A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

Abstract

This paper proposes a high-gain observer for a class of nonlinear fractional-order systems. Indeed, this approach is based on Caputo derivative to solve the estimation problem for nonlinear systems. The proposed high-gain observer is used to estimate the unknown states of a nonlinear fractional system. The use of Lyapunov convergence functions to establish stability of system is detailed. The influence of different fractional orders on the estimation is presented. Ultimately, numerical simulation examples demonstrate the efficiency of the proposed approach.

Application of fractional controller in longitudinal control of aircraft

“…The fractional order controller adds the differential order, which can adjust the integral action slightly based on the integral gain adjustment. The integration order can ensure that the regulation time and overshoot of the system are within the index range [1] . The system's reaction time is faster when the integration order is small.…”

“…Through the above analysis, we know that based on the mediation of the integer order controller, the two new parameters of the fractional order controller, the integral order and the differential order, make the control function of the integral and differential links of the controller more flexible. The fractional controller is a kind of "rational" controller, which takes into account the stability and dynamic performance of the system, and improves the steady-state performance of the system at the same time [1] so that the control system can meet the requirements of the control index. Based on this, this paper proposes a fractional controller whose control form is as follows:…”

Spatially modulated ablation driven by chaotic attractors in human lung epithelial cancer cells

“…Dynamical systems that tend to converge toward mathematical attractors are highly sensitive for measuring a variety of physical characteristics, including light intensity, optical chaos and temperature [29]. In this direction, the Arneodo differential equations have been analyzed to explore complex frequency-dependent processes; comparative complexity to differential equations that describes strange attractors has been pointed out [30]. The Arneodo attractor is a chaotic system with spiral structure, it was chosen for the study presented in this report due to its dynamic behavior, transient chaos, fixed points and a control easier than others [31,32].…”

Stability Analysis of Finite Time for a Class of Nonlinear Time-Delay Fractional-Order Systems

“…Their utility spans diverse domains, including electricity, thermal systems, chemistry, signal processing, and control theory. These concepts find applications in various scenarios, including, but not limited to, asymptotic stability [2], finite-time stability [3,4], observer design [5], stabilization [6], and fault estimation [7]. The versatility of non-integer-order calculus renders it an invaluable tool for comprehending and analyzing the intricate behaviors exhibited by complex systems in scientific and engineering disciplines.…”