Journal of Mathematical Sciences

, Volume 220, Issue 3, pp 301–317

# Two-Point Problem for Systems Satisfying the Controllability Condition with Lie Brackets of the Second Order

• V. V. Grushkovskaya
• A. L. Zuev
Article

We study a two-point control problem for systems linear in control. The class of problems under consideration satisfies a controllability condition with Lie brackets up to the second order, inclusively. To solve the problem, we use trigonometric polynomials whose coefficients are computed by expanding the solutions into the Volterra series. The proposed method allows one to reduce the two-point control problem to a system of algebraic equations. It is shown that this algebraic system has (locally) at least one real solution. The proposed method for the construction of control functions is illustrated by several examples.

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## Authors and Affiliations

• V. V. Grushkovskaya
• 1
• A. L. Zuev
• 2
1. 1.Institute of MathematicsUkrainian Natonal Academy of SciencesKievUkraine
2. 2.Max Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany