Nonlinear sampled-data systems research project



Summary

In the vast literature on nonlinear control design, an area that has received scant attention is sampled-data control. In this problem, a continuous time plant is typically controlled by a discrete-time feedback algorithm. A sample and hold device provides the interface between continuous time and discrete-time. One way to address sampled-data control is to implement a continuous time control algorithm with a sufficiently small sampling period. However, the hardware used to sample and hold the plant measurements or compute the feedback control action may make it impossible to reduce the sampling period to a level that guarantees acceptable closed-loop performance. In this case, it becomes interesting to investigate the application of sampled-data control algorithms based on a discrete-time model of the process. We have developed a framework for controller design for sampled-data nonlinear systems via their approximate discrete-time models. A range of controller design tools to be used within this framework has also been proposed. Finally, we investigated different techniques for emulation and continuous-time controller redesign for sampled-data implementation. Our ultimate goal is to develop a rigorous methodology for nonlinear sampled-data controller design.

Collaborators

  • Prof. A.R. Teel
  • Prof. P.V. Kokotovic
  • Prof. E.D. Sontag
  • Dr. L. Gruene
  • Dr. M. Arcak
  • Dr. L. Zaccarian
  • Dr. A. Loria
  • Dr. D.S. Laila (former PhD student)
  • Selected publications

  • D. Nesic and A.R. Teel, "A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models" , IEEE Trans. Automat. Contr., vol. 49 (2004), pp. 1103-1034.
  • D. Nesic and L. Grune, "A receding horizon control approach to sampled-data implementation of continuous-time controllers", to appear in Syst. Contr. Lett., 2005.
  • D.S. Laila, D. Nesic and A.R. Teel, "Open and closed loop dissipation inequalities under sampling and controller emulation" , Europ. J. Contr., vol. 18 (2002), pp. 109-125.
  • L. Zaccarian, A.R. Teel and D. Nesic, "On finite gain Lp stability of nonlinear sampled-data systems", Systems and Contol Letters, vol. 49 (2001), pp. 201-212.
  • D. Nesic, A. R. Teel and E. D. Sontag, "Formulas relating KL-stability estimates of discrete-time and sampled-data nonlinear systems" , Sys. Contr. Lett., vol. 38, No.1 (1999), pp. 49-60.
  • D. Nesic, A. R. Teel and P. V. Kokotovic, "Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations", Sys. Contr. Lett., vol. 38, No. 4-5 (1999), pp. 259-270.
  • L. Grune and D. Nesic, "Optimization based stabilization of sampled-data nonlinear systems via their approximate discrete-time models" , SIAM J. Opt. Contr., vol. 42 (2003), pp. 98-122.
  • D.S. Laila and D. Nesic, "Changing supply rates for input-output to state stable discrete-time nonlinear systems with applications" , Automatica, vol. 39 (2001), pp. 821-835.