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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
##### Keywords:
degree of nonholonomy; polynomial vector fields
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##### References:
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