Chun Yin

Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems

This paper develops a fractional-order sliding mode based extremum seeking controller (FO SM-ESC) for the optimization of nonlinear systems. The proposed FO SM-ESC, involving an FO derivative function 0 D t q sgn ( e ) , 0 ? q < 1 is shown to achieve faster tracking and higher control accuracy than the integer-order (IO) SM-ESC. The tradeoff between control performance and parameters selection is analyzed and visualized. The comparison between the FO/IO SM-ESC is given to reveal the potential advantages of the FO controller over the IO controller. Simulation and experimental results show that the FO SM-ESC can have a faster convergence speed and a smaller neighborhood around the optimal operational point.

Design an adaptive sliding mode controller for drive-response synchronization of two different uncertain fractional-order chaotic systems with fully unknown parameters☆

Abstract In this paper, design an adaptive sliding mode controller (ASMC) for master–slave synchronization of two different fractional-order chaotic systems with fully unknown parameters, uncertainties and external disturbances is proposed. The bounds of the unknown parameters, uncertainties and external disturbances are assumed to be unknown in advance. Appropriate adaptive laws are designed to tackle the unknown parameters, uncertainties and external disturbances. Based on the adaptive laws, the ASMC is constructed in order to ensure the occurrence of the sliding motion and synchronization of two different fractional-order systems. The analytical conditions for synchronization of the systems are obtained by utilizing Laplace transform. Finally, numerical examples are provided to illustrate the effectiveness of the proposed ASMC scheme.

Robust stability analysis of fractional-order uncertain singular nonlinear system with external disturbance

This paper investigates robust stability for fractional-order (FO) singular nonlinear systems. The FO system is disturbed by external uncertainty and disturbance. A central analysis technique is enabled by proposing a fundamental boundedness lemma, for the first time. This lemma is used for robust stability analysis of FO systems, especially for Mittag-Leffler stability analysis of FO nonlinear systems. More importantly, how to obtain a more accurate bound is given to reduce conservative. An FO proportional-derivative (PD) controller is proposed to normalize the FO singular system. Furthermore, a criterion for stability of the normalized FO nonlinear systems is provided by linear matrix inequalities (LMIs). Finally, two illustrative simulation examples are presented to illustrate effectiveness of the proposed stability notion.

Fractional-order switching type control law design for adaptive sliding mode technique of 3D fractional-order nonlinear systems

In this article, an adaptive sliding mode technique based on a fractional-order (FO) switching type control law is designed to guarantee robust stability for a class of uncertain three-dimensional FO nonlinear systems with external disturbance. A novel FO switching type control law is proposed to ensure the existence of the sliding motion in finite time. Appropriate adaptive laws are shown to tackle the uncertainty and external disturbance. The calculation formula of the reaching time is analyzed and computed. The reachability analysis is visualized to show how to obtain a shorter reaching time. A stability criteria of the FO sliding mode dynamics is derived based on indirect approach to Lyapunov stability. Effectiveness of the proposed control scheme is illustrated through numerical simulations.

LMI based design of a sliding mode controller for a class of uncertain fractional-order nonlinear systems

In this paper, the problem of designing a sliding mode controller for a class of uncertain fractional-order nonlinear systems with 0 <; β <; 1 is addressed by using linear matrix inequality (LMI) method. A key analysis technique is enabled by proposed a fundamental boundedness lemma, which is used for rigorous stability analysis of fractional-order systems, especially for Mittag-Leffler stability analysis of fractional-order nonlinear systems. A new switching law is given to guarantee the reachability condition. This sliding mode control law is utilized to obtain a controller capable of drawing the state trajectories onto the sliding surface and maintain the sliding motion. Numerical simulation results are presented to show the effectiveness of the proposed sliding mode control scheme.

Delay-partitioning approach design for stochastic stability analysis of uncertain neutral-type neural networks with Markovian jumping parameters

This paper investigates the problem of stability analysis for uncertain neutral-type neural networks with Markovian jumping parameters and interval time-varying delays. By separating the delay interval into multiple subintervals, a Lyapunov-Krasovskii methodology is established, which contains triple and quadruple integrals. The time-varying delay is considered to locate into any subintervals, which is different from existing delay-partitioning methods. Based on the proposed delay-partitioning approach, a stability criterion is derived to reduce the conservatism. Numerical examples show the effectiveness of the proposed methods. HighlightsNovel Lyapunov functions are constructed involving triple and quadruple integrals.The delay interval is decomposed into m equivalent subintervals.Newton-Leibniz formulas apply in each subinterval and derive weight-free matrices.A new inequality is used to reduce conservatism by reciprocally convex inequality.

Successive approximation method for the measurement of thickness using pulsed eddy current

In pulsed eddy-current testing (PECT), material thickness and defect depth are indicated by features such as time to peak and peak value. Before testing, the relationship between thickness/depth and features must be established in advance. This requires multiple reference samples with known thickness/depth. On the other hand, the parameters of each material, such as electrical conductivity and magnetic permeability should be known in advance when calculating by computer. It is time consuming and expensive. In this paper, a new processing scheme is proposed to separate the geometric and conductivity parameters. The thickness/depth of the specimen is quantified into a series of formal unit thickness. There is an excitation frequency which corresponds to every unit thickness level. Using the rich frequency components of the pulsed eddy current response signal, they can be used to scan the thickness of the specimen step by step. When the scanned thickness is close to the thickness, the current frequency is very different with the reference frequency. So this frequency is used to calculate the thickness. In this method, the initial values of the thickness and frequency are detected first to calculate the thickness. It is help to separate the geometric and conductivity parameters. Thus this scheme only requires one reference sample and one known thickness/depth specimen for each material, which significantly reduces the cost of testing.

Permanence, extinction and periodic solutions in a mathematical model of cell populations affected by periodic radiation

A periodic mathematical model of cell populations affected by periodic radiation is presented and studied in this paper. We obtain some sufficient conditions on the permanence and extinction of the system. Furthermore, criteria on the existence and global asymptotic stability of unique positive periodic solutions are established. Some numerical examples are shown to verify our results. A discussion is presented for further study.

Minimum Energy Cognitive Lighting Control: Stability Analysis and Experiments

Energy is one of the most important foundations of the world. However, the demand for lighting consumes a significant amount of electricity. In order to save lighting electricity and reduce cost, one obvious way is to supplement artificial light with natural light. The mixing of artificial and natural lighting, known as hybrid lighting, can be used to indoors for all lighting needs. In order to maintain the overall illumination level at the rated value, the amount of artificial light needs to change according to the varying natural light. To meet the desired energy saving potential, a suitable means for minimizing energy usage throughout the day must be developed. Minimum energy point tracking (MEPT) algorithms can be utilized to tackle this minimization problem. In this paper, a minimum energy cognitive lighting control prototype is proposed, designed and developed. A simple PID control law is implemented to maintain an arbitrary level of illumination while a sliding mode based extremum seeking controller (SM-ESC) is employed to minimize energy usage in the lights. Furthermore, this paper presents the experiment results of our MEPT research and tracking control for light level. The experimental results can show the practicality and effectiveness of the proposed minimum cognitive energy lighting control scheme.© 2013 ASME

Extremum seeking control with fractional-order switching technique design for maximum power point tracking in photovoltaic systems

This paper considers a novel extremum seeking control with fractional-order switching technique (ESC-FOST) as a maximum power point tracking (MPPT) algorithm for a PV system. The proposed ESC-FOST combines extremum seeking controller with FO sliding mode dynamics, in which FO proportional-integral (PI) switching surface is adopted. The ESC-FOST can not only guarantee the output power is maintained around the maximum power point but that it will also have a faster tracking performance and higher accuracy than the ESC with integer-order switching technique (ESC-IOST). Simulation and experimental results demonstrate the effectiveness and benefit of the ESC-FOST for the PV plant.