TY - GEN
T1 - Stabilization of an ODE-Schrödinger cascade
AU - Ren, Beibei
AU - Wang, Jun Ming
AU - Krstic, Miroslav
PY - 2012
Y1 - 2012
N2 - In this paper, we consider a problem of stabilization of an ODE-Schrodinger cascade, where the interconnection between them is bi-directional at a single point. By using the backstepping approach, which uses an invertible Volterra integral transformation together with the boundary feedback to convert the unstable plant into a well-damped target system, the target system in our case is given as a PDE-ODE cascade with exponential stability at the pre-designed decay rate. Instead of one-step backstepping control, which results in difficulty in finding the kernels, we develop a two-step backstepping control design by introducing an intermediate target system and an intermediate control. The exponential stability of the closed-loop system is investigated using the Lyapunov method. A numerical simulation is provided to illustrate the effectiveness of the proposed design.
AB - In this paper, we consider a problem of stabilization of an ODE-Schrodinger cascade, where the interconnection between them is bi-directional at a single point. By using the backstepping approach, which uses an invertible Volterra integral transformation together with the boundary feedback to convert the unstable plant into a well-damped target system, the target system in our case is given as a PDE-ODE cascade with exponential stability at the pre-designed decay rate. Instead of one-step backstepping control, which results in difficulty in finding the kernels, we develop a two-step backstepping control design by introducing an intermediate target system and an intermediate control. The exponential stability of the closed-loop system is investigated using the Lyapunov method. A numerical simulation is provided to illustrate the effectiveness of the proposed design.
UR - http://www.scopus.com/inward/record.url?scp=84869380840&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84869380840
SN - 9781457710957
T3 - Proceedings of the American Control Conference
SP - 4345
EP - 4350
BT - 2012 American Control Conference, ACC 2012
T2 - 2012 American Control Conference, ACC 2012
Y2 - 27 June 2012 through 29 June 2012
ER -