TY - GEN

T1 - Template-based stabilization of relative equilibria

AU - Ahuja, Sunil

AU - Kevrekidis, Yannis

AU - Rowley, Clarence Worth

PY - 2006

Y1 - 2006

N2 - We present an approach to the design of feedback control laws that stabilize the relative equilibria of general nonlinear systems with continuous symmetry. Using a template-based method, we factor out the dynamics associated with the symmetry variables and obtain evolution equations in a reduced frame that evolves in the symmetry direction. The relative equilibria of the original system are fixed points of these reduced equations. Our controller design methodology is based on the linearization of the reduced equations about such fixed points. Assuming equivariant actuation, we derive feedback laws for the reduced system that are optimal in the sense that they minimize a quadratic cost function. We illustrate the method by stabilizing unstable traveling waves of a dissipative PDE possessing translational invariance.

AB - We present an approach to the design of feedback control laws that stabilize the relative equilibria of general nonlinear systems with continuous symmetry. Using a template-based method, we factor out the dynamics associated with the symmetry variables and obtain evolution equations in a reduced frame that evolves in the symmetry direction. The relative equilibria of the original system are fixed points of these reduced equations. Our controller design methodology is based on the linearization of the reduced equations about such fixed points. Assuming equivariant actuation, we derive feedback laws for the reduced system that are optimal in the sense that they minimize a quadratic cost function. We illustrate the method by stabilizing unstable traveling waves of a dissipative PDE possessing translational invariance.

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M3 - Conference contribution

AN - SCOPUS:34047222159

SN - 1424402107

SN - 9781424402106

T3 - Proceedings of the American Control Conference

SP - 3606

EP - 3611

BT - Proceedings of the 2006 American Control Conference

T2 - 2006 American Control Conference

Y2 - 14 June 2006 through 16 June 2006

ER -