Boundary controllability between sub- and supercritical flow

SIAM Journal on Control and Optimization

Volumn 42, Issue 3, 2003, Pages 1056-1070

  Gugat, Martin ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

De St. Venant equations; Global controllability; Subcritical states; Supercritical states

Indexed keywords

DE ST VENANT EQUATIONS; GLOBAL CONTROLLABILITY; SUBCRITICAL STATES; SUPERCRITICAL STATES;

EIGENVALUES AND EIGENFUNCTIONS; FRICTION; HYDROELECTRIC POWER; PHASE TRANSITIONS; THEOREM PROVING;

BOUNDARY VALUE PROBLEMS;

EID: 2942541365     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902409660     Document Type: Article

References (15)

1. E. ARNOLD, H. LINKE, AND W. SIEBERT, Ein modell-praediktives regelungsverfahren zur optimierten Wasserbewirtschaftung des mittellandkanals und des elbe-seitenkanals, Automatisierungstechnik, 47 (1999), pp. 399-407.
2. C. BARDOS, A. Y. LEROUX, AND J. C. NEDELEC, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, 4 (1979), pp. 1017-1034.
3. M. CIRINÀ, Boundary controllability of nonlinear hyperbolic systems, SIAM J. Control, 7 (1969), pp. 198-212.
4. M. CIRINA, Nonlinear hyperbolic problems with solutions on preassigned sets, Michigan Math. J., 17 (1970), pp. 193-209.
5. J. M. CORON, Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, ESAIM Control Optim. Calc. Var., 8 (2002), pp. 513-554.
6. J. M. CORON, B. D'ANDREA NOVEL, AND G. BASTIN, A Lyapunov approach to control irrigation canals modeled by Saint-Venant equations, in Advance in Control, Springer-Verlag, Berlin, 1999.
7. M. GUGAT AND G. LEUGERING, Global boundary controllability of the de St. Venant equations between steady states, Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), pp. 1-11.
8. M. GUGAT, G. LEUGERING, K. SCHITTKOWSKI, AND E. J. P. G. SCHMIDT, Modelling, stabilization, and control of flow in networks of open channels, in Online Optimization of Large Scale Systems, Martin Groetschel et al., eds., Springer, Berlin, 2001, pp. 251-270.
9. M. GUGAT, G. LEUGERING, AND E. J. P. G. SCHMIDT, Global controllability between steady supercritical flows in channel networks, Math. Methods Appl. Sci., to appear.
10. G. LEUGERING AND E. J. P. GEORG SCHMIDT, On the modelling and stabilization of flows in networks of open canals, SIAM J. Control Optim., 41 (2002), pp. 164-180.
11. P. O. LlNDBERG AND A. WOLF, Optimization of the short term operation of a cascade of hydro power stations, in Optimal Control: Theory, Algorithms, and Applications, W. H. Hager and P. M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998, pp. 326-345.
12. E. J. P. GEORG SCHMIDT, On a non-linear wave equation and the control of an elastic string from one equilibrium to another, J. Math. Anal. Appl., to appear.
13. LI TA-TSIEN, Global Classical Solutions for Quasilinear Hyperbolic Systems, Masson, Paris, 1994.
14. 1 solution and exact boundary controllability for reducible quasilinear hyperbolic systems, M2AN Math. Model. Numer. Anal., 34 (2000), pp. 399-408.
15. 1 semi-globale et contrôlabilité exacte frontière de systèmes hyperboliques quasi linéaires réductibles, C. R. Acad. Sci. Paris Sér. I Math., 330 (2000), pp. 205-210.