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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 $dz/dt=Z(z,\epsilon,u)$. 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.
Reviewer: A.Dontchev

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
Full Text: DOI
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