair, “Systems engineering for irrigation systems: successes and challenges”, Annual Reviews in Control,  Elsevier, The Netherlands, vol.29, no.2, pp. 191-204, 2005. 

  6. G. N. Nair, R. J. Evans, I. M. Y. Mareels & W. Moran, "Topological feedback entropy and nonlinear stabilization", IEEE Transactions on Automatic Control, Institute of Electrical & Electronics Engineers, USA, vol. 49, no. 9, pp. 1585-97, Sep. 2004. 

  7. G. N. Nair & R. J. Evans, "Stabilizability of stochastic linear systems with finite feedback data rates", SIAM Journal on Control and Optimization, Society for Industrial & Applied Mathematics, USA, vol. 43, no. 2, pp. 413-36, July 2, 2004. [SIAM Outstanding Paper Prize, 2006]. 

  8. G. N. Nair & R. J. Evans, "Exponential stabilisability of finite-dimensional linear systems with limited data rates'', Automatica, Elsevier, The Netherlands, vol. 39, pp. 585-93, Apr. 2003. 

  9. G. N. Nair & R. J. Evans, "Stabilization with data-rate-limited feedback: tightest attainable bounds", Systems & Control Letters, Elsevier, The Netherlands, vol. 41, no. 1, pp. 49-56, Sep. 2000.

Conference Papers

  1. A. Gurt & G. N. Nair, "Internal stability of dynamically quantised control for stochastic scalar plants", Proc. 17th Triennial IFAC World Congress, July 2008 (6 pages)
  2. P. Minero, M. Franceschetti , S. Dey & G. Nair, "Data rate theorem for stabilization over fading channels",  Proc. 45th Annual Allerton Conf. Communications, Control and Computing, pp. 182-9, Uni. Illinois Urbana-Champaign, USA, Sep. 2007.
  3. A. Gurt & G. N. Nair, “Performance analysis of bit-rate-limited stochastic control systems”, Proc. 15th Mediterranean Conf. Control & Automation (MED'07), IEEE, Athens, Greece, June 27-29, 2007 (6 pages. ISBN 978-960-254-664-2)
  4. G. N. Nair & R. J. Evans, “Cooperative networked stabilisability of linear systems with measurement noise”, Proc. 15th Mediterranean Conf. Control & Automation, IEEE, Athens, Greece, June 27-29, 2007 (6 pages. ISBN 978-960-254-664-2) Abstract: This paper investigates the problem of stabilising a linear, time-invariant plant with multiple controllers and noisy sensors over a digital network. A necessary and (almost) sufficient condition for determining networked uniform stabilisability, is derived, in terms of the feasibility of a set of linear inequalities involving the unstable eigenvalues of the plant and the various channel data rates. This provides a nearly exact characterisation, up to boundary points, of the region of all channel data rate combinations that permit uniform stability to be achieved. The auxiliary variables in this characterisation have a natural interpretation as the effective rates of information flow through the network, associated with each unstable mode. When channel rates are set to either zero or infinity, this agrees with a classical result on decentralised stabilisability under linear time-varying control.
  5. P. Minero, M. Franceschetti, S. Dey & G. Nair, "Towards control over fading channels", Proc. Workshop on Control over Communication Channels, IEEE, Limassol, Cyprus, April 2007. (5 pages).
  6. G. N. Nair & J. Baillieul, “Time to failure of quantized control via a binary symmetric channel”, Proc. 45th IEEE Conference on Decision and Control (CDC'06), pp. 2883-8, San Diego, USA, 2006.
  7. G. N. Nair, M. Huang & R. J. Evans, "Optimal infinite horizon control under a low data rate", Proc. 14th IFAC Symp. Modelling, Identification and Signal Processing (SYSID 2006), Newcastle, Australia, Mar. 2006. (6 pages) Abstract: This paper considers the optimal control of linear systems where measurement data is transmitted from the plant output to the controller over a noiseless communication channel with limited instantaneous data rate. The cost is defined to be the average, over a random initial state, of the usual infinite horizon quadratic regulation criterion, and the number of bits transported by the channel during each sampling interval is bounded. Several fundamental properties of the optimal cost functional are derived for initial state densities that satisfy a mild moment condition. Using these properties, precise expressions for the optimal cost and policy are obtained assuming a uniformly distributed initial state. These expressions agree with the classical optimal LQR results in the high data rate limit and with recent minimum rate results in the low rate regime. Extensions to the case of non-uniform densities and vector-valued states are discussed.
  8. G. Z. Zhang, G. N. Nair, R. J. Evans, B. Wittenmark, "A data-rate-limited view of adaptive control", Proc. 14th IFAC Symp. Modelling, Identification and Signal Processing, Newcastle, Australia, Mar. 2006. (6 pages)
  9. M. Huang, G. N. Nair & R. J. Evans, "Finite horizon LQ optimal control and computation with data rate constraints", Proc. 44th IEEE Conf. Decision & Control, Sevilla, Spain, pp. 179-84, Dec. 2005.
  10. M. Huang & G. N. Nair, "Detection of random targets in sensor networks with applications", Proc. 16th  World Congress Int. Fed. Automatic Control (IFAC), Praha, Czech Republic, July 2005. (6 pages)
  11. G. N. Nair, R.J. Evans & P.E. Caines, “Stabilising decentralised linear systems under data rate constraints”, Proc. 43rd IEEE Conf. Decision & Control, pp. 3992-7, Nassau, Bahamas, 2004.
  12. G. N. Nair, R. J. Evans, I. M. Y. Mareels & W. Moran, "Topological feedback entropy for nonlinear stabilization", Proc. 6th IFAC Symp. Nonlinear Control Systems (NOLCOS 2004), Stuttgart, Germany, pp. 1283-8, Vol.3, Sep. 2004.
  13. G. N. Nair, S. Dey & R. J. Evans, ``Infimum data rates for stabilising Markov jump linear systems", Proc. 42nd IEEE Conf. Decision & Control, pp. 1176-81, Maui, USA, Dec. 2003. 
  14. G. N. Nair, R. J. Evans, I. M. Y. Mareels & W. Moran, "Feedback data rates for nonlinear systems", Proc. European Control Conference, European Control Association, pp. 731-6, Cambridge, UK, Sep. 2003. 
  15. G. N. Nair & R. J. Evans,``Mean square stabilisability of stochastic linear systems with data rate constraints", Proc. 41st IEEE Conf. Dec. Contr., pp. 1632-7, Las Vegas, USA, 2002. 
  16. G. N. Nair, S. Dey & R. J. Evans,  "Communication-limited stabilisability of jump Markov linear systems", Proc. 15th Int. Symp. Mathematical Theory of Networks & Systems, Uni. Notre Dame, Indiana, USA, Aug. 2002. (10 pages)
  17. G. N. Nair & R. J. Evans,``Exponential stabilisability of multidimensional linear systems with finite data rates'', Proc. 15th World Congress IFAC, Barcelona, Spain, July 2002. (6 pages)
  18. G. N. Nair & R. J. Evans, "Optimal control under a data rate constraint'', Proc. UKACC Int. Conf. Control, IEE ZZ057, Cambridge, UK, 2000 (6 pages) [Best Theory Paper Prize] 
  19. G. N. Nair & R. J. Evans, ``Communication-limited stabilization of linear systems'', Proc. 39th IEEE Conf. Dec. Contr., Sydney, Australia, pp. 1005-10, 2000.
  20. G. N. Nair & R. J. Evans, ``A finite-dimensional coder-estimator for rate- constrained state estimation'', Proc. 14th World Congress IFAC, Beijing, China, vol. I, pp. 19-24, July 1999.
  21. G. N. Nair & R. J. Evans, "Structural results for finite bit-rate state estimation'', Proc. Information, Decision &  Control, Adelaide, Australia, IEEE, pp. 47-51, Feb. 1999.
  22. G. N. Nair & R. J. Evans,  "State estimation under bit-rate constraints'', Proc. 37th IEEE Conf. Dec. Contr., Tampa, USA, pp. 251-6, 1998.
  23. G. N. Nair & R. J. Evans, "State estimation via a capacity-limited communication channel'', Proc. 36th IEEE Conf. Dec. Contr., San Diego, USA, pp. 866-71, 1997.

Manuscripts under Review

1. A. Gurt & G. N. Nair, "Internal stability of dynamically quantised control for stochastic linear plants",  submitted to Automatica, May 2008.

CV

Qualifications

  • Ph.D., Dept. Electrical & Electronic Eng., University of Melbourne, 2000. 
  • B.Sc., University of Melbourne, 1995. Majors in mathematics & physics.
  • B.E. (Elec)(1st Class Hons), University of Melbourne, 1994.

Prizes

  • 2000: Best Theory Paper Prize, UKACC International Conference on Control, Cambridge, UK.
  • 1996-9: Overseas Postgraduate Research & Melbourne University Malaysia Alumni Scholarships
  • (1996: Cambridge Commonwealth Trust (Blue Circle) & St. John's College Scholarship offers - declined.)
  • 1994: L. R. East Medal for Best Performance in Final Year Engineering
  • 1994: Dixson Prize in Electrical Engineering
  • 1994: Dean's Honour List in Electrical Engineering - 4th Year
  • 1994: Dean's Honour List in Science - 2nd Year
  • 1992: Siemens Prize in Electrical Engineering - 2nd Year
  • 1992: Dixson Prize in Applied Mathematics - 2nd Year
  • 1992: Dixson Prize in Pure Mathematics - 2nd Year
  • 1991: Exhibition Prize in Engineering Mathematics - 1st Year
  • 1991: Dixson Prize in Applied Mathematics - 1st Year
  • 1991: Dixson Prize in Pure Mathematics - 1st Year
  • 1991-5: Australian Government Merit Scholarship
  • 1990: Individual Second Prize, National Mathematics Competition, Malaysian Mathematical Society

Employment

  • From 2008: Associate Professor, Dept. Elec. & Electr. Eng., Uni. Melb.
  • 2003 - 7: Senior Lecturer (continuing), Dept. Elec. &  Electr. Eng., Uni. Melb.
  • 2002-3: Senior Lecturer (fixed term), Dept. Elec. & Electr. Eng., Uni Melb.
  • Sep. 1999-2001: Lecturer (fixed term), Dept. Elec. & Electr. Eng., Uni. Melb.

Professional Activities


This page, its contents and style, are the responsibility of the author and do not necessarily represent the views, policies or opinions of the University of Melbourne.

Created : 10th September, 1997


Last Modified :  19/8 2008.

HTML by : Melissa Labura
Maintained by: Girish Nair