Corresponding author: [email protected] Heng Liu Department of Applied Mathematics, Huainan Normal University, Huainan 232038, China College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China Shenggang Li College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China e-mail: [email protected] Guanjun Lia, Hongxing Wan...

This paper presents a new strategy for digital control and parameters identification of robust fractional order controllers based on fractional reference model. The model consists on an ideal closed-loop system whose open-loop is given by the Bode’s ideal transfer function with the suitable parameters. This technique suggests an online parameters tuning of fractional order PID controller (FPID)...

Temperature control in buildings has been a highly studied area of research and interest since it affects the comfort occupants. Commonly, temperature systems like centralized air conditioning or heating work with fixed set point locally at thermostat, but users turn on off system when they feel is too hot cold. This configuration clearly not optimal terms energy consumption even thermal for us...

and Applied Analysis 3 Fractional calculus is a generalization of integer-order integration and differentiation to non-integer-order ones. Let symbol aDt denote the fractional-order fundamental operator, defined as follows 20, 21 : D aDt ⎧ ⎪ ⎪⎨ ⎪ ⎪⎩ d dtλ R λ > 0, 1 R λ 0, ∫ t a dτ −λ R λ < 0, 2.1 where a and t are the limits of the operation, λ is the order of the operation, and generally λ ∈ ...

Two classes of partially known systems are considered in this note; both of them have a fractional parameterization of the unknowns. The first class consists of nonlinear systems whose uncertainties are bounded by a function of fractional parameterization, and the second class compromises those systems whose unknown dynamics can directly, but nonlinearly, be parameterized. It is shown that adap...

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

*Correspondence: [email protected] Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, Xidian University, Xi’an, China School of Civil & Environmental Engineering, University of New South Wales, Sydney, Australia Abstract This paper investigates the problems of robust stability and stabilization of LTI fractional-order systems with poly-topic and two-norm bounded ...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...