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This paper combines the fractional-order iterative learning control (FOILC) and the high-gain universal adaptive stabilizer (UAS) into a high-gain adaptive FOILC scheme, which is a feedforward-plus-feedback one. Allowing for the commonality of FOILC and UAS, the proposed scheme requires only the structural information of fractional-order systems, and the convergence condition remains the same with...
This paper reveals a previously ignored problem for fractional order iterative learning control (FOILC) that the fractional order system may have different behaviors when it is initialized differently. To implement a novel scheme of FOILC for this so-called initialized fractional order system, a Dα-type control law is applied, and the convergence condition is derived by using the short memory principle...
This paper discusses the stability issues of fractional-order nonlinear scalar systems by using the distributed-order operators and the order sensitivity method. A positivity check method is proposed by the use of initialized fractional calculus. By doing so, the fractional-order system is converted to a corresponding distributed-order one, and a group of Lyapunov function candidates of the distributed-order...
This paper discusses the parameter and differentiation order identification of continuous fractional order Hammerstein systems in ARX and OE forms. The least squares method is applied to the identification of nonlinear and linear parameters, in which the Grünwald-Letnikov definition and short memory principle are applied to compute the fractional order derivatives. A P-type order learning law is...
The fractional-order Hammerstein system is a cascading system composed of a static nonlinearity followed by a fractional-order linear dynamics, which is a typical nonlinear system satisfying the local Lipschitz condition, and exhibits quasi-linear properties. This paper combines the fractional-order iterative learning control (FOILC) and the fractional-order iterative learning identification (FOILI),...
In this paper, a practical Identification strategy is applied to the optimal design of fractional-order iterative learning control (FOILC). The initialized fractional-order gray-box system with commensurate order or non-commensurate order is identified by using the fractional-order iterative learning Identification and the least square or instrumental variable method. The optimal Dα-type FOILC is...
In the real world, many physical systems are subject to nonholonomic constraints. In this paper, the problem of output consensus is investigated for such kind of systems in chained form. First, the consensus controller is developed for the strongly connected topology using the backstepping design technique. Then, the result is extended to the general directed topology via graph decomposition where...
We deal with the stability problem of the scalar linear time invariant (LTI) stochastic system driven by fractional Brownian motion (fBm). Firstly, the necessary and sufficient conditions are provided for the almost sure asymptotic stability and pth moment asymptotic stability by means of the largest Lyapunov exponent and the Lyapunov exponent of the pth mean, respectively. Furthermore, we obtain...
In this paper, we discuss in time domain the convergence of the iterative process for fractional-order nonlinear systems. A linear adaptive generalized fractional-order iterative learning control scheme is derived, which guarantees the convergence of the algorithm without the knowledge of the system order. The implementation of generalized fractional-order iterative learning controllers can be achieved...
An autonomous, unmanned, aerial, remote sensing platform called AggieAir™ has been developed at Utah State University (USU) to produce multispectral aerial imagery. Its independence of a runway, low cost, and rapid turn-around time for imagery make it an efficient platform for applications in riparian areas and in wetlands management. Using third-party software, the imagery from AggieAir can be stitched...
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