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A geometric approach to nonlinear singularly perturbed control systems. (English) Zbl 0633.93033
The paper considers a class of nonlinear control systems depending on a parameter dz/dt=Z(z,ϵ,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/dτ=ϵX(x,y,ϵ,u), dy/dτ=Y(x,y,ϵ,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.
Reviewer: A.Dontchev
MSC:
93C10Nonlinear control systems
93B27Geometric methods in systems theory
34E15Asymptotic singular perturbations, general theory (ODE)
70Q05Control of mechanical systems (general mechanics)
93C15Control systems governed by ODE
93C95Applications of control theory