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Singularities of attainability domains with a pulse-limited control action. (English. Russian original) Zbl 1467.93026

Mech. Solids 53, Suppl. 2, 76-86 (2018); translation from Prikl. Mat. Mekh. 82, No. 5, 631-643 (2018).
Summary: Linear stationary systems with single-control (perturbing) action are considered. The impulse of control actions is considered limited. Some properties of the boundaries of attainability domains are studied. It is shown that the boundary of the attainability domain can have flat regions, regions of ruled surfaces, edges, and conical angular points. An attainability domain is not strictly convex if there are straight edges and/or flat regions on the boundary. The behavior of the boundaries of the attainability domains with increasing time is studied. A third-order system with a threefold zero eigenvalue (triple integrator) is considered as an example. The structure of the attainability domain of this system is analytically investigated in three-dimensional space. An attainability domain is constructed numerically for some time values.

MSC:

93B03 Attainable sets, reachability
93C70 Time-scale analysis and singular perturbations in control/observation systems
93C05 Linear systems in control theory
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