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A bound for the degree of nonholonomy in the plane. (English) Zbl 0871.93024
Summary: Let \(\Sigma =(V_{1},\ldots,V_{s})\) be a system made with vector fields \(V_{1},\ldots,V_{s}\) in \({\mathbb{R}}^{n}\) whose coordinates are polynomials of degree \(\leq\) d. To such a system is associated the control system ẋ=\(\sum u_{i}V_{i}\). It is proven that in the case n=2, the degree of nonholonomy of such a system is bounded by a function \(\phi \)(2,d)\(\leq 6d^{2}-2d+2.\)

MSC:
93C10 Nonlinear systems in control theory
70F25 Nonholonomic systems related to the dynamics of a system of particles
58E25 Applications of variational problems to control theory
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