A robustness study of a finite‐time/exponential tracking continuous control scheme for constrained‐input mechanical systems: Analysis and experiments

Abstract

The closed-loop analysis of a recently proposed continuous scheme for the finite-time or exponential tracking control of constrained-input mechanical systems is reformulated under the consideration of an input-matching bounded perturbation term. This is motivated by the poor number of works devoted to support the so-cited argument claiming that continuous finite-time controllers are more robust than asymptotical (infinite-time) ones under uncertainties and the limitations of their results. We achieve to analytically prove that, for a perturbation term with sufficiently small bound, the considered tracking continuous control scheme leads the closed-loop error variable trajectories to get into an origin-centered ball whose radius becomes smaller in the finite-time convergence case, entailing smaller posttransient variations than in the exponential case. Moreover, this is shown to be achieved for any initial condition, avoiding to restrain any of the parameters involved in the control design, and under the suitable consideration of the nonautonomous nature of the closed loop. The study is further corroborated through experimental tests on a multi-degree-of-freedom robotic manipulator, which do not only confirm the analytical result but also explore the scope or limitations of its conclusions under adverse perturbation conditions. K E Y W O R D Sconstrained inputs, input-matching perturbation, mechanical systems, robustness, tracking continuous control, uniform finite-time stability INTRODUCTIONControl synthesis aiming at the accomplishment of a regulation or trajectory tracking goal in finite time through continuous feedback has been the subject of intensive research in the last years. Numerous works with such a design objective formulation have been motivated arguing benefits of the finite-time algorithms over the asymptotic (infinite-time) ones, such as faster convergence and improved robustness under uncertainties. [1][2][3][4] However, this has not yet been exhaustively explored or brought to the fore through formal analysis or implementation tests. The only analysis treating one of those aspects, that the authors are aware of, was developed by Bhat and Bernstein, 5 who studied the robustness issue. More Int J Robust Nonlinear Control. 2020;30:3923-3944. wileyonlinelibrary.com/journal/rnc

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