Title :
Nonlinear boundary feedback control of the one-dimensional wave equation
Author :
Chen, Goong ; Huang, Tingwen ; Hsu, Sze-Bi
Author_Institution :
Dept. of Math., Texas A&M Univ., College Station, TX, USA
Abstract :
In this paper, we analyze the dynamical behavior of the linear wave equation on an interval, where the right endpoint has a van der Pol type nonlinearity or boundary controller, while the left endpoint has a boundary condition involving displacement. The asymptotic behavior of the system can be classified into two basic types: classical unbounded instability, or spatial pointwise convergence to periodic points of a nonlinear map corresponding to the van der Pol condition
Keywords :
boundary-value problems; chaos; convergence; feedback; nonlinear control systems; wave equations; 1D wave equation; asymptotic behavior; boundary controller; displacement; dynamical behavior; left endpoint boundary condition; linear wave equation; nonlinear boundary feedback control; nonlinear map; periodic points; spatial pointwise convergence; unbounded instability; van der Pol type nonlinearity; Boundary conditions; Chaos; Feedback control; Force feedback; Instruments; Mathematics; Negative feedback; Partial differential equations; Pediatrics; Underwater acoustics;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2000.914097
