Levant, Arie ( formerly Levantovsky, Lev )
Professor of the Applied Mathematics Dept. School of Mathematical Sciences, E-mail: levant@tauex.tau.ac.il
Tel-Aviv University,
Ramat-Aviv.
Tel-Aviv 69978
Israel
Tel.: +972-3-6408812 (office), Fax: +972-3-6407543
"Real-time" differentiation of the noisy signal f = f0 +h,
representing the "unknown" basic signal f0(t) = sin(0.5 t) + 0.5 cos(t)
corrupted by the noise
h = 107 cos(104 t)
- 2 107 sin(1.7 105 t) + 5 107
cos(1.33 105 t)
and sampled with the time period 10-5.
Filtering differentiator
of the order 3 and the filtering order 7 is applied
Teaching My papers on Google Scholar
Spring 2022. Reception Hours: Tuesday, 14:10 - 15:00, on ZOOM. In better times: Room 123b, Schreiber building
Education:
1987 Ph.D. Thesis "Higher-order sliding modes and their application in control of uncertain processes". Adviser: Prof S.V. Emelyanov. Opponent (secondary adviser): Prof M.A. Krasnoselsky.
1983-1987 Postgraduate studies in mathematical control theory, Institute for System Studies of the USSR Academy of Sciences, Moscow.
1980 B.Sc. and M.Sc. from the Moscow State University, Faculty of Mechanics and Mathematics, majored in the Theory of Differential Equations.
1980 M.Sc. Thesis "Singularities of Stability Region Boundary." Scientific Adviser: Prof V.I. Arnold.
Research Interests:
Nonlinear Control Theory, Sliding Mode Control, Homogeneous Discontinuous Control, Nonlinear Finite-Time-Exact Tracking and Observation, Robust Exact High-Order Differentiation.
Main scientific results:
Establishment of new branches of the Sliding-Mode Control (SMC) Theory - High-Order SMC and Homogeneous SMC; Real-Time Robust Exact Differentiation
Some papers in the PDF format:
Introduction of High-Order SMs:
A.Levant-Robust exact differentiation via sliding mode technique, Automatica, 34(3), 379-384, 1998
Introduction of homogeneous SMC:
A.Levant-Homogeneity approach to high-order sliding mode design. - Automatica, 41(5), 823-830, 2005
A.Levant-Homogeneous quasi-continuous sliding-mode control. Lecture Notes in Control and Information Sciences, 334, 143--168, "Advances in Variable Structure and Sliding Mode Control", 2006
A.Levant-Construction principles of 2-sliding mode design. Automatica, 43(4), 576-586, 2007
A.Levant,L.Alelishvili-Integral
High-Order Sliding Modes, IEEE Transactions on Automatic Control, 52(7), 1278 - 1282, 2007
Proofs for High-Order Integral Sliding Modes - see here and here
Artificial increase of the output relative degree:
A.Levant-Chattering Analysis, IEEE Transactions on Automatic Control, 55(6), 1380 - 1389, 2010
Introduction of Practical Relative Degree:
Feasibility of fixed-time convergence:
A.Levant-On Fixed and Finite Time Stability in Sliding Mode Control. Corrected version. In_Proc._of_the 52th IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, December 10-13, 2013
Arbitrary convergence-time function realization, including acceleration of MIMO finite-time convergence up to fixed-time convergence
Discretization of homogeneous SMC:
S.Ding, A.Levant, S.Li - Simple homogeneous sliding-mode controller, Automatica, 67(5),22-32,2016
General weighted homogeneity of differerntial inclusions:
Asymptotic optimality of SM-based differentiators:
A.Levant, M.Livne, X.Yu-Sliding-Mode-Based Differentiation and Its Application, 20th IFAC World Congress, Toulouse, July 9-14, France, 2017. A typo has been corrected in the simulation section.
Universal homogeneous control templates:
A.Levant-Non-Lyapunov SISO homogeneous control design, IEEE CDC2017
Fast-convergent SM-based differentiators with variable gains:
A.Levant-Filtering Differentiators and Observers, VSS, Graz, Austria, July 9-11, 2018
Filtering unbounded noises in differentiation (still exact without noises!):
A.Levant,X.Yu-Sliding Mode Based Differentiation and Filtering, IEEE TAC, 63(9), 3061-3067, 2018
A.Levant-Homogeneous filtering and differentiation based on sliding modes, IEEE CDC'2019
Presentation of Filtering Differentiators (December, 2019)
Discretization of differentiators, event-triggered sampling:
SMC for students: survey-tutorial, 2019
Lecture "Homogeneous Control and Observation of Uncertain SISO Systems", Dalian Maritime University, China, July 27, 2020, Mexico, January 13, 2021 ZOOM recording of July 27, 2020
A.Hanan, A.Jbara,A.Levant-Low-chattering discretization of sliding mode control, presented at IEEE CDC'2021, December 17