Colloquium

Colloquium
Stabilization of relative equilibria for underactuated systems on Riemannian manifolds. Kumagai Aatsutoshi 1st October (Fri) 15:00 In this talk, I'll introduce a systematic procedure to asymptotically stabilize relative equilibria of mechanical systems after the paper "F.Bullo .[2000] Stabilization of relative equilibria for underactuated systems on Riemannian manifolds, Automatica. The Journal of IFAC, 36(12),1819-1834." In the procedure, potential shaping and dissipative control are employed. To obtain full asymptotical stabilization of the desired trajectory, we need two conditions that the effective potential be positive definite over a specified subspace and that the system be linearly controllable. Reference: [1]F.Bullo , Stabilization of relative equilibria for underactuated systems on Riemannian manifolds, Automatica. The Journal of IFAC, 36(12),1819-1834 (2000) [2]F.Bullo and A.D.Lewis , Geometric Control of Mechanical Systems , Texts in Applied Mathematics, Springer (2004) [3]M.C.Munoz-Lecanda and F.J.Yaniz , Dissipative control of mechanical systems:a geometric approach , SIAM Journal of Control and Optimization, 40(5):1505-1516 (2002)

Stabilization of relative equilibria for underactuated systems on Riemannian manifolds.

Kumagai Aatsutoshi

1st October (Fri) 15:00

In this talk, I'll introduce a systematic procedure to asymptotically stabilize relative equilibria of mechanical systems after the paper "F.Bullo .[2000] Stabilization of relative equilibria for underactuated systems on Riemannian manifolds, Automatica. The Journal of IFAC, 36(12),1819-1834." In the procedure, potential shaping and dissipative control are employed. To obtain full asymptotical stabilization of the desired trajectory, we need two conditions that the effective potential be positive definite over a specified subspace and that the system be linearly controllable.

Reference:
[1]F.Bullo , Stabilization of relative equilibria for underactuated systems on Riemannian manifolds, Automatica. The Journal of IFAC, 36(12),1819-1834 (2000)
[2]F.Bullo and A.D.Lewis , Geometric Control of Mechanical Systems , Texts in Applied Mathematics, Springer (2004)
[3]M.C.Munoz-Lecanda and F.J.Yaniz , Dissipative control of mechanical systems:a geometric approach , SIAM Journal of Control and Optimization, 40(5):1505-1516 (2002)