Switching curve deformation in a time-optimal closed-loop system

The dynamics of a closed-loop system resulting from the solution of a time-optimal problem of a two-dimensional differential inclusion are discussed. It is shown that internal uncertainties (such as variations in resistances or parameter changes) cause trajectories of the closed-loop motion to (1) spiral convergently around the target and reach it in a finite time; (2) spiral divergently around the target and reach a limit curve; and (3) reach the target in a finite time in a sliding mode. Some suggestion for practical applications are given.<
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