This paper presents fractional order fixed-time nonsingular terminal sliding mode control for stabilization and synchronization of fractional order chaotic systems with uncertainties and disturbances. First, a novel fractional order terminal sliding mode surface is proposed to guarantee the fixed-time convergence of system states along the sliding surface. Second, a nonsingular terminal sliding mode controller is designed to force the system states to reach the sliding surface within fixed-time and remain on it forever. Furthermore, the fractional Lyapunov stability theory is used to prove the fixed-time stability and the robustness of the proposed control scheme and estimate the upper bound of convergence time. Next, the proposed control scheme is applied to the synchronization of two nonidentical fractional order Liu chaotic systems and chaos suppression of fractional order power system. Simulation results verify the effectiveness of the proposed control scheme. Finally, some application issues about the proposed scheme are discussed.
相似文献In this paper, we propose a stabilization method for dynamic gaits of quadrupedal walking robots covering a wide range of speeds and various types of gait. Our stabilization method is based on adjusting the contact time between the four legs and ground. By modulating the contact time, the impact applied to the body can be controlled and stabilized. The stability provided by the proposed algorithm was proved in the sense of Lyapunov. The proposed algorithm also demonstrated robust performance under large external disturbances, and the performance was compared with other algorithms through simulations. Simulation results of bounding gaits under different ground conditions were compared, and the various types of stable gait implemented by the proposed algorithm are also presented.
相似文献This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional-order models. When differentiation orders are assumed known, least squares and prediction error methods, being direct extensions to fractional-order models of the classic methods used for integer-order models, are compared to our new method, the long-memory recursive prediction error method. Given the long-memory property of fractional models, Monte Carlo simulations prove the efficiency of our proposed algorithm. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation-order estimation. The performances of the new proposed recursive algorithm are studied through Monte Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfers in lungs are modeled by using thermal two-port network formalism with fractional models.
相似文献Aiming at the difficult identification of fractional order Hammerstein nonlinear systems, including many identification parameters and coupling variables, unmeasurable intermediate variables, difficulty in estimating the fractional order, and low accuracy of identification algorithms, a multiple innovation Levenberg–Marquardt algorithm (MILM) hybrid identification method based on the fractional order neuro-fuzzy Hammerstein model is proposed. First, a fractional order discrete neuro-fuzzy Hammerstein system model is constructed; secondly, the neuro-fuzzy network structure and network parameters are determined based on fuzzy clustering, and the self-learning clustering algorithm is used to determine the antecedent parameters of the neuro-fuzzy network model; then the multiple innovation principle is combined with the Levenberg–Marquardt algorithm, and the MILM hybrid algorithm is used to estimate the linear module parameters and fractional order. Finally, the academic example of the fractional order Hammerstein nonlinear system and the example of a flexible manipulator are identified to prove the effectiveness of the proposed algorithm.
相似文献This paper investigates a logistic map derived from a difference equation in the framework of discrete fractional calculus. Through the Poincaré plots and Julia sets, the map’s chaotic and fractal characteristics are studied comparing with those of a quadratic map to be proposed. The memory effect of fractional difference maps is reflected in these dynamics, and some reasonable explanations are given by combining with quantitative analysis. A coupled controller is designed to realize synchronization between fractional difference logistic map and fractional difference quadratic map.
相似文献In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.
相似文献After defining the fractional Λ-derivative, having all the requirements for corresponding to a differential, the fractional Λ-strain is established. Contrary to the common strain, that has a local character, fractional strain access a non-local character, quite important for expressing deformations in non-homogeneous media with microcracks and inhomogeneities, that may change during deformation. The purpose of the present work is the establishement of the principles and laws of the non-linear Λ-fractional Elasticity. The Λ-fractional non-linear stress–strain relations are derived. The restriction into the linear fields is presented. Further, fractional deformation of a fractal bar is discussed. The Fractional deformations and fractional elastic problems are set up with the definition of stresses and displacements in the initial space. Further, the Λ-fractional analysis with its conjugate Λ-fractional space is presented, considering fractional derivatives of both sides in the bending of a cantilever beam under uniform continuously distributed loading.
相似文献This paper investigates the Mittag-Leffler stability (MLS) of nonlinear uncertain dynamic systems (NUDSs) with impulsive effects involving the random-order fractional derivative (ROFD) under the fuzzy concept. The major tool used in this paper is Lyapunov’s direct method, which brings high efficiency in surveying the stability theory of dynamic systems. Some algebraic inequalities on the ROFD are established, which is necessary to study the MLS of NUDSs. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.
相似文献Divergence and flutter instabilities of pipes conveying fluid with fractional viscoelastic model has been investigated in the present work. Attention is concentrated on the boundaries of the stability. Based on the Euler–Bernoulli beam theory for structural dynamics, viscoelastic fractional model for damping and, plug flow model for fluid flow, equation of motion has been derived. The effects of gravity, and distributed follower forces are also considered. By transferring the equation of motion to the Laplace domain and using the Galerkin method, the characteristic equations are obtained. By solving the eigenvalue problem, frequencies and dampings of the system have been obtained versus flow velocity. Some numerical test cases have been studied with viscoelastic fractional model and the effect of the fractional derivative order and the retardation time is investigated for various boundary conditions.
相似文献The stress–strain response of over-consolidated soft soil, e.g., clay, is dependent on its pre-consolidation history and material state. In this study, a state-dependent constitutive model for over-consolidated soft soils is proposed by extending the fractional plasticity originally developed for granular soil. The state-dependent stress-dilatancy and peak failure behaviour of over-consolidated soft soil are analytically captured through stress-fractional gradient of the current yielding surface. In addition, a reference yielding surface describing the pre-consolidation history of soft soil is proposed. A combined hardening rule expressed as a function of both the incremental plastic volumetric and shear strains is suggested. To validate the proposed model, a series of drained and undrained test results of different soft soils with a wide range of over-consolidation ratios are simulated and compared. It is found that without using additional plastic potentials and state parameters, the developed fractional model can capture the state-dependent hardening and softening responses of soft soils subjected to different over-consolidation states.
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