TY - GEN

T1 - Nonlinear stabilization via control-Lyapunov measure

AU - Vaidya, Umesh

AU - Mehta, Prashant G.

AU - Shanbhag, Vinayak V.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is based upon a set-oriented numerical approach. Using this approach, the codesign problem leads to a finite number of linear inequalities whose solutions define the feasible set of stabilizing controllers. We provide a proof of existence for a stochastic version of such a controller while the deterministic restriction is posed as the solution of a related integer programming problem. Mathematical programming techniques may be employed to obtain such controllers. Finally, an example is provided to illustrate the ideas.

AB - This paper is concerned with computational methods for Lyapunov-based control design of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. This paper poses and solves the co-design problem of jointly obtaining the control Lyapunov measure and a controller. The computational framework is based upon a set-oriented numerical approach. Using this approach, the codesign problem leads to a finite number of linear inequalities whose solutions define the feasible set of stabilizing controllers. We provide a proof of existence for a stochastic version of such a controller while the deterministic restriction is posed as the solution of a related integer programming problem. Mathematical programming techniques may be employed to obtain such controllers. Finally, an example is provided to illustrate the ideas.

UR - http://www.scopus.com/inward/record.url?scp=51349104128&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51349104128&partnerID=8YFLogxK

U2 - 10.1109/CDC.2007.4434956

DO - 10.1109/CDC.2007.4434956

M3 - Conference contribution

AN - SCOPUS:51349104128

SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1722

EP - 1727

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

T2 - 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -