Quotient Methods

Feedback linearization is a technique that globally transforms a nonlinear system into a linear one. A feedback control law is then applied to the transformed system so as to achieve global asymptotical stable closed-loop dynamics. The construction of the required elements can be simplified if suitable equivalence classes of vectorfields and associated submanifolds are properly chosen. This leads to quotient vector bundles, and quotient submanifolds that foliates the original manifold into a nested sequence of foliations. The construction is performed both analytically and numerically. The interesting aspect of the construction is that it can be applied to systems that are not feedback linearizable. It also helps circumventing singularities in a variety of applications, especially in the case of the field controlled DC motor.  

S. S. Willson, P. Müllhaupt and D. BonvinNumerical algorithm for feedback linearizable systems10th Int. Conference of Numerical Analysis and Applied Mathematics, Kos, Greece, 2012.

S. S. Willson, P. Müllhaupt and D. BonvinAvoiding Feedback-Linearization Singularity Using a Quotient Method — The Field-Controlled DC Motor CaseAmerican Control Conference, Montreal, Canada, 2012.

S. S. Willson, K. M. Daly, P. Müllhaupt and D. BonvinQuotient method for stabilising a ball-on-a-wheel system – Experimental resultsIEEE CDC 2012, Hawaii, 2012.

S. S. Willson, P. Müllhaupt and D. Bonvin. A Quotient Method for Designing Nonlinear Controllerssubmitted to European Journal of Control, 2012.

D. Ingram, S. S. Willson, P. Müllhaupt and D. BonvinStabilization of the cart-pendulum system through approximate manifold decompositionIFAC, Milano, Italy 2011, 2011.

S. S. Willson, P. Mullhaupt and D. BonvinQuotient method for controlling the acrobotCDC 2009, Shanghai, 2009.