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June  2009, 4(2): 267-285. doi: 10.3934/nhm.2009.4.267

Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems

Didier Georges 1,

1. 

Control systems department, Gipsa-lab, Grenoble, Grenoble INP-Ense3, BP 46, 38402 Saint-Martin d’Hères, France

Received  November 2008 Revised  January 2009 Published  June 2009

A nonlinear predictive control design based on Saint Venant equations is presented in this paper in order to regulate both water depth and water flow rate in a single pool of an open-channel hydraulic system. Thanks to variational calculus, some necessary optimality conditions are given. The adjoint partial differential equations of Saint Venant partial differential equations are also derived. The resulting two-point boundary value problem is solved numerically by using both time and space discretization and operator approximations based on nonlinear time-implicit finite differences. The practical effectiveness of the control design is demonstrated by a simulation example. A extension of the predictive control scheme to a multi-pool system is proposed by using a decomposition-coordination approach based on two-level algorithm and the use of an augmented Lagrangian, which can take advantage of communication networks used for distributed control. This approach may be easily applied to other problems governed by hyperbolic PDEs, such as road traffic systems.
Keywords: open-channel hydraulic systems., Nonlinear model predictive control, nonlinear hyperbolic partial differential equations.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Didier Georges. Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems. Networks & Heterogeneous Media, 2009, 4 (2) : 267-285. doi: 10.3934/nhm.2009.4.267
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