Simple finite-time sliding mode control approach for jerk systems

Nguazon, Tekou; Nguekeng, Tekou; Tchitnga, Robert; Fomethe, A.

doi:10.1177/1687814018822211

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…Notable is the quality of research work conducted toward the characterization and application of third-order circuits (often termed 'jerk' circuits) [8][9][10]. Jerk-type systems are not confined to the field of electrical circuit theory, as they are encountered in mechanics [11,12] and biomechanics [13], to name a few.…”

Section: Introductionmentioning

confidence: 99%

A Coordinate-Free Variational Approach to Fourth-Order Dynamical Systems on Manifolds: A System and Control Theoretic Viewpoint

Fiori

2024

Mathematics

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The present paper describes, in a theoretical fashion, a variational approach to formulate fourth-order dynamical systems on differentiable manifolds on the basis of the Hamilton–d’Alembert principle of analytic mechanics. The discussed approach relies on the introduction of a Lagrangian function that depends on the kinetic energy and the covariant acceleration energy, as well as a potential energy function that accounts for conservative forces. In addition, the present paper introduces the notion of Rayleigh differential form to account for non-conservative forces. The corresponding fourth-order equation of motion is derived, and an interpretation of the obtained terms is provided from a system and control theoretic viewpoint. A specific form of the Rayleigh differential form is introduced, which yields non-conservative forcing terms assimilable to linear friction and jerk-type friction. The general theoretical discussion is complemented by a brief excursus about the numerical simulation of the introduced differential model.

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Section: Introductionmentioning

confidence: 99%

A Coordinate-Free Variational Approach to Fourth-Order Dynamical Systems on Manifolds: A System and Control Theoretic Viewpoint

Fiori

2024

Mathematics

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“…Since Lorenz [4] found the first chaotic attractor in 1963 while describing the simplified Rayleigh–Benard problem, the theory of chaos has obtained recognition in many fields of science and engineering. It can be encountered in medicine [5], in chemistry [6] in electromechanical [7, 8, 9] and in optical systems [10], in control, secure communications and crypto systems [11, 12, 13], or in neurosystems [14, 15], just to name some. One of the most active fields for chaos and applications remains that of electronic circuits.…”

Section: Introductionmentioning

confidence: 99%

Didactic model of a simple driven microwave resonant T-L circuit for chaos, multistability and antimonotonicity

Talla

Tchitnga

Kengne

et al. 2019

Heliyon

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A simple driven bipolar junction transistor (BJT) based two-component circuit is presented, to be used as didactic tool by Lecturers, seeking to introduce some elements of complex dynamics to undergraduate and graduate students, using familiar electronic components to avoid the traditional black-box consideration of active elements. Although the effect of the base-emitter (BE) junction is practically suppressed in the model, chaotic phenomena are detected in the circuit at high frequencies (HF), due to both the reactant behavior of the second component, a coil, and to the birth of parasitic capacitances as well as to the effect of the weak nonlinearity from the base-collector (BC) junction of the BJT, which is otherwise always neglected to the favor of the predominant but now suppressed base-emitter one. The behavior of the circuit is analyzed in terms of stability, phase space, time series and bifurcation diagrams, Lyapunov exponents, as well as frequency spectra and Poincaré map section. We find that a limit cycle attractor widens to chaotic attractors through the splitting and the inverse splitting of periods known as antimonotonicity. Coexisting bifurcations confirm the existence of multi-stability behaviors, marked by the simultaneous apparition of different attractors (periodic and chaotic ones) for the same values of system parameters and different initial conditions. This contribution provides an enriching complement in the dynamics of simple chaotic circuits functioning at high frequencies. Experimental lab results are completed with PSpice simulations and theoretical ones.

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State Synchronization for a Class of n-Dimensional Nonlinear Systems with Sector Input Nonlinearity via Adaptive Two-Stage Sliding Mode Control

Yang

Wang

et al. 2020

Mathematical Problems in Engineering

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This study addresses an adaptive two-stage sliding mode control (SMC) scheme for the state synchronization between two identical systems, which belong to a kind of n-dimensional chaotic system, by considering the appearance of lumped system uncertainties and external disturbances. The controlled system is assumed to be attached to sector nonlinearity for the control input. The proposed adaptive control scheme involves time-variable state-feedback gains, which are updated in accordance with the appropriate adapted rules without foreknown the certain information of nonlinear system dynamics, bounds of lumped system uncertainties and external disturbances, and sector input nonlinearity. The derivation of the control scheme is found based on the introduced sequence of two sliding functions. The stage 1 sliding function is defined by the states of the error dynamical system, where the asymptotical stability is inherent. Then, the stage 2 sliding function is formed by the stage 1 function, where the finite-time stabilization is guaranteed. The proposed adaptive control scheme can cope with the effect of sector nonlinearity for the control to meet the control goal. The sufficient conditions of the stability of the error dynamical system are proven mathematically by means of the Lyapunov theorem. Besides, the capacity of the present scheme is carried out by the numerical studies.

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Simple finite-time sliding mode control approach for jerk systems

Cited by 3 publications

References 29 publications

A Coordinate-Free Variational Approach to Fourth-Order Dynamical Systems on Manifolds: A System and Control Theoretic Viewpoint

A Coordinate-Free Variational Approach to Fourth-Order Dynamical Systems on Manifolds: A System and Control Theoretic Viewpoint

Didactic model of a simple driven microwave resonant T-L circuit for chaos, multistability and antimonotonicity

State Synchronization for a Class of n-Dimensional Nonlinear Systems with Sector Input Nonlinearity via Adaptive Two-Stage Sliding Mode Control

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