11,936 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
New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems
This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of TakagiâSugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2âdecades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parametersâ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use
On the interpretation and identification of dynamic Takagi-Sugenofuzzy models
Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
We survey some representative results on fuzzy fractional differential
equations, controllability, approximate controllability, optimal control, and
optimal feedback control for several different kinds of fractional evolution
equations. Optimality and relaxation of multiple control problems, described by
nonlinear fractional differential equations with nonlocal control conditions in
Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Applied Mathematics', ISSN: 0377-0427.
Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication
20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515
On approximation properties of smooth fuzzy models
This Paper Addresses The Approximation Properties Of The Smooth Fuzzy Models. It Is Widely Recognized That The Fuzzy Models Can Approximate A Nonlinear Function To Any Degree Of Accuracy In A Convex Compact Region. However, In Many Applications, It Is Desirable To Go Beyond That And Acquire A Model To Approximate The Nonlinear Function On A Smooth Surface To Gain Better Performance And Stability Properties. Especially In The Region Around The Steady States, When Both Error And Change In Error Are Approaching Zero, It Is Much Desired To Avoid Abrupt Changes And Discontinuity In The Approximation Of The Input-Output Mapping. This Problem Has Been Remedied In Our Approach By Application Of The Smooth Compositions In The Fuzzy Modeling Scheme. In The Fuzzy Decomposition Stage Of Fuzzy Modeling, We Have Discretized The Parameters And Then Calculated The Result Through Partitioning Them Into A Dense Grid. This Could Enable Us To Present The Formulations By Convolution And Fourier Transformation Of The Parameters And Then Obtain The Approximation Properties By Studying The Structural Properties Of The Fourier Transformation And Convolution Of The Parameters. We Could Show That, Irrespective To The Shape Of The Membership Function, One Can Approximate The Dynamics And Derivative Of The Continuous Systems Together, Using The Smooth Fuzzy Structure. The Results Of The Paper Have Been Tested And Evaluated On A Discrete Event System In The Hybrid And Switched Systems Framework
Quantum Mechanics of Extended Objects
We propose a quantum mechanics of extended objects that accounts for the
finite extent of a particle defined via its Compton wavelength. The Hilbert
space representation theory of such a quantum mechanics is presented and this
representation is used to demonstrate the quantization of spacetime. The
quantum mechanics of extended objects is then applied to two paradigm examples,
namely, the fuzzy (extended object) harmonic oscillator and the Yukawa
potential. In the second example, we theoretically predict the phenomenological
coupling constant of the meson, which mediates the short range and
repulsive nucleon force, as well as the repulsive core radius.Comment: RevTex, 24 pages, 1 eps and 5 ps figures, format change
Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory
We construct an approximation to field theories on the noncommutative torus
based on soliton projections and partial isometries which together form a
matrix algebra of functions on the sum of two circles. The matrix quantum
mechanics is applied to the perturbative dynamics of scalar field theory, to
tachyon dynamics in string field theory, and to the Hamiltonian dynamics of
noncommutative gauge theory in two dimensions. We also describe the adiabatic
dynamics of solitons on the noncommutative torus and compare various classes of
noncommutative solitons on the torus and the plane.Comment: 70 pages, 4 figures; v2: References added and update
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