Title :
A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws
Author :
Coron, Jean-Michel ; D´Andrea-Novel, Brigitte ; Bastin, Georges
Author_Institution :
Dept. de Math., Univ. de Paris-Sud, Orsay, France
Abstract :
We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants. The time derivative of this Lyapunov function can be made strictly definite negative by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state only measured at the boundaries. The control design method is illustrated with a hydraulic application, namely the level and flow regulation in a horizontal open channel.
Keywords :
Lyapunov methods; conservation laws; control system synthesis; distributed parameter systems; flow control; hyperbolic equations; level control; Riemann invariants; boundary conditions; boundary control; conservation laws; control design method; flow regulation; horizontal open channel; hydraulic application; hyperbolic systems; level regulation; strict Lyapunov function; time derivative; Boundary conditions; Control design; Control systems; Entropy; Lyapunov method; Mathematics; Partial differential equations; Robots; State feedback; Steady-state;
Conference_Titel :
Decision and Control, 2004. CDC. 43rd IEEE Conference on
Conference_Location :
Nassau
Print_ISBN :
0-7803-8682-5
DOI :
10.1109/CDC.2004.1428994