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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

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
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References:
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