arXiv subjects

Leonid Fridman

Publications and source records attributed to Leonid Fridman.

21 records · Page 2Linked to original sources

arXiv2018

Non-Uniform Stability, Detectability, and, Sliding Mode Observer Design for Time Varying Systems with Unknown Inputs

This paper discusses stability and robustness properties of a recently proposed observer algorithm for linear time varying systems. The observer is based on the approximation and subsequent modification of the non-negative Lyapunov exponents which yields a (non-uniform) exponentially stable error system. Theoretical insights in the construction of the observer are given and the error system is analyzed with respect to bounded unknown inputs. Therefor, new conditions for bounded input bounded state stability for linear time varying systems are presented. It is shown that for a specific class of linear time varying systems, a cascaded observer based on higher order sliding mode differentiators can be designed to achieve finite time exact reconstruction of the system states despite the unknown input. A numerical simulation example shows the applicability of the proposed approach.

math.OC↗

arXiv2017

Is It Reasonable to Substitute Discontinuous SMC by Continuous HOSMC?

Professor Utkin in his discussion paper proposed an example showing that the amplitude of chattering caused by the presence of parasitic dynamics in systems governed by First-Order Sliding-Mode Control (FOSMC) is lower than the obtained using Super-Twisting Algorithm (STA). This example served to motivate this research reconsidering the problem of comparison of chattering magnitude in systems governed by FOSMC that produces a discontinuous control signal and by STA that produces a continuous one, using Harmonic Balance (HB) methodology. With this aim the Averaged Power (AP) criteria for chattering measurements is revisited. The STA gains are redesigned to minimize amplitude or AP of oscillations predicted by HB. The comparison of the chattering produced by FOSMC and STA with redesigned gains is analyzed taking into account their amplitudes, frequencies and values of AP allowing to conclude that: (a) for any value of upperbound of disturbance and Actuator Time Constant (ATC) there exist a bounded disturbance for which the amplitude and AP of chattering produced by FOSMC is lower than the caused by STA; (b) if the upperbound of disturbance and upperbound of time-derivative disturbance are given, then for all sufficiently small values of ATC the amplitude of chattering and AP produced by STA will be smaller than the caused by FOSMC; (c) critical values of ATC are predicted by HB for which the parameters, amplitude of chattering and AP, produced by FOSMC and STA are the same. Also the frequency of self-exited oscillations caused by FOSMC is always grater than the produced by STA.

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arXiv2013

Pole-placement in higher-order sliding-mode control

We show that the well-known formula by Ackermann and Utkin can be generalized to the case of higher-order sliding modes. By interpreting the eigenvalue assignment of the sliding dynamics as a zero-placement problem, the generalization becomes straightforward and the proof is greatly simplified. The generalized formula retains the simplicity of the original one while allowing to construct the sliding variable of a single-input linear time-invariant system in such a way that it has desired relative degree and desired sliding-mode dynamics. The formula can be used as part of a higher-order sliding-mode control design methodology, achieving high accuracy and robustness at the same time.

math.OC↗