Abstract
This paper contributes to the theory of approximations of continuous-time control/uncertain systems by discrete-time ones. Discrete approximations of higher than first order accuracy are known for affine control systems only in the case of commutative controlled vector fields. The novelty in this paper is that constructive second order discrete approximations are obtained in the case of two non-commutative vector fields. An explicit parameterization of the reachable set of the Brockett non-holonomic integrator is a key auxiliary tool. The approach is not limited to the present deterministic framework and may be extended to stochastic differential equations, where similar difficulties appear in the non-commutative case.
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Krastanov, M.I., Veliov, V.M. (2010). High-Order Approximations to Nonholonomic Affine Control Systems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_34
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DOI: https://doi.org/10.1007/978-3-642-12535-5_34
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