Nonlinear Delay Systems Research Articles

RBF Neural Network Sliding Mode Control for Passification of Nonlinear Time-Varying Delay Systems with Application to Offshore Cranes.

This paper is devoted to studying the passivity-based sliding mode control for nonlinear systems and its application to dock cranes through an adaptive neural network approach, where the system suffers from time-varying delay, external disturbance and unknown nonlinearity. First, relying on the generalized Lagrange formula, the mathematical model for the crane system is established. Second, by virtue of an integral-type sliding surface function and the equivalent control theory, a sliding mode dynamic system can be obtained with a satisfactory dynamic property. Third, based on the RBF neural network approach, an adaptive control law is designed to ensure the finite-time existence of sliding motion in the face of unknown nonlinearity. Fourth, feasible easy-checking linear matrix inequality conditions are developed to analyze passification performance of the resulting sliding motion. Finally, a simulation study is provided to confirm the validity of the proposed method.

Stability of highly nonlinear neutral stochastic delay systems with non-random switching signals

For the last few decades, many works on stability criteria have been established for neutral stochastic delay systems, which are modeled by stochastic differential delay equations. Some of these works do not involve switching signals, and others contain Markovian switching signals. This paper studies highly nonlinear neutral stochastic delay systems with non-random switching signals. Firstly, the rule of non-random switching signals is imposed. Then, by using the Lyapunov function method and the mode-dependent average dwell time approach, the existence and boundedness of unique global solution is discussed for highly nonlinear neutral stochastic delay systems with non-random switching signals. In addition, without the linear growth condition, asymptotic stability and exponential stability are obtained. In the last part of the article, an illustrative example is provided to show the effectiveness of the obtained results.

Optimal control of nonlinear fractional order delay systems governed by Fredholm integral equations based on a new fractional derivative operator

We aim to develop a direct transcription approach for solving a notable category of optimal control problems governed by nonlinear fractional Fredholm integral equations having delays in both input and output signals. The foundation of the new methodology is based on a multi domains decomposition scheme by utilizing the fractional-order Legendre functions. A new fractional derivative operator associated with the fractional basis is introduced by using the Caputo fractional derivative operator. With the use of derivative and delay operators, one can transform the dynamical system related to the fractional control problem into a new system containing algebraic equations. A wide variety of challenging test problems are studied to provide a detailed explanation of the designed approach.

Global stabilization via output feedback for a class of uncertainty nonlinear systems with time-varying delay and zero dynamics

This paper proposes a new control strategy to deal with three different types of uncertainties for a class of time-varying delay nonlinear systems. Quite different from related celebrated works, the considered systems allow the existence of parameter uncertainties in the output function and nonlinearities, dynamic uncertainties of the unmeasurable state, and continuous external disturbances, which invokes the motivation of the paper. The objective is to construct a continuous output feedback controller by utilizing a new restructured integral function and the double-domination method. The novelty control design is the capability of tackling zero-dynamic and unknown output function simultaneously, thereby guaranteeing the state convergence of the closed-loop system. Finally, the proposed scheme is applied to a practical example and a numerical one simultaneously to demonstrate the effectiveness and the superiority.

Discrete-time control for highly nonlinear neutral stochastic delay systems

This work explores the discrete-time state feedback control problem for neutral stochastic delay systems(NSDSs) in which coefficients satisfy highly nonlinear. Due to the highly nonlinear, the neutral term and discrete time observation value, many conventional methods are not applicable. A more general Lyapunov function is constructed to prove that the designed controller can stabilize the corresponding systems. In addition, H∞-stable, asymptotically stable and exponentially stable of the corresponding studied systems are presented. Then, a numerical case is demonstrated to verify the correctness and validity of the proposed theoretical results.

Periodic event-triggered modified repetitive control with equivalent-input-disturbance estimator based on T-S fuzzy model for nonlinear systems

In this paper, the periodic signal tracking and the disturbance rejection problems are considered for a class of time-varying delay nonlinear systems with unknown exogenous disturbances under limited communication resources. The Takagi–Sugeno (T-S) fuzzy model is used to approximate the nonlinear system. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection effectiveley. This can be operated by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC) scheme. Moreover, a fuzzy periodic event-triggered feedback observer (FPETFO) is proposed for the purpose of reducing the computational burden, energy consumption and saving communication resources. The periodic event-triggered technique is designed to observe the occurrence of an event which is described by an error signal. When this error signal exceeds a prescribed threshold, the event occurs and the current data are transmitted; otherwise, there is a zero-order hold to keep data unchanged. The overall system consists of MRC, EID and FPETFO based on a T-S fuzzy model. Then, some sufficient conditions are derived to gurantee the asymptotic stability of the overall system subjected to unknown disturbances using the Lyapunov–Krasovskii functional (LKF) stability theory and linear matrix inequalities (LMIs). The fuzzy state feedback controller and observer gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme with comparative study.

A generalization of Müntz-Legendre polynomials and its implementation in optimal control of nonlinear fractional delay systems

A hybrid of Müntz-Legendre polynomials (MLPs) and block-pulse functions (BPFs) is defined and carried out to analyze nonlinear fractional optimal control problems consisting of multiple delays. Instead of using the Caputo fractional derivative, an alternative fractional derivative operator is utilized. The primary optimization problem reduces to an alternative optimization one involving unknown parameters. For this purpose, the fractional Legendre-Gauss quadrature formula is utilized for approximating the associated cost functional and the fractional Legendre-Gaussian nodes are taken as the collocation points. Some new aspects of the proposed basis are demonstrated to verify the effectiveness of the proposed approach based on the Müntz-Legendre basis (MLB) against the classical orthogonal bases. The simulation results certify the feasibility and reliability of the proposed method. Numerous fractional control problems, e.g., bang-bang controls and control systems with any irregularities in the structure of control input can be handled successfully by employing the new fractional basis.

Input-to-state stability of discrete-time time-varying impulsive delay systems

This paper investigates the input-to-state stability (ISS) of nonlinear discrete-time time-varying impulsive delay systems with the coexistence of stabilising and destabilising impulses. Some ISS criteria are established for discrete-time impulsive delay systems by employing the Lyapunov functional where the coefficient of the estimated upper bound of the time difference of the Lyapunov functional is allowed to be a time-varying function which can take both negative and positive values. In addition, the ISS of a class of discrete-time linear time-varying impulsive delay systems is discussed by utilising a non-quadratic Lyapunov functional. Numerical examples are presented to verify the effectiveness of the main results.

Preface

The 2022 2nd International Conference on Industrial Manufacturing and Structural Materials (IMSM 2022) was planned to be held on March 25-27, 2022 in Hangzhou, China. Due to the impact of COVID-19, many communities from all over the world were under strict health measures and strict travel restrictions, and participants of IMSM 2022 also meet with the difficulty of travel restrictions. According to the current epidemic prevention policy in Mainland China, our meeting was a virtual conference. IMSM is an annual conference which explored the development and implications in the related fields of Industrial Manufacturing and Structural Materials with an objective to present the novel and fundamental advancements. IMSM is to bring together innovative academics and industrial experts in the field of Industrial Manufacturing and Structural Materials to a common forum. The primary goal of the conference is to promote research and developmental activities industrial manufacturing and structural materials and another goal is to promote scientific information interchange between researchers, developers, engineers, students, and practitioners working all around the world. During the conference, the conference model was divided into three sessions, including oral presentations, keynote speeches, and online Q&A discussion. In the first part, some scholars, whose submissions were selected as the excellent papers, were given about 5-10 minutes to perform their oral presentations one by one. Then in the second part, keynote speakers were each allocated 30-45 minutes to hold their speeches. In the second part, we invited two professors as our keynote speakers. Prof. Quanxin Zhu, Hunan Normal University, China, performed a speech: Stability and event-triggered control of stochastic nonlinear delay systems. And then we had Prof. Kamal Z. ZAMLI, Universiti Malaysia Pahang, Malaysia. Their insightful speeches had triggered heated discussion in the third session of the conference. Every participant praised this conference for disseminating useful and insightful knowledge. The proceedings are a compilation of the accepted papers and represent an interesting outcome of the conference. Topics include but are not limited to the following areas: Industrial Manufacturing Technology, Structural Materials and other related topics. All the papers have been through rigorous review and process to meet the requirements of international publication standard. We would like to acknowledge all of those who supported IMSM 2022. The help and contribution of each individual and institution was instrumental in the success of the conference. In particular, we would like to thank the organizing committee for its valuable inputs in shaping the conference program and reviewing the submitted papers. We sincerely hope that the IMSM 2022 turned out to be a forum for excellent discussions that enabled new ideas to come about, promoting collaborative research. We are sure that the proceedings will serve as an important research source of references and knowledge, which will lead to not only scientific and engineering findings but also new products and technologies. The Committee of IMSM 2022 Committee member are available in the pdf

From quasilinear structures to population dynamics: Global stability analysis of an uncertain nonlinear delay system with interval approach

In this paper, we analyze a new continuous-time epidemic model including nonlinear delay differential equations by using parameters and functions selected from a class of intervals whose algebraic basis is based on quasilinear spaces. The main idea in the model’s generic structure is based on uncertainties in the values of parameters and functions forming the model. Therefore, using an interval coefficient approach rather than the exact value of parameters and functions that define transmissions between the compartments in the population dynamics will better represent the reality. Furthermore, preferring such an approach provides more realistic scenarios for temporal and stability dynamics of a population exposed to a disease. In this study, the quasilinear space is defined to explain the mathematical background of the interval approach in the fictional chain of the model. Next, descriptions belonging to the introduced model are included. After this compartmental system is presented as two systems formed by the lower and upper endpoints of the intervals determining parameters and functions, local and global dynamics related to stabilities of the models are analyzed separately for each. Then, using some interval analysis and functional analysis methods, these results are combined, and a conclusion about the stability of the proposed epidemic model has been reached. Alongside, the performance of the proposed approach is demonstrated by a visual simulation.

Intermittent state estimation for nonlinear delay systems with redundant communication channels

AbstractThis article investigates state estimation for discrete‐time nonlinear systems with Markov delay, where a redundant communication channel is considered to improve transmission reliability. As the channel capacity is limited, we use two Bernoulli stochastic variables to describe the packet dropout conditions of the main channel and the redundant one. In addition, a mode‐dependent estimator based on both the current state and the delayed state is designed. Combining with an intermittent approach, the efficiency of the estimator is improved. An augmented estimation error system is proposed to deal with the Markov delay in the nonlinear system. Subsequently, a sufficient condition is obtained to ensure the asymptotic stability of the augmented error system by constructing a Lyapunov function, and the gains of the intermittent estimator are derived. Finally, a numerical example of a moving vehicle is utilized to illustrate the developed results.

An improved time delay neural network model for predicting dynamic heat and mass transfer characteristics of a packed liquid desiccant dehumidifier

Researches on packed liquid desiccant dehumidifiers are abundant. However, only a few works concentrate on modeling the dynamic dehumidification process as it requires detailed heat and mass transfer coefficients along the dehumidifier, which are impacted by many factors such as flow pattern of liquid desiccant and hard to be obtained, hindering the development of dynamic models. Data driven modeling method could eliminate the requirement for detailed heat and mass transfer coefficient along the dehumidifier. A time delay neural network (TDNN) model is a general way to describe the dynamic process without the requirement of much knowledge on physical mechanism, yet the number of time steps for each inlet parameter is hard to be determined. In this paper, an improved time delay neural network (iTDNN) model was proposed. Through analyzing characteristics of dehumidification process, model inputs were simplified, which is the core of improvement of TDNN model. Besides, a new combined algorithm including back propagation (BP) algorithm and improved genetic algorithm (GA) was proposed to acquire the optimal weight values globally. The predicted results agree well with the experimental data for validation part. The method presented in the paper provides a reference for modeling multi-variables and large delay nonlinear dynamic systems.

Stability of stochastic nonlinear delay systems with delayed impulses

In this paper, we study the input-to-state stability of a class of stochastic delay differential equations with delay impulses. We consider the two cases where the continuous stochastic delay system is stable and unstable, and establish different types of stability conditions by using the average dwell time and the vector Lyapunov function method. Finally, two examples are used to verify the validity of our results.

Sliding mode observer based control for T-S fuzzy descriptor systems

<p style='text-indent:20px;'>In this paper, the problem of sliding mode observer (SMO) based sliding mode control (SMC) for nonlinear descriptor delay systems is studied. First, based on the T-S fuzzy dynamic modeling technique, the nonlinear descriptor system is transformed into a combination of local linear models. Then, a integral-type sliding surface (ITSS) based SMO is constructed for the error system. In the sequel, sufficient linear matrix inequality (LMI) conditions are established to ensure the admissibility of the sliding motions and obtain the observer gain matrix. Furthermore, two novel SMC laws are developed to ensure the reachability conditions and stabilize the descriptor systems. Finally, simulations are provided to show the effectiveness of the method.</p>

Further results on finite-time stability of neutral nonlinear multi-term fractional order time-varying delay systems

In this paper, the finite-time stability for nonlinear neutral multi-term fractional order systems with time-varying input and state delays is investigated. By use of the generalized Gronwall inequality and extended form of the generalized Gronwall inequality, new sufficient conditions for finite-time stability of such systems are obtained. Finally, numerical examples are given to illustrate the effectiveness and applicability of the proposed theoretical results.

Robust stability of switched nonlinear systems with delay and sampling

AbstractThis article investigates the stability issue for a class of switched nonlinear systems whose control inputs include time delay and sampling. It is assumed that a stabilizing controller is predesigned for the nominal system such that it is stable under a certain switching signal. However, in the presence of input delay and sampling, the system may not be stable under the same stability criteria. Besides, the switching signals are discussed in two cases, that is, the switching signal of the system is transmitted to the controller in real time and only the sampled information of the switching signal is available to the controller at each sampling instant. For the latter, the asynchronous motions between the subsystems and the candidate controllers are caused and the closed‐loop system is rewritten as sampled switched nonlinear delay system with an augmented switching signal. By constructing sampling interval‐dependent Lyapunov–Krasovskii functional and using the theory of the asynchronous switched delay system, we establish the stability conditions on the switching signal which depends on the size of the delay, the upper bound of the sampling interval, and the dwell time. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.

Advances in stabilization of highly nonlinear hybrid delay systems

Given an unstable highly nonlinear hybrid stochastic differential delay equation (SDDE, also known as an SDDE with Markovian switching), can we design a delay feedback control to make the controlled hybrid SDDE become exponentially stable? Recent work by Li and Mao in 2020 gave a positive answer when the delay in the given SDDE is a positive constant. It is also noted that in their paper the time lag in the feedback control is another constant. However, time delay in a real-world system is often a variable of time while it is difficult to implement the feedback control in practice if the time lag involved is a strict constant. Mathematically speaking, the stabilization problem becomes much harder if these delays are time-varying, in particular, if they are not differentiable. The aim of this paper is to tackle the stabilization problem under non-differentiable time delays. One more new feature in this paper is that the feedback control function used is bounded.

Estimates for Solutions to a Class of Nonlinear Time-Varying Delay Systems

Estimates for Solutions to a Class of Nonlinear Time-Varying Delay Systems

Quantized Stabilization for Highly Nonlinear Stochastic Delay Systems by Discrete-Time Control

Quantized Stabilization for Highly Nonlinear Stochastic Delay Systems by Discrete-Time Control

Stability of nonlinear distributed delay system with parameter uncertainties: Integral‐based event‐triggered impulsive control strategy

AbstractThis article investigates the stability of nonlinear uncertain distributed delay system via integral‐based event‐triggered impulsive control (IETIC) strategy. First, a IETIC mechanism is presented to reduce the redundant data transmission over the system, in which the integral‐based event‐triggered mechanism uses the integration of system states over a time period in the past. Second, a new lemma is proposed to eliminate the Zeno behavior of the established model through the IETIC mechanism. Third, a novel Lyapunov–Krasovskii functional (LKF) method related to probability density function is constructed to guarantee the stability of the established model based on LMI conditions, where a probability density function is introduced as a distributed delay kernel. Compared with existing methods, the constructed novel LKF method is less conservative or requiring less number of decision variables. Numerical examples are further provided to confirm the effectiveness and advantages of the proposed approach.