226 research outputs found
Adaptive Backstepping Control for Fractional-Order Nonlinear Systems with External Disturbance and Uncertain Parameters Using Smooth Control
In this paper, we consider controlling a class of single-input-single-output
(SISO) commensurate fractional-order nonlinear systems with parametric
uncertainty and external disturbance. Based on backstepping approach, an
adaptive controller is proposed with adaptive laws that are used to estimate
the unknown system parameters and the bound of unknown disturbance. Instead of
using discontinuous functions such as the function, an
auxiliary function is employed to obtain a smooth control input that is still
able to achieve perfect tracking in the presence of bounded disturbances.
Indeed, global boundedness of all closed-loop signals and asymptotic perfect
tracking of fractional-order system output to a given reference trajectory are
proved by using fractional directed Lyapunov method. To verify the
effectiveness of the proposed control method, simulation examples are
presented.Comment: Accepted by the IEEE Transactions on Systems, Man and Cybernetics:
Systems with Minor Revision
Global output feedback stabilization for nonlinear fractional order time delay systems
summary:This paper investigates the problem of global stabilization by state and output-feedback for a family of for nonlinear Riemann-Liouville and Caputo fractional order time delay systems written in triangular form satisfying linear growth conditions. By constructing a appropriate Lyapunov-Krasovskii functional, global asymptotic stability of the closed-loop systems is achieved. Moreover, sufficient conditions for the stability, for the particular class of fractional order time-delay system are obtained. Finally, simulation results dealing with typical bioreactor example, are given to illustrate that the proposed design procedures are very efficient and simple
Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems
Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods
A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent
asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and
Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National
Research Council of Thailand and Khon Kaen University, Thailand (6200069)
Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI
We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying 0<Ī±<1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finslerās Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations
A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent
asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and
Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National
Research Council of Thailand and Khon Kaen University, Thailand (6200069)
Stability and stabilization of fractional order time delay systems
U ovom radu predstavljeni su neki osnovni rezultati koji se odnose na kriterijume stabilnosti sistema necelobrojnog reda sa kaÅ”njenjem kao i za sisteme necelobrojnog reda bez kaÅ”njenja.TakoÄe, dobijeni su i predstavljeni dovoljni uslovi za konaÄnom vremenskom stabilnost i stabilizacija za (ne)linearne (ne)homogene kao i za perturbovane sisteme necelobrojnog reda sa vremenskim kaÅ”njenjem. Nekoliko kriterijuma stabilnosti za ovu klasu sistema necelobrojnog reda je predloženo koriÅ”Äenjem nedavno dobijene generalizovane Gronval nejednakosti, kao i 'klasiÄne' Belman-Gronval nejednakosti. Neki zakljuÄci koji se odnose na stabilnost sistema necelobrojnog reda su sliÄni onima koji se odnose na klasiÄne sisteme celobrojnog reda. Na kraju, numeriÄki primer je dat u cilju ilustracije znaÄaja predloženog postupka.In this paper, some basic results of the stability criteria of fractional order system with time delay as well as free delay are presented. Also, we obtained and presented sufficient conditions for finite time stability and stabilization for (non)linear (non)homogeneous as well as perturbed fractional order time delay systems. Several stability criteria for this class of fractional order systems are proposed using a recently suggested generalized Gronwall inequality as well as 'classical' Bellman-Gronwall inequality. Some conclusions for stability are similar to those of classical integerorder differential equations. Finally, a numerical example is given to illustrate the validity of the proposed procedure
Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy
In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme
Dynamic analysis of a fractional-order SIRS model with time delay
Mathematical modeling plays a vital role in the epidemiology of infectious diseases. Policy makers can provide the effective interventions by the relevant results of the epidemic models. In this paper, we build a fractional-order SIRS epidemic model with time delay and logistic growth, and we discuss the dynamical behavior of the model, such as the local stability of the equilibria and the existence of Hopf bifurcation around the endemic equilibrium. We present the numerical simulations to verify the theoretical analysis
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