This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.
Event-triggered communication mechanism (ETCM) provides an efficient way to reduce unwanted network traffic. This article studies the co-design of an ETCM and an annular finite-time (AFT) H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter for networked switched systems (NSSs). First, the AFT definition and ETCM are presented. Second, a set of mode-dependent average dwell-time (MADT) switching rules is given. By resorting to a delay-dependent Lyapunov functional approach, some feasible AFT H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters are designed. Third, it is proved that the filtering error system (FES) has a good performance in attenuating the external disturbances. Finally, the feasibility of the developed method is verified via simulation.
This paper deals with the problem of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℒ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℒ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>model reduction for continuous-time nonlinear uncertain systems. The approach of the construction of a reduced-order model is presented for high-order nonlinear uncertain systems described by the T-S fuzzy systems, which not only approximates the original high-order system well with an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℒ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℒ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>error performance level<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>γ</mml:mi></mml:mrow></mml:math>but also translates it into a linear lower-dimensional system. Then, the model approximation is converted into a convex optimization problem by using a linearization procedure. Finally, a numerical example is presented to show the effectiveness of the proposed method.
No abstract is provided for this article.
An important challenge in the static output-feedback control context is to provide an isolated gain matrix possessing a zero–nonzero structure, mainly in problems presenting information structure constraints. Although some previous works have contributed some relevant results to this issue, a fully satisfactory solution has not yet been achieved up to now. In this note, by using a Linear Matrix Inequality approach and based on previous results given in the literature, we present an efficient methodology which permits us to obtain an isolated static output-feedback gain matrix having, simultaneously, a zero–nonzero structure imposed a priori.
This article investigates the problem of sliding mode control (SMC) for semi-Markov switching systems (S-MSSs) with quantized measurement in finite-time level. The transition between different subsystems obeys a stochastic semi-Markov process related to nonexponential distribution. Additionally, due to the sensor information constraints, the state vectors are not always measurable in practice. Moreover, compared with existing results in literature, the output quantization is first considered for finite-time SMC problem via a logarithmic quantizer. Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance onto the overall performance of the system under consideration. First, by the key points of stochastic semi-Markov Lyapunov function and observer design theory, a desired SMC law is constructed to guarantee that the system trajectories can arrive at the specified sliding surface (SSS) within an assigned finite-time level. Then, ST-dependent sufficient conditions are established to ensure the required finite-time boundedness performance including both reaching phase and sliding motion phase. Finally, the applicability of the proposed results is demonstrated by a single-link robot arm model.
This paper studies the problem of finite-impulse response (FIR) filtering design of time-delay system. The time-delay considered here is time-varying meanwhile with a certain stochastic characteristic, and the probability of delay distribution is assumed to be known. Furthermore, the requirement of pulse-shape is also considered in filter design. Employing the information about the size and probability distribution of delay, a delay-probability-distribution-dependent criterion is proposed for the filtering error system. Based on a Lyapunov-Krasovskii functional, a set of linear matrix inequalities (LMIs) are formulated to solve the problem. At last, a numerical example is used to demonstrate the effectiveness of the filter design approach proposed in the paper.
This book presents analysis and design for a class of stochastic systems with semi-Markovian jump parameters. It explores systematic analysis of semi-Markovian jump systems via sliding mode control strategy which makes up the shortages in the analysis and design of stochastic systems. This text provides a novel estimation method to deal with the stochastic stability of semi-Markovian jump systems along with design of novel integral sliding surface. Finally, Takagi-Sugeno fuzzy model approach is brought to deal with system nonlinearities and fuzzy sliding mode control laws are provided to ensure the stabilization purpose. Features: Presents systematic work on sliding mode control (SMC) of semi-Markvoain jump systems. Explores SMC methods, such as fuzzy SMC, adaptive SMC, with the presence of generally uncertain transition rates. Provides novel method in dealing with stochastic systems with unknown switching information. Proposes more general theories for semi-Markovian jump systems with generally uncertain transition rates. Discusses practical examples to verify the effectiveness of SMC theory in semi-Markovian jump systems. This book aims at graduate and postgraduate students and for researchers in all engineering disciplines, including mechanical engineering, electrical engineering and applied mathematics, control engineering, signal processing, process control, control theory and robotics.
In most synthesis evaluation systems and decision‐making systems, data are represented by objects and attributes of objects with a degree of belief. Formally, these data can be abstracted by the form ( objects; attributes; P ), where P represents a kind degree of belief between objects and attributes, such that, P is a basic probability assignment. In the paper, we provide a kind of probability information system to describe these data and then employ rough sets theory to extract probability decision rules. By extension of Dempster‐Shafer evidence theory, we can get probabilities of antecedents and conclusion of probability decision rules. Furthermore, we analyze the consistency of probability decision rules. Based on consistency of probability decision rules, we provide an inference method to finish inference of probability decision rules, which can be used to decide the class of a new object x ′ . The conclusion points out that the inference method of the paper not only deals with precise information, but also imprecise or uncertain information as well.
This paper consists of designing fuzzy and PID controllers for controlling the vehicle speed. The dynamic of the system is modeled to provide a transfer function for the plant. Fuzzy and PID controller are designed for linear model. The external disturbances such road grade is considered to stabilizing the system. Both controllers are modeled using MATLAB Simulink software. Finally, a comparative assessment of each simulated result is done based on the response characteristics.
No abstract is provided for this article.
No abstract is provided for this article.
This article presents a new approach to the vibration mitigation problem in structures subject to seismic motions. These kinds of structures are characterised by the uncertainties of the parameters that describe their dynamics, such as stiffness and damping coefficients. Moreover, the dampers used to mitigate the vibrations caused by earthquakes are usually nonlinear devices with frictional or hysteretic dynamics. We propose an adaptive backstepping controller to account for the uncertainties and the nonlinearities. The controller is formulated in such a way that it satisfies an H ∞ performance. It is designed for a 10-storey building whose base is isolated with a frictional damper (passive device) and a magnetorheological damper (semiactive device). Controller performance is analysed through numerical simulations.
The micro-vibrations generated by mechanical systems onboard spacecraft can affect the performance of instruments with high pointing accuracy and stability. This paper provides a micro-vibration generating control system based on Real Time Application Interface (RTAI), a real time Linux extension, for ground tests purposes. The vibration generating control algorithm is filtered-X adaptive inverse control method. A voice coil actuator is used in the vibration generating experiments. The experiments show that the system can generate different frequency precision sine vibration whose error is less than 2 mg which is in environmental and electrical noise level.
This paper is concerned with the problem of general output feedback stabilization for fractional order linear time-invariant (FO-LTI) systems with the fractional commensurate order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>α</mml:mi><mml:mo><</mml:mo><mml:mn>2</mml:mn></mml:math>. The objective is to design suitable output feedback controllers that guarantee the stability of the resulting closed-loop systems. Based on the slack variable method and our previous stability criteria, some new results in the form of linear matrix inequality (LMI) are developed to the static and dynamic output feedback controllers synthesis for the FO-LTI system with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>α</mml:mi><mml:mo><</mml:mo><mml:mn>1</mml:mn></mml:math>. Furthermore, the results are extended to stabilize the FO-LTI systems with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>α</mml:mi><mml:mo><</mml:mo><mml:mn>2</mml:mn></mml:math>. Finally, robust output feedback control is discussed. Numerical examples are given to illustrate the effectiveness of the proposed design methods.
Recently, due to the difficulty of collecting condition data covering all mechanical fault types in industrial scenarios, the fault diagnosis problem under incomplete data is receiving increasing attention where no target prior information can be available. The existing open-set or universal domain adaptation (DA) diagnosis methods typically treat private fault samples in the target as a generalized “unknown” fault class, neglecting their inherent structure. This oversight can lead to confusion in latent feature space representations and difficulties in separating unknown samples. Therefore, a universal DA method with unsupervised clustering is developed to explore the intrinsic structure of the target samples for mechanical fault diagnosis, where multi-source information on different working conditions is considered to transfer complementary knowledge. First, a composite clustering metric combining single-domain and cross-domain evaluation is constructed to recognize shared and unknown health classes on source–target domains. Second, to alleviate the intra-class shift while enlarging the inter-class gap, a class-wise DA algorithm is suggested which operates on the basis of maximum mean discrepancy. Finally, an entropy regularization criterion is utilized to facilitate clustering of different health classes. The efficacy of the presented approach in the fault diagnosis issues when monitoring data is inadequate has been verified through extensive experiments on three rotating machinery datasets.
