Citation
Saurabh Amin, Alexandre Bayen, Laurent El Ghaoui, Shankar Sastry. "Robust feasibility for control of water flow in a canal reservoir system". Decision and Control, 2007 46th IEEE Conference on, 1571-1577, December, 2007.

Abstract
A robust control problem for distant downstream control of a reservoir-canal system modeled by Saint-Venant equations is investigated. The problem is to regulate the release of water at the upstream end such that the measured water level (or stage) at the downstream end does not deviate outside of prescribed bounds under the effect of downstream perturbations. Under the assumption of small perturbations, the Saint-Venant model is linearized around a steady state flow. The resulting linear model is discretized to obtain a linear state-space model using a method of characteristics based numerical scheme. For the state space model, the control is the upstream discharge deviation, the disturbance is the downstream discharge deviation and the output is the downstream stage deviation; the deviations are defined with respect to the steady state. The sets of admissible control, disturbance and output trajectories are modeled by polytopes. It is shown that the control problem can be formulated as a robust feasibility problem. Using linear programming duality, conditions for existence of a robustly feasible solution are derived. These conditions, being affine in the control variables, are checked using linear programming. The proposed method is applied to control a typical reservoir- canal system.

Electronic downloads

• cdc07b.pdf · application/pdf · 412 kbytes
• http://dx.doi.org/10.1109/CDC.2007.4434391

• HTML

  Saurabh Amin, Alexandre Bayen, Laurent El Ghaoui, Shankar
  Sastry. <a
  href="http://chess.eecs.berkeley.edu/pubs/451.html"
  >Robust feasibility for control of water flow in a canal
  reservoir system</a>, Decision and Control, 2007 46th
  IEEE Conference on,  1571-1577, December, 2007.

• Plain text

  Saurabh Amin, Alexandre Bayen, Laurent El Ghaoui, Shankar
  Sastry. "Robust feasibility for control of water flow
  in a canal reservoir system". Decision and Control,
  2007 46th IEEE Conference on,  1571-1577, December, 2007.

• BibTeX

  @inproceedings{AminBayenElGhaouiSastry07_RobustFeasibilityForControlOfWaterFlowInCanalReservoir,
      author = {Saurabh Amin and Alexandre Bayen and Laurent El
                Ghaoui and Shankar Sastry},
      title = {Robust feasibility for control of water flow in a
                canal reservoir system},
      booktitle = {Decision and Control, 2007 46th IEEE Conference on},
      pages = { 1571-1577},
      month = {December},
      year = {2007},
      abstract = {A robust control problem for distant downstream
                control of a reservoir-canal system modeled by
                Saint-Venant equations is investigated. The
                problem is to regulate the release of water at the
                upstream end such that the measured water level
                (or stage) at the downstream end does not deviate
                outside of prescribed bounds under the effect of
                downstream perturbations. Under the assumption of
                small perturbations, the Saint-Venant model is
                linearized around a steady state flow. The
                resulting linear model is discretized to obtain a
                linear state-space model using a method of
                characteristics based numerical scheme. For the
                state space model, the control is the upstream
                discharge deviation, the disturbance is the
                downstream discharge deviation and the output is
                the downstream stage deviation; the deviations are
                defined with respect to the steady state. The sets
                of admissible control, disturbance and output
                trajectories are modeled by polytopes. It is shown
                that the control problem can be formulated as a
                robust feasibility problem. Using linear
                programming duality, conditions for existence of a
                robustly feasible solution are derived. These
                conditions, being affine in the control variables,
                are checked using linear programming. The proposed
                method is applied to control a typical reservoir-
                canal system.},
      URL = {http://chess.eecs.berkeley.edu/pubs/451.html}
  }
  

Posted by Saurabh Amin on 23 Jun 2008.
For additional information, see the Publications FAQ or contact webmaster at chess eecs berkeley edu.