Nonlinear output regulation for over-actuated linear systems

We present results for the definition of nonlinear steady-state manifolds achieving output regulation for input-saturating over-actuated systems. By defining steady-state manifolds of polynomial form and exposing the structure of the studied systems, we derive homogeneous polynomial equations corresponding to the steady-state conditions and present existence conditions for their solution. The numerical computation of the polynomial feedforward inputs that satisfy the zero-error steady state is performed by solving a sum-of-squares program. The solution to this convex problem maximizes the set of exogenous signals for which regulation can be achieved inside the given input bounds.