The problem of an admissible synthesis of inertia controls for non-stationary systems with a multidimensional control with geometrical constraints on the control and its derivatives is considered. The problem is solved analytically for a linear system: a constructive structure of a family of controls is given, each of which solves the problem, the time of motion from the initial point at zero is calculated and the corresponding trajectory is found. For a non-linear system the problem is solved to a first approximation in the case when there are constraints on the control and on its derivatives. © 2003 Elsevier Ltd. All rights reserved.
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