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Boundary Feedback Control Design
and Stability of Open-Channel Networks
Lihui Cen 1 , 2 ,YugengXi 2 , Dewei Li 2 , and Yigang Cen 3
1 Department of Control Engineering, Central South University, Changsha, China
2 Key Laboratory of System Control and Information Processing,
Ministry of Education, and Department of Automation,
Shanghai Jiaotong University, Shanghai, China
3 School of Computer and Information Technology, Beijing Jiaotong University,
Beijing, China
lhcen@csu.edu.cn, { ygxi,dwli } @sjtu.edu.cn, ygcen@bjtu.edu.cn
Abstract. This paper proposed a boundary feedback control design for
open-channel networks with trapezoidal cross sections by using a Rie-
mann invariants approach. The open-channel network is well modeled by
the nonlinear Saint-Venant equations. Based on the characteristic form
in terms of Riemann invariants, the stabilizing boundary control is devel-
oped for a single canal. The stability condition and the boundary control
design are subsequently generalized to open-channel networks composed
by multireaches in cascade. The design of the boundary feedback control
laws either for a single canal or for the cascaded networks is illustrated
in a unified design framework.
Keywords: Open canals, Saint-Venant equations, Riemann invariants,
boundary feedback control, stability analysis.
1 Introduction
The well-known Saint-Venant equations are commonly used in hydraulics to
describe the water flow in open channels [1]. As a standard tool for solving
engineering problems regarding the dynamics of open channels, these coupled
quasi-linear hyperbolic partial differential equations play a key role in modeling
and control of irrigation canals and rivers.
The control of open channels has attracting more increasing attention in
the last decade. Many regulation methods about boundary control have been
proposed ranging from the simplest to the most sophisticated ones in the last
decades. In [2], a simplified irrigation model was proposed for controller design.
Decentralized predictive control was applied to the linear discrete time model of
irrigation canals in [3] and [4]. Litrico linearized the Saint-Venant equations and
designed the controllers using control policies [5].
On the other hand, the boundary feedback control of open canals attracts
increasing attention of scientists and engineers. The common method uses a
Riemann invariant or Lyapunov approaches to investigate the existence of the
 
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