Search

This paper investigates the problem of global uniform finite-time output feedback stabilization for a class of generalized disturbed high-order nonlinear uncertain systems. The presence of nonlinear uncertainties and unknown disturbances makes it challenging to design a state observer and an output feedback controller. To address this problem, a new technique of output feedback design is proposed. Firstly, based on a backstepping-like method, a finite-time extended state observer (FT-ESO) is constructed to estimate the unmeasured states and unknown disturbances of the system. Then, utilizing the nonseparation principle and disturbance-estimation--compensation method, a continuous output--based finite-time active anti-disturbance control (FT-AADC) method is developed by integrating the finite-time state feedback controller with the proposed FT-ESO. The global uniform finite-time stability of the entire observer-control system is proven using Lyapunov theory. Simulation results are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We justify an analytical method for constructing periodic solutions of nonlinear systems of ordinary differential equations of polynomial type. Periodic solutions are constructed in the form of Fourier series in which the coefficients are polynomials depending on a parameter, which is not assumed to be small. Two examples are considered: the van der Pol equation and the Lorenz system. [ABSTRACT FROM AUTHOR]

It is well known that unknown modeling errors cannot be avoided in practice. Such unmeasured uncertainties are usually denoted as unknown nonlinear functions that exist in every channel of the system equation. This paper aims to develop an output feedback adaptive control scheme by constructing state estimation filters to address such unknown modeling errors. In the controller design, these uncertainties caused by modeling errors will be accumulated to the last step for compensation. Unknown parameters existing in the upper bound functions of unknown nonlinear functions and system parameters are estimated synchronously based on tuning function approaches. It is shown that the designed output feedback controller can ensure the stability and tracking performance of the closed‐loop system, and the transient performance in terms of a truncated norm is also established. [ABSTRACT FROM AUTHOR]

A new finite-time adaptive tracking control scheme based on prescribed performance was developed to solve the control problem of non-strict feedback systems with input delays and dynamic uncertainties. The time-delay systems were transformed into delay-free systems by Pade approximation and auxiliary intermediate variable, and the unmodeled dynamics was handled by the dynamic signal generated by the first-order auxiliary system. The prescribed performance adaptive tracking control was implemented by the hyperbolic tangent function, and the stability analysis was presented based on dynamic surface control method. Taking the second-order nonlinear system with unmodeled dynamics and input delay as example, the numerical simulation of the proposed control strategy was conducted in MATLAB environment. The results show that the proposed control scheme can avoid the singularity in the derivation of virtual control, and all signals in the closed-loop system are bounded in finite time. The tracking error can converge to prescribed time-varying region, and the control algorithm is effective. [ABSTRACT FROM AUTHOR]

In general, the construction of observers for nonlinear descriptor systems depends on the solvability of a linear matrix inequality involving system matrices, and it is based on the system's nonlinearity. Therefore, the type of nonlinearity present in the system heavily affects the observer design process. There are significant developments in the literature for observer design for descriptor systems with various types of nonlinearity. Motivated by this, the current work reviews the literature on observer design for nonlinear descriptor systems with an extensive discussion on the type of nonlinearities that are considered. Here, an analysis and the comparison on the most common nonlinearities is presented, providing a roadmap to all researchers in the field. Furthermore, less common nonlinearities have been identified, presenting under-explored areas within the literature, and can open new domains for future research. [ABSTRACT FROM AUTHOR]

Mitigating the ground effect has become a big challenge for autonomous aerial vehicles. This paper proposes a sliding mode based on the Proportional Integral Derivative sliding surface control with backstepping (hybrid control) to improve quadcopter flight tracking performance during take-off and soft landing on the ground in a disrupted and windy environment. The proposed controller provided a quick adaptation and high robustness of the vehicle's fight control in the face of disturbances. Using the Lyapunov stability criterion condition has been derived to ensure that the Quadcopter system with a proposed hybrid controller is stable even when the upper bound for disturbance is unknown. The simulation results show that the total thrust generated by rotors increases linearly as the vehicle gets closer to the ground. Proposed controller during landing state reduces 4.77% settling time as compared to PIDSMC and 10% to SMC of the system with no load and with load it reduced 2.70% compared to PIDSMC and 7.35% to SMC. In terms of chattering effect and control effort, proposed controller PIDSMCBS outperformances the PIDSMC and SMC. [ABSTRACT FROM AUTHOR]

Copyright of Journal of South China Normal University (Natural Science Edition) / Huanan Shifan Daxue Xuebao (Ziran Kexue Ban) is the property of Journal of South China Normal University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article presents the design of a nonlinear hybrid controller for an underactuated Duffing oscillator with 2 degrees of freedom. The main control purpose is to reduce the frequency‐response to specific resonant‐frequencies while maintaining its robustness to external disturbances. The resulting hybrid controller uses sliding mode control (SMC) with a positive position feedback (PPF) scheme. This is structured such that the SMC provides system robustness and tracking, while the PPF allows damping specific resonant frequencies. The system was evaluated using frequency sweeps in terms of acceleration in the second degree of freedom. In this case, the control input is applied through the first degree of freedom. Moreover, multi‐objective optimization is implemented to tune of the control parameters. Simulation results show that the system response to external vibrations can be reduced up to 83.88% by using the proposed PPF + SMC scheme. [ABSTRACT FROM AUTHOR]

A novel 2D chaotic system is presented, which is inspired by Styblinski Tang (ST) function employed as optimization test function. It is a challenge function because of having many local optima. The performance of the chaotic system namely 2D Styblinski Tang (2D-ST) map is corroborated through an extensive comparison with the literature in terms of the sensitive chaos metrics as well as its randomness is verified over TestU0. The 2D-ST map manifests the best hyperchaotic behavior due to higher ergodicity and complexity characteristics. Moreover, the 2D-ST map is implemented to a microcontroller hardware, and it is seen that the results manifests that the proposed 2D-ST can be a potential practical candidate thanks to excellent hyperchaotic performance. [ABSTRACT FROM AUTHOR]

In this paper, a holistic nonlinear state-space model of a system with multiple converters is developed, where the converters correspond to the wind turbines in a wind farm and are equipped with grid-following control. A novel generalized methodology is developed, based on the number of the system's converters, to compute the equilibrium points around which the model is linearized. This is a more solid approach compared with selecting operating points for linearizing the model or utilizing EMT simulation tools to estimate the system's steady state. The dynamics of both the inner and outer control loops of the power converters are included, as well as the dynamics of the electrical elements of the system and the digital time delay, in order to study the dynamic issues in both high- and low-frequency ranges. The system's stability is assessed through an eigenvalue-based stability analysis. A participation factor analysis is also used to give an insight into the interactions caused by the control topology of the converters. Time domain simulations and the corresponding frequency analysis are performed in order to validate the model for all the control interactions under study. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the adaptive tracking control in a prescribed‐time for a class of uncertain nonlinear systems with a full state constraint. Firstly, in order to restrict the state constraints, the barrier Lyapunov function is employed and parameter uncertainty is handled based on linear‐in‐the‐parameters (LIP). A prescribed‐time adaptive controller is then designed by backstepping to ensure that the closed‐loop system can reach zero in a prescribed finite time under any given initial conditions. The prescribed‐time is independent of the design of the parameters. Finally, two simulation examples verify the effectiveness and usability of the proposed method. [ABSTRACT FROM AUTHOR]

With the rapid development of computer network technology, it is often necessary to collect weak signals to collect favorable information. The development of signal detection technology is ongoing; however, various issues arise during the detection process. These issues include low efficiency and a high signal noise threshold. However, many problems will be encountered in the process of detection. In order to solve these problems, the nonlinear chaos theory is introduced to detect signals, and the simulation experiments of weak pulse signals and weak partial discharge signals are carried out respectively. The experimental results showed that the detection effect was remarkable in the quasi periodic state, and it had a good detection effect for weak pulse signals. At a signal-to-noise ratio of - 25 dB, double coupling system, two-way ring coupling system, and single ring coupling system displayed detection success rates exceeding 98%. Meanwhile, the detection success rate of the strong coupling system was only 12%. Even at a noise signal ratio as low as - 40 dB, the dual coupling system still maintained a detection success rate above 80%. The simulation results of partial discharge signal detection showed that there was a high fluctuation only at 2 ms, and the rest was basically stable at about 0 V, indicating that the system had a strong suppression effect on Gaussian white noise. When comparing the simulation results of the detection of the new chaotic system and the double coupling system, it was found that the new chaotic system has a superior impact in detecting weakly attenuated partial discharge signals. Through analysis of the system's dynamic behavior, the research confirms its rich dynamic characteristics and sheds light on the reasons for phase state mutation and missed detection. The noise system is utilized for comparing the performance of various systems, with the goal of enhancing the system's detection capability. [ABSTRACT FROM AUTHOR]

This work introduces a novel adaptive fixed-time control strategy for nonlinear systems subject to external disturbances. The focus pertains to the introduction of the fixed-time terminal sliding mode control (FxSMC) technique. The proposed scheme exhibits rapid convergence, chatter-free and smooth control inputs, and stability within a fixed time. The utilization of an adaptive methodology in combination with the FxSMC yields the proposed strategy. This approach is employed to address the dynamic system in the presence of external disturbances. The results obtained from the Lyapunov analysis will provide insights into the stability of the closed-loop system in a fixed time. In the end, the simulation results are presented in order to assess and demonstrate the effectiveness of the methodology. [ABSTRACT FROM AUTHOR]

In this paper, the tracking problem is concerned for a class of nonlinear system. The primary objective is to achieve fixed‐time control performance in the presence of nonvanishing mismatched uncertainties and nonparametric external disturbance. Firstly, in order to estimate disturbance, a fixed‐time extended state observer with fractional power term is developed, the order of which is reduced to alleviate peaking value phenomenon. By reasonably switching among different estimation patterns, both transient and steady‐state performances are balanced. Secondly, by means of fuzzy logic system theory, an ESO‐based adaptive fuzzy control strategy with time‐varying gains is presented, and thus the mismatched nonlinearities are approximated, and the external disturbance is compensated in real time simultaneously. Moreover, by constructing a mixed barrier and quadratic type of Lyapunov function, the fixed‐time stability analysis is put forward for tracking error dynamics based on backstepping methodology. Finally, the advantages and effectiveness are illustrated by a numerical example on wheeled mobile robot. The main characteristic of this paper is to integrate ESO methodology into fuzzy control architecture in fixed‐time sense. As a consequence, not only the output tracking purpose, but also desirable transient performance can be achieved. [ABSTRACT FROM AUTHOR]

Of concern, the present article is a theoretical investigation on the reaction–diffusion interacting species model system including prey harvesting and the alternative food source for the predator maintained partially by Beverton–Holt‐like food. Major attention is focused on the influence of alternative food source for the predator in the event of prey harvesting on the dynamical complexity of the system. The existence of equilibria together with their topological classification concerning positive coexisting equilibria of the system is thoroughly explored. The threshold of extinction for interacting species, the stability of feasible equilibria, and the persistence scenario as well are examined analytically. The parametric constraint for subcritical Hopf bifurcation emerging from altering harvesting efforts is established through normal form setting. The perception of the local bifurcation structure of codimensions 1 and 2 depending on the model parameters of significance is also explored. Special emphasis is paid on the sensitivity analysis of the model system so as to examine the effect of harvesting and alternative food source for sustaining biomass balance. The existence and stability of nonnegative equilibria together with Turing instability corresponding to spatiotemporal system are, however, not ruled out from the present pursuit. The evolution of diffusion‐driven pattern formation with the inclusion of spots, stripes, labyrinthine, stripe‐hole mixtures, and hole replication is well‐depicted in 2D$$ 2D $$ space influenced by both the harvesting and additional food source of the dynamical system. Extensive numerical simulations are performed in order to establish all the theoretical outcomes in terms of stability of the system and its sustainable development. [ABSTRACT FROM AUTHOR]

A neural network (NN) optimal control for discrete-time nonlinear dynamic systems with known internal dynamics is designed. The control is described by an algebraic equation with a variable structure. This algebraic equation is derived analytically. A functional block diagram of the controlled system is given and analyzed. Software and hardware implementation aspects of the controller are discussed. The controller does not need any training and has moderate complexity. The discrete-time state variable trajectories of the controlled system are shown to be globally asymptotically stable and convergent to unique steady states. It is proved that these trajectories converge to steady-state neighborhood in a finite number of steps. Sliding mode analysis of controller operation is fulfilled. A correctness of controller operation in the case of disturbances of its nonlinearities is analyzed. Using the controller for a special case of optimal tracking control is discussed. Results of presented computer simulations of optimal control of discrete-time two-dimensional and three-dimensional affine nonlinear systems and optimal tracking control of permanent-magnet motor of linear type applied for accurate positioning and nonlinear cooling continuous stirred tank reactor confirm theoretical statements of the paper and illustrate a performance of the controller. [ABSTRACT FROM AUTHOR]

Multilayer neural networks can approximate endogenous disturbances with relatively high accuracy. However, for multilayer‐neural‐network‐based control methods of high‐order uncertain nonlinear systems, hard to handle large exogenous disturbances especially for mismatched types, complex controller scheme and so on, make them difficult to be practical. Therefore, a novel high‐performance multilayer neurocontroller which can simultaneously reject matched and mismatched disturbances will be proposed in this paper. Specially, strong endogenous and exogenous disturbances will be feedforwardly compensated. Additionally, the proposed controller not only protects from "explosion of complexity," but also owns a simple scheme. [ABSTRACT FROM AUTHOR]

This paper considers the prescribed‐time non‐singular terminal sliding mode control (TSMC) for nonlinear systems with uncertainties bounded by non‐negative functions. At first, a new Lyapunov theorem for prescribed‐time stability is introduced. Then, a novel terminal sliding surface together with a non‐singular TSMC input is constructed by using a time‐varying scaling function. Strict analysis shows that the proposed controller is able to ensure the exact reaching of the sliding surface as well as the system states to zero in a prescribed time independent of the system initial conditions. Moreover, all the state signals and the control input remain uniformly bounded. Finally, simulation comparison with the existing fixed‐ and prescribed‐time TSMC is given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a Newton-type iterative scheme for solving nonlinear systems is designed. In the process of proving the convergence order, we use the higher derivatives of the function and show that the convergence order of this iterative method is six. In order to avoid the influence of the existence of higher derivatives on the proof of convergence, we mainly discuss the convergence of this iterative method under weak conditions. In Banach space, the local convergence of the iterative scheme is established by using the ω -continuity condition of the first-order Fréchet derivative, and the application range of the iterative method is extended. In addition, we also give the radius of a convergence sphere and the uniqueness of its solution. Finally, the superiority of the new iterative method is illustrated by drawing attractive basins and comparing them with the average iterative times of other same-order iterative methods. Additionally, we utilize this iterative method to solve both nonlinear systems and nonlinear matrix sign functions. The applicability of this study is demonstrated by solving practical chemical problems. [ABSTRACT FROM AUTHOR]

High dimensional and complex nonlinear systems widely exist in practical engineering rotor systems such as aviation, aerospace and shipbuilding. In the key research fields such as aviation engine rotor systems and gas turbine rotor systems, these high-dimensional complex systems are often difficult to directly process data and analyze statistics. A method of construction of dynamical reduced order model of uncertain rotor systems and identification of model dispersion parameters was proposed to address the problem of high model dimensions in uncertain rotor systems. Firstly, based on the deterministic dynamic model and the static matrix reduction method, the deterministic dynamic reduction model was further improved. Then, based on random matrix theory and non-parametric dynamic modeling methods, an uncertain dynamic reduction model was proposed. Finally, the divergent parameters of the uncertain dynamic model were identified using the first-order critical speed, vibration mode, and experimental data of the system deterministic model. The identification results of divergence parameters were experimentally verified on a rotor experimental platform. The research results indicate that the difference between the experimental results and the mean vibration response after reducing the order is small, and the difference between the experimental results and the uncertain dynamic model is not more than 10%, indicating that the theoretical model used has high accuracy and reliability in describing the behavior of the rotor system. This model can provide a reference for further research on the uncertain rotor system of the model. [ABSTRACT FROM AUTHOR]

An adaptive event-triggered tracking control method with preset performance is proposed for a class of uncertain nonlinear systems with full-state constraints and unknown time-varying disturbances. Firstly, a performance function is designed and the original system error is converted. In order to eliminate the influence of state constraints on the system, a barrier Lyapunov function is introduced. Secondly, the influence of unknown function is solved by using radial basis function neural network (RBFNN). Simultaneously, eventtriggering mechanism was used to reduce the update frequency of control signals, thereby the communication burden is reduced. Then, based on the Lyapunov stability theorem, all signals of the closed-loop control system are verified to be bounded, all states do not violate the predefined interval, and the Zeno behavior does not occur. Finally, the effectiveness of the proposed method was verified using a single-link flexible manipulator as a simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates the full-state constraint event-triggered adaptive control for a class of uncertain strict-feedback systems. The lack of information on the coupling dynamics of virtual variables in backstepping increases the complexity of feedback design. Given this, the requirements of shaping system performance constraints, eliminating initial dependence, and reducing data transfer costs together give rise to an interesting and challenging problem. Constructing the time-receding horizon (TRH) and stitching it with the quadratic Lyapunov function (QLF) is the key to constrained tracking. Specifying TRHs as a set of smooth bounds with fixed-time convergence and forcing the system to stabilize within the constrained region before the prescribed settling time provide a sufficient condition for practical finite-time stability (PFS). For relaxing the initial dependence, a tuning function is designed to match the performance constraints under arbitrary system initial conditions. A dual-channel event-triggered mechanism (ETM) is developed to automatically adjust the controller and estimator data flow updates with less transmission burden. By combining a specific inequality with backstepping, uncertainties are overcome without the "complexity explosion" in recursion steps. Finally, simulations demonstrate the effectiveness of the proposed method. • The tracking issue of strict-feedback systems with full-state constraints is studied. • An approximation-free event-triggered adaptive control scheme is developed. • The tuning function removes the initial dependence inherent in constrained control. • Novel time-receding horizons for the practically finite-time stability are proposed. • The dual-channel event-triggered mechanism reduces the data-transmission burden. [ABSTRACT FROM AUTHOR]

A nonlinear filter is presented by using a formal linearization method and the Extended Kalman Filter (EKF) approach in this paper. Defining a linearization function that consists of polynomials, a given nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function. Introducing a new augmented measurement vector that consists of polynomials of measurement data for a given measurement equation, this equation is also transformed into an augmented linear one with respect to the linearization function in the same way. As a result, the EKF theory can be applied to these augmented linearized systems and a nonlinear filter is synthesized. In order to show the performance of the method, numerical experiments are carried out by comparing with the EKF as a conventional method. [ABSTRACT FROM AUTHOR]

This manuscript proposes an internal model controller (IMC) for conical tank system with hybrid approach. The hybrid approach is the combination of lotus effect optimization (LEA) and attentive evolutionary generative adversarial network (AEGAN) algorithm; hence it is known as LEA-AEGAN approach. The main purpose of the work is to enhanced drainage of process fluid. Process fluids can be of various mixes of solids, semisolids, slurries, and liquids. The inclination angle of the tank aids drainage eliminates sediments, and so on, but it also adds non-linearity into the system. The IMC is used to nonlinear systems, which is required to regulate the level of a conical tank. The proposed LEA is utilized to find the optimal controller parameters and minimize the error of the system. And the AEGAN is used to predicts the control parameters and ensure the controller tuning. By using the proposed system, it is implemented by MATLAB platform and compared with the existing techniques. The settling time, overshoot, and rise time of the proposed controller is 21.9sec, 11.11%, and 2.2sec, respectively. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of the estimation of non-uniformly nonlinear systems with time-varying delays in the state and input. In addition, the problem of the sampled output measurement is also been addressed. Thus, an observer design for a class of uncertain, non-uniformly nonlinear systems in the presence of time-varying delay is proposed. A continuous–discrete observer based on a high-gain approach is designed to achieve undelayed estimation. Thus, sufficient conditions to ensure the convergence of the observer are obtained. The analysis is based on a Lyapunov–Krasovskii functional, which shows that the bounded observation error depends on the sizes of the known upper delay and the upper sampling rate. The performance of the proposed algorithm is evaluated by considering a control-based observer for a two-degrees-of-freedom helicopter system with a known time-varying delay and sampled output measurements. [ABSTRACT FROM AUTHOR]

This work introduces a novel adaptive fixed-time control strategy for nonlinear systems subject to external disturbances. The focus pertains to the introduction of the fixed-time terminal sliding mode control (FxSMC) technique. The proposed scheme exhibits rapid convergence, chatter-free and smooth control inputs, and stability within a fixed time. The utilization of an adaptive methodology in combination with the FxSMC yields the proposed strategy. This approach is employed to address the dynamic system in the presence of external disturbances. The results obtained from the Lyapunov analysis will provide insights into the stability of the closed-loop system in a fixed time. In the end, the simulation results are presented in order to assess and demonstrate the effectiveness of the methodology.

In this paper, a new-type time-varying asymmetric integral barrier function is designed to handle the state constraint of nonlinear systems. The barrier Lyapunov function is developed by building an integral upper limit function with respect to transformation errors over an open set to cope with the position constraint of the robotic system. We know that the symmetric time-invariant constraint is only a particular situation of the asymmetric time-variant constraint, and thus compared to existing methods, it is capable of handling more general and broad practical engineering issues. We show that under the integral barrier Lyapunov function combining a disturbance observer-based tracking controller, the position vector tracks a desired trajectory successfully, while the constraint boundary is never violated. It can certify the exponential asymptotic stability of the robotic tracking system by using the given inequality relationship on barrier function and Lyapunov analysis. Finally, the feasibility of the presented algorithm is indicated by completing the simulations.

This paper investigates the dynamic observer (DO) design problem for a class of disturbed Lipschitz nonlinear vehicle systems with uncertainties, where the uncertainties are assumed to be in both system matrix and input matrix. The proposed DO has a unified form and the popularly used proportional observer and proportional integral observer can be considered as the particular cases of the proposed DO. Based on the algebraic constraints, the observer design issue is transformed into the asymptotically stability analysis problem. The sufficient criterion of the DO design is derived in terms of linear matrix equality (LMI), by constructing a Lyapunov function to guarantee the H-infinity performance. A numerical example is used to illustrate the performance of the proposed DO.

A new second-order matrix formulation is proposed in this work to model any nonlinear electronic system. This new formulation is developed and implemented by using a recasting method that increases the number of variables but limits the non-linearity to a quadratic form. Nonlinearity is modeled without any approximation and can model complex nonlinearities such as exponential and Tanh-based models. The new quadratic method is applied to the extended tanh MOSFET model and an exponential diode model to illustrate the power and reliability of this method. The method also has the advantage of directly stamping transistors and diodes into matrix forms in ways similar to linear elements. To demonstrate the validity of the new formulation, several circuits are examined, and the results compare very well to SPICE simulations. The simulation time as well as numerical stability improve significantly when using time marching techniques with the quadratic formulation as compared to directly stamping transistor and diode exponential nonlinearities.

Nonlinear discrete control system theory, which is increasingly garnering attention, has important applications in computer control theory. In this study, the robust control problem of nonlinear discrete systems with perturbations is investigated. Using the Lyapunov theory and linear matrix inequality method, the sufficient conditions for fast convergence of the state observer estimation error and fast stability of the state feedback closed-loop system are formulated, thereby showing that the independent solution of the gain matrix of the state observer and robust controller is more convenient. When designing the state observer and observer-based robust controller, the gain matrix was constrained twice, reducing the time required for robust control. The proposed robust control method based on the state observer reduces the conservatism of the system and improves the robust control effect of nonlinear discrete systems. Concurrently, the observer-based robust control method in normal systems is extended to the generalized system form. Finally, the proposed robust control method was simulated using the longitudinal motion model of an aircraft and the DOLPHIN MARK II autonomous underwater vehicle motion model, as research objects. In comparisons with two control methods from the literature, the average error of state estimation was significantly reduced, and the closed-loop control system rapidly achieved robust stabilization, demonstrating the effectiveness and superiority of the control method proposed in this paper.

Piezoelectric actuators (PEAs) are extensively used for scanning and positioning in scanning probe microscopy (SPM) due to their high precision, simple construction, and fast response. However, there are significant challenges for instrument designers due to their nonlinear properties. Nonlinear properties make precise and accurate control difficult in cases where position feedback sensors cannot be employed. However, the performance of PEA-driven scanners can be significantly improved without position feedback sensors if an accurate mathematical model with low computational costs is applied to reduce hysteresis and other nonlinear effects. Various methods have been proposed for modeling PEAs, but most of them have limitations in terms of their accuracy and computational efficiencies. In this research, we propose a variant DenseNet-type neural network (NN) model for modeling PEAs in an AFM scanner where position feedback sensors are not available. To improve the performance of this model, the mapping of the forward and backward directions is carried out separately. The experimental results successfully demonstrate the efficacy of the proposed model by reducing the relative root-mean-square (RMS) error to less than 0.1%.

In order to solve the coordinated operation of voltage and frequency of microgrids and achieve effective distribution of output power, we propose the application of fractional-order nonlinear equations in coordination. This method designs a distributed impulse coordinated control strategy, to achieve the coordinated operation of the system. The distributed coordinated control structure and mathematical model are established, and the distributed two-level coordinated control strategy of the microgrid system is adopted. Aiming at the secondary control problem of microgrids, a distributed coordinated control protocol is designed. The results showed that after adding the distributed second-level coordination control of frequency at 3 s, the output active power of the four distributed power sources in the microgrid model is maintained to an evenly divided state after about 1 s. The output voltage and frequency utilizing the microgrid’s decentralized power supply quickly reach the ideal reference value, within the allowable error range, the output of the system can achieve coordinated control, and the active power can be distributed proportionally.

Abstract This study simulates the separation of stable Neon isotopes in a transient square cascade using the Crank–Nicolson method and the q-iteration method. The simulations show that each isotope has an optimal value in either the product or waste streams at a specific time, which affects the cost of separation. The results demonstrate that the optimal separation time for Ne-20 increases with the feed concentration and is influenced by the unit separation factor. Depending on the feed concentration and separation parameter, Ne-21 may be enriched in either the product or waste stream. The optimal separation time for Ne-22 is the maximum operation time and is not affected by changes in feed concentration or unit separation factor. Calculating the optimal separation time is crucial for obtaining target isotopes with specific purity at a designated time, depending on their intended applications.

Using specific examples, we constructively show that, in dimensions greater than , the Lyapunov extreme instability of a differential system, i.e., the property that the phase curves of all nonzero solutions starting sufficiently close to zero leave any prescribed compact set, does not imply that these solutions go arbitrarily far away from zero in the sense of Perron or in the upper-limit sense as . Namely, we construct two Lyapunov extremely unstable systems such that all solutions of the first system tend to zero, while the solutions of the second system are divided into two types: all nonzero solutions starting in the closed unit ball tend to infinity in norm, and all the other solutions tend to zero. Further, both systems constructed in the paper have zero first approximation along the zero solution. [ABSTRACT FROM AUTHOR]

The paper considers adaptive event‐triggered control for nonlinear systems with time‐varying parameter uncertainties. The time‐varying uncertainties do not need to be differentiable, but their variation amplitudes are required to be known. Such uncertainties appear not only in the system nonlinearities but also as the control coefficient. We pursue a tight design scheme by combining tuning functions and the congelation of variables method, thereby avoiding the overuse of dominations and obtaining a less conservative controller. In view of the essence of the control problem, we don't design a continuous controller first and then search for a complex and suitable event‐triggering mechanism, as emulation methods done in the literature. In contrast, we adopt a simple event‐triggering mechanism with the relative threshold, while seeking a complex and appropriate adaptive controller which contains the new adaptive treatment for execution error due to the unknown time‐varying control coefficient. Note that there are three parameter dynamic compensators in the adaptive controller, and one is specialized to the execution error, which is not required in the continuous feedback context. It is shown that with the proposed adaptive event‐triggered controller, all the closed‐loop signals are bounded, the system state converges to zero, and no Zeno behavior occurs. A comparative simulation is provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This article studies the parameter estimation problems of nonlinear systems with colored noise using the covariance matrix adaptation evolution strategy (CMA‐ES), which is one of the most competitive evolutionary algorithms available and has been applied in the area of reinforcement learning and process control. However, a major limitation that impedes the application of the CMA‐ES is the high computational complexity caused by matrix decomposition. To solve this problem, an efficient Cholesky CMA‐ES which uses the Cholesky factor instead of the covariance matrix to reduce the computational complexity, and updates the search direction and distribution mean based on the conjugate gradient method to improve the search accuracy is proposed. By using the auxiliary model identification idea, the Cholesky CMA‐ES can be applied to solve the parameter estimation problems of the Hammerstein nonlinear systems with colored noise. Two simulation examples are provided to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

This paper begins by exploring the challenge of event-triggered state estimations in nonlinear systems, grappling with packet dropout and correlated noise. A communication mechanism is introduced that determines whether to transmit measurement values based on whether event-triggered conditions are violated, thereby minimizing redundant communication data. In designing the filter, noise decorrelation is initially conducted, followed by the integration of the event-triggered mechanism and the unreliable network transmission system for state estimator development. Subsequently, by combining the three-degree spherical–radial cubature rule, the numerical implementation steps of the proposed state estimation framework are outlined. The performance estimation analysis highlights that by adjusting the event-triggered threshold appropriately, the estimation performance and transmission rate can be effectively balanced. It is established that when there is a lower bound on the packet dropout rate, the covariance matrix of the state estimation error remains bounded, and the stochastic stability of the state estimation error is also confirmed. Ultimately, the algorithm and conclusions that are proposed in this paper are validated through a simulation example of a target tracking system. [ABSTRACT FROM AUTHOR]

Purpose: This paper investigates a vibration energy harvester with a triangular structure for lowfrequency vibrations, focusing on the analysis of nonlinear stiffness and damping characteristics generated by the structure itself for advantageous harvesting performance. Methods: First, Euler–Lagrange equation of the system is established based on Hamilton's principle. Then, with the mathematical modeling, the dynamic response of the system is derived using Harmonic Balance Method, which is discussed by numerical analysis. Based on the analytical solutions, the effects on harvesting power changed by different assembly angles, connecting rod length and excitation amplitudes are studied particularly. The advantageous harvesting performance of the proposed system is shown by comparing it with a corresponding conventional linear system. Results: The result shows that the triangular structure in the system is beneficial for expanding the power output and energy-harvesting bandwidth. Further, the resonant frequency of the system can be tuned to a desired value by adjusting the assembly angle according to the characteristics of surrounding vibration sources. Conclusions: Therefore, the harvester system in this work is demonstrated to provide an effective method for design to scavenge the low-frequency vibration energy from the ambient environment in engineering. [ABSTRACT FROM AUTHOR]

A dynamic model is established to investigate the shimmy instability of a landing gear system, considering the influence of nonlinear damping. The stability criterion is utilized to determine the critical speed at which the landing gear system becomes unstable. The central manifold theorem and canonical method are employed to simplify the dynamic model of the landing gear. The first Lyapunov coefficient of the system is theoretically derived and verified using numerical simulation. Further investigation on the Hopf bifurcation characteristics and stability of the shimmy in the landing gear system is conducted. The results indicate that above a certain threshold speed, with a tire stability distance greater than half the tire length in contact with the ground plus the slack length, the aircraft remains stable during taxiing. At critical speeds, a shimmy system with higher-order nonlinear damping will undergo supercritical Hopf bifurcation. Quantitative analysis suggests an increase in the linear damping coefficient within a range that ensures a stability margin to mitigate undesired oscillation, while the nonlinear damping coefficient should be designed within a reasonable range to decrease the amplitude of the limit cycle. [ABSTRACT FROM AUTHOR]

The identification problem of nonlinear system with missing data is focused in this article. In order to overcome the system unavailable outputs, an auxiliary model‐based interval‐varying recursive identification method is derived by changing the sampling interval and substituting the missing output with the output of an auxiliary model. Based on the maximum likelihood principle and the least‐squares method, a maximum likelihood‐based interval‐varying recursive least‐squares method is investigated. The validity of the proposed maximum likelihood method is tested by a numerical simulation example and a practical continuous stirred tank reactor (CSTR) process. [ABSTRACT FROM AUTHOR]

This article investigates the parameter identification problems of the stochastic systems described by the input‐nonlinear output‐error (IN‐OE) model. This IN‐OE model consists of two submodels, one is an input nonlinear model and the other is a linear output‐error model. The difficulty in the parameter identification of the IN‐OE model is that the information vector contains the unknown variables, which are the noise‐free (true) outputs of the system, the approach taken here is to replace the unknown terms with the outputs of the auxiliary model. Based on the over‐parameterization model and the hierarchical identification principle, an over‐parameterization auxiliary model hierarchical gradient‐based iterative algorithm and an over‐parameterization auxiliary model hierarchical least‐squares‐based iterative algorithm are proposed to estimate the unknown parameters of the IN‐OE systems. Finally, two numerical simulation examples are given to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article explores recursive algorithms for parameter identification issues of Hammerstein output‐error systems. The proposed approach includes the key term separation auxiliary model recursive gradient algorithm, which utilizes the gradient search and the key term separation. To enhance computational efficiency, the system is decomposed into two or three subsystems through the hierarchical identification principle. Based on this, a key term separation based auxiliary model two‐stage recursive gradient algorithm and a key term separation based auxiliary model three‐stage recursive gradient algorithm are presented. The simulation results verify the validity of the obtained algorithms. [ABSTRACT FROM AUTHOR]

This paper examines the boundary stabilisation results for time fractional-order reaction-diffusion systems involving with time-varying delays. The main goal is to design the boundary control for the system by proving the well-posedness of the kernel function using the backstepping method. An invertible Volterra integral transformation is used to convert the considered system into a stable target system. Different from the existing results, the stability results for fractional RDEs are discussed in the sense of the Lyapunov–Krasovskii theory and sufficient conditions are derived with the help of the linear matrix inequality (LMI) approach. Finally, to show the application of the results, the proposed conditions are numerically validated over a time fractional-order reaction-diffusion cellular neural network model. [ABSTRACT FROM AUTHOR]

Applying the signals and systems theory and control theory studied in electrical engineering and mechanical engineering courses requires sophisticated, expensive and delicate handling devices. The mathematical tools that are taught in the disciplines of signals and systems and control theory in the undergraduate course are often abstract, especially in terms of practical application in an industrial setting, which makes it necessary to use didactic control plants to complement teaching and hands-on experimentation. This paper presents a low-cost two-wheeled self-balancing car system as a teaching tool for engineering. The two-wheeled self-balancing car is a dynamic benchmark system designed to control the car in a vertical position. The car is able to remain balanced through calculations that analyze the angle of the gyroscope and the position of the wheels. DC motor drivers are used to compensate for tilt and balance the car. As the purpose of the article is to serve as support material for undergraduate students who are taking their first steps in the study of signals and systems and control theory, detailed modeling by the laws of physics are presented, together with the simulation of the nonlinear model of the system and a complete linearization of the model. [ABSTRACT FROM AUTHOR]

Purpose: Online question-and-answer (Q&A) communities serve as important channels for knowledge diffusion. The purpose of this study is to investigate the dynamic development process of online knowledge systems and explore the final or progressive state of system development. By measuring the nonlinear characteristics of knowledge systems from the perspective of complexity science, the authors aim to enrich the perspective and method of the research on the dynamics of knowledge systems, and to deeply understand the behavior rules of knowledge systems. Design/methodology/approach: The authors collected data from the programming-related Q&A site Stack Overflow for a ten-year period (2008–2017) and included 48,373 tags in the analyses. The number of tags is taken as the time series, the correlation dimension and the maximum Lyapunov index are used to examine the chaos of the system and the Volterra series multistep forecast method is used to predict the system state. Findings: There are strange attractors in the system, the whole system is complex but bounded and its evolution is bound to approach a relatively stable range. Empirical analyses indicate that chaos exists in the process of knowledge sharing in this social labeling system, and the period of change over time is about one week. Originality/value: This study contributes to revealing the evolutionary cycle of knowledge stock in online knowledge systems and further indicates how this dynamic evolution can help in the setting of platform mechanics and resource inputs. [ABSTRACT FROM AUTHOR]

The current study aims to analyze the dynamic characteristics of the nonlinear system excited parametrically in the presence of internal resonance. The method of multiple time scales (MMS) is directly adopted to simplify the higher-order integro-partial differential equation of motion to get an approximate solution that leads to a set of first-order partial differential equations. To develop a suitable model for a moving beam, the parameters incorporated are viscoelasticity and viscous damping, geometric nonlinearity, Coriolis acceleration, harmonically varying velocity, and axially varying tension. The stability and bifurcations of the steady-state solution are examined under a subcritical speed regime. The investigation focuses on the changes in the stability and bifurcation features of steady-state solutions accounting for the effects of variations in the system parameters like internal and parametric frequency detuning parameters, the amplitude of fluctuating speed, and axial stiffness. The outcomes of this investigation are unique, interesting, and not available in the existing literature, which may provide theoretical insight in designing a traveling system. [ABSTRACT FROM AUTHOR]

The Compressed Air Pressure Process (CAPP) is very important in an industrial environment. Because compressed air is used in many applications such as pneumatic-based actuation such as pneumatics valves, pneumatic-based tools, etc. In this process, the minute linkages are very difficult to arrest and also nonlinear behavior of conversion elements such as pressure (3–15) psi to current (4–20) mA (P/I) as well as current (4–20) mA to voltage (0–5) v (I/V) converters are making the process highly nonlinear. To maintain the process variable at a certain prescribed value and to design a good and effective controller, the non-linear process must be controlled, and the best model is needed. In this research work optimized integer with non-integer designs are gained and based on the models the PID controller with optimized controller parameters is selected depending on the model using optimized methods such as Fmin–GA and also Internal Model controllers (IMC) are designed, the Investigations are done by comparing the dynamic behaviors. The performance of the proposed technique is implemented in the MATLAB platform and the experimental prototype is also presented. [ABSTRACT FROM AUTHOR]

This paper proposes a novel filter-based immersion and invariance (I&I) adaptive method for nonlinear systems with additive disturbances and parameter uncertainties. The key innovation of the proposed method is a filter construction that involves the dynamics of the system, based on which the I&I parameter estimator with a sigma modification term is designed. Comparing existing I&I methods, the expression for the novel filter-based I&I estimator is given in terms of total derivatives rather than partial derivatives, which is no longer subject to the integrability condition. In combining the sigma modification term, the proposed parameter estimator also guarantee the uniformly ultimately bounded stability of the parameter estimation error when the system is disturbed, which cannot be achieved by the original I&I method. Furthermore, Lyapunov theory demonstrates that the proposed method can guarantee the stability of the nonlinear systems discussed in this paper. Simulation and experimental results confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Miniaturized microelectromechanical system (MEMS) microspeakers are currently trending in the development of acoustic transducers. When a transducer is scaled down to fit on a microelectronic chip, its physics differ from the macroscopic world, and some common modeling assumptions become invalid. One of the effects observed in MEMS microspeakers is nonlinear squeeze film damping. Understanding this effect is crucial, as non-linearities in the speaker can result in perceptible harmonic distortions, which are undesirable in audio applications. In this study, we analyze the influence of squeeze film damping on harmonic distortions using a lumped parameter model of a MEMS microspeaker. This leads to a nonlinear ordinary differential equation, and an approximate analytical solution for moderate non-linearities is obtained using homotopy. We present our solution strategy, including the resulting closed-form expression, and verify our findings against numerical solutions. [ABSTRACT FROM AUTHOR]