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One of the most important control problems is control under heavy uncertainty conditions. While there are a number of sophisticated methods like adaptation based on identi cation and observation, or absolute stability methods, the most obvious way to withstand the uncertainty is to keep some constraints by "brutal force". Indeed any strictly kept equality(More)
A universal finite-time-convergent controller is developed capable to control the output of any uncertain single-input-single-output system with a known permanent relative degree . The tracking error is steered to zero by means of a control dependent only on _ . . . and continuous everywhere except the set = _ = = = 0. A robust output-feedback controller(More)
It is shown that a general uncertain single-input–single-output regulation problem is solvable only by means of discontinuous control laws, giving rise to the so-called high-order sliding modes. The homogeneity properties of the corresponding controllers yield a number of practically important features. In particular, finite-time convergence is proved, and(More)
The super-twisting second-order sliding-mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems. The finite time convergence of the observer is proved. Thus, the observer can be designed independently of the controller. A discrete version of the observer is considered and the corresponding accuracy is estimated.
Second-order sliding modes are used to keep exactly a constraint of the second relative degree or just to avoid chattering, i.e. in the cases when the standard (first order) sliding mode implementation might be involved or impossible. Design of a number of new 2-sliding controllers is demonstrated by means of the proposed homogeneity-based approach. A(More)
Arbitrary-order homogeneous differentiators based on highorder sliding modes are generalized to ensure exact robust kth-order differentiation of signals with a given functional bound of the th derivative. The asymptotic accuracies in the presence of noises and discrete sampling are estimated. The results are applicable for the global observation of system(More)
Control of high-performance low-cost unmanned air vehicles involves the problems of incomplete measurements, external disturbances and modeling uncertainties. Sliding mode control combines high precision with robustness to the aforementioned factors. The idea behind this approach is the choice of a particular constraint which, when maintained, will provide(More)