A geometric approach to nonlinear singularly perturbed control systems (Q1096569)

The paper considers a class of nonlinear control systems depending on a parameter \(dz/dt=Z(z,\epsilon,u)\). A necessary and sufficient condition including ``conservation'', ``equilibrium'' and ``transversality'' properties is presented under which the system can be transformed into a singular perturbation system \(dx/d\tau =\epsilon X(x,y,\epsilon,u)\), \(dy/d\tau =Y(x,y,\epsilon,u)\) such that \(\{\) (x,y), \(Y(x,y,0,u)=0\}\) is a smooth control-dependent manifold of constant dimension. As examples a point-mass model of an aircraft and a model of a manipulator with flexible joints are discussed.