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In this study, we simultaneously evaluate the multiple‐fault diagnosis problem of a class of Lipschitz nonlinear systems with actuator and sensor faults and unknown input disturbances. A nonsingular system transformation is used to transform the original system into two subsystems for multiple‐fault diagnosis: subsystems 1 and 2. At the system level, two robust sliding‐mode observers (RSMOs) are proposed. An RSMO is designed for subsystem 1 to detect actuator faults subjected to unknown input disturbances, and another RSMO is designed for subsystem 2 to detect sensor faults subjected to actuator faults. At the component level, a bank of RSMOs is proposed to detect and isolate actuators (sensors) with faults using a dedicated observer scheme. The reachability of RSMOs is comprehensively investigated in the estimation error space. Accordingly, the proposed observer parameters are designed as an optimization problem and solved using the linear matrix inequality (LMI) optimization technique. The effectiveness of the proposed multiple‐fault diagnosis scheme was validated through simulations of a modified seventh‐order aircraft system. [ABSTRACT FROM AUTHOR]

In this paper, a new robust model predictive control (RMPC) for uncertain nonlinear systems subject to actuator saturation is designed to regulate the terminal voltage of a photovoltaic generator (PVG) that feeds a DC motor-pump via a buck DC–DC converter. The considered system is a combination of a PVG-converter and DC motor-pump, which possesses nonlinear behavior along with under a saturating control signal highly dependent on the operation point and climate conditions of solar radiation and temperature. As a result, the control task is complex due to the nonlinearity of the system and its dependence on climate conditions. Based on the dead-zone property, the presented paper introduces a new RMPC technique to provide an innovative and efficient solution to ensure the closed-loop system's robust stability in the presence of actuator nonlinearity. In this paper, the nonlinear system is described in polytypic form, and an appropriate linear feedback control law is designed and used to minimize an infinite horizon cost function under the framework of linear matrix inequalities (LMIs). Furthermore, sufficient state-feedback control law conditions are synthesized to guarantee the robust stability of the closed-loop system in the presence of polytypic uncertainties. Simulation results are provided, in which the results illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes an interval vibration analysis method for nonlinear systems subjected to uncertain excitations, through which its dynamic displacement response bounds can be calculated effectively. In the proposed method, the uncertain excitations are described using the interval process model developed by the authors in recent years. Firstly, the displacement response of a certain degree of freedom for a nonlinear system at an arbitrary time point is expressed as a function of several standard uncorrelated interval variables by using the interval K–L expansion. Secondly, two constrained optimization models are established for the lower and upper bounds of the displacement response of the nonlinear system at the time point. Thirdly, the efficient global optimization (EGO) method is used to solve the above optimization models, and the dynamic displacement response bounds of the nonlinear system can be further obtained. Finally, the effectiveness of the proposed method is verified by investigating two numerical examples. [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.

The article gives the possibilities of applications of the backstepping method for solving the problem of synthesis of a control system for the nonlinear dynamic plant with indefinably changing parameters. Has been modified the well-known method of backstepping inclusion in the control system of the state observer, allows for the restoration of unmeasured coordinates with a differentiating unit, due to which substantially simplified the definition of customizable parameters of control device and provides the desired dynamic accuracy of control.

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.

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.

In order to increase a nonlinear system’s state estimate precision, an iterated orthogonal simplex cubature Kalman filter (IOSCKF) is presented in this study for target tracking. The Gaussian-weighted integral is decomposed into a spherical integral and a radial integral, which are approximated using the spherical simplex-radial rule and second-order Gauss–Laguerre quadrature rule, respectively, and result in the novel simplex cubature rule. To decrease the high-order error terms, cubature points with appropriate weights are taken from the cubature rule and processed using the provided orthogonal matrix. The structure supporting the nonlinear Kalman filter incorporates the altered points and weights and the calculation steps; from this, the updated time and measurement can be inferred. The Gauss–Newton iteration is employed repeatedly to adjust the measurement update until the termination condition is met and the IOSCKF is attained. The proposed algorithms are applied in target tracking, including CV target tracking and spacecraft orbit tracking, and the simulation results reveal that the IOSCKF can achieve higher accuracy compared to the CKF, SCKF, and OSCKF. In spacecraft orbit tracking simulation, compared with the SCKF, the position tracking accuracy and velocity tracking accuracy of the OSCKF are increased by 2.21% and 1.94%, respectively, which indicates that the orthogonal transformation can improve the tracking accuracy. Furthermore, compared with the OSCKF, the position tracking accuracy and velocity tracking accuracy of the IOSCKF are increased by 2.71% and 2.97%, respectively, which indicates that the tracking accuracy can be effectively improved by introducing iterative calculation into the measurement equation, thus verifying the effectiveness of the method presented in this paper.

Since 1993, Devices based on CNTs have applicationsranging from nanoelectronics to optoelectronics. Thechallenging issue in designing these devices is that thenonequilibrium Green's function (NEGF) method has tobe employed to solve the Schrödinger and Poissonequations, which is complex and time consuming. In thepresent study, a novel smart and optimal algorithm ispresented for fast and accurate modeling of CNT fieldeffecttransistors (CNTFETs) based on an artificial neuralnetwork. A new and efficient way is presented forincrementally constructing radial basis function (RBF)networks with optimized neuron radii to obtain theestimator network. An incremental extreme learningmachine (I-ELM) algorithm is used to train the RBFnetwork. To ensure the optimal radii for incrementalneurons, this algorithm utilizes a modified version of anoptimization algorithm known as the Nelder-Meadsimplex algorithm. Results confirm that the proposedapproach reduces the network size for faster errorconvergence while preserving the estimation accuracy.

The nonlinear characteristics of multilateration(MLAT) system were analyzed by simplified frequency-domain Volterra series when the S-mode signal response pulse was input.Firstly, take the typical super heterodyne receiver system for example, the model based on simplified frequency-domain Volterra series and error rate model of MLAT system were explored and created.Secondly, the S-mode response pulse signal model based on kernel function was researched and established.Finally, the model error rate of S-mode signal receiver system based on simplified frequency-domain Volterra series was analyzed when the S-mode signal based on kernel function was input.The results show that the minimum error rate of the receiver system based on 15 dB SNR simplified frequency-domain Volterra series is less than 23.23% when the S-mode signal based on kernel function is input.When the actual S-mode test signal with 16.25 dB SNR is input, the minimum error rate of the model is less than 22%, which is less than the error rate threshold.It shows that the receiver system model based on simplified frequency-domain Volterra series can accurately describe the characteristics of S-mode signal receiver system, which provides the theoretical foundation for the identification of preamble arrival timestamp in MLAT system.

In this investigation, the nonlinear dynamics of an axially accelerating viscoelastic beam on a pully mounting system have been analyzed. The axial tension of the beam is modeled as a function of the traveling velocity, support stiffness parameter as well as spatial coordinate. Geometric cubic nonlinearity in the equation of motion is due to elongation in the neutral axis of the beam. The integro-partial differential equation of motion of the axially accelerating beam associated with the simply supported end conditions is solved analytically by adopting the direct perturbation method of multiple time scales. As a result, a set of complex variable modulation equations is generated, which governs the modulation of amplitude and phase. This set of modulated equations is numerically solved to explore the influence of the support stiffness parameter upon the stability and bifurcation of the beam which has not been addressed in the existing literature. Apart from this, the impact of fluctuating velocity component, viscoelastic coefficient, longitudinal stiffness parameter, internal and parametric frequency detuning parameters on the stability and bifurcation analysis is studied, revealing significant dynamic characteristics of the traveling system. The fourth-order Runge–Kutta method is applied is to find the dynamic solution of the system. The system displays stable periodic, quasi-periodic, and mixed-mode dynamic responses along with the unstable chaotic behavior for a specific set of system parameters. The results obtained through an analytical–numerical approach may help the design and operation of an axially moving beam. [ABSTRACT FROM AUTHOR]

In linear systems, it is well known that any combination of stabilizing state feedback controller and a state observer results in the output feedback controller which asymptotically stabilizes the closed-loop system. This is known as the separation principle, which does not generally hold for nonlinear systems. For nonlinear systems, the output feedback problem is usually pursued by extending the results of observer synthesis, which itself is a challenging problem. In this paper, we investigate the stabilization via an observer configuration problem for some classes of nonlinear time-varying systems by using new integral inequalities of Gronwall type. Given that the sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimated state feedback from the proposed practical observer will achieve the global practical exponential stabilization. Furthermore, the effectiveness of the proposed scheme is shown through simulation for two numerical examples. [ABSTRACT FROM AUTHOR]

In anaerobic digestion plants, it is often crucial to measure state variables such as the substrate or biomass densities for monitoring the process. But, this task can be very difficult to achieve because the sensors are sometimes unavailable, unreliable or very expensive. For these reasons software sensors can be sought instead, using indirect measurements. In this paper, we design a new observer for the chemostat model with the single measurement of biogas flow rate. This observer is positive and we show its adjustable convergence. Through simulations we also show its robustness under noise measurements. The key point is to construct a non-linear observer using hidden symmetries in the framework of the theory of symmetry preserving nonlinear systems. The effectiveness of the proposed methodology is shown through simulations. • Definition and design of an invariant observer for the chemostat model with the biogas as the measured output. • Positivity of the observer with an asymptotic convergence. • Design of the observer based on the symmetries of the dynamical system. • Numerical simulations results showing the effectiveness of the proposed observer. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a new family of iterative methods for approximating the solution of nonlinear systems for non-differentiable operators. The novelty of this family is that it is a m-step generalization of the Steffensen-type method by updating the divided difference operator in the first two steps but not in the following ones. This procedure allows us to increase both the order of convergence and the efficiency index with respect to that obtained in the family that updates divided differences only in the first step. We perform a semilocal convergence study that allows us to fix the convergence domain and uniqueness for real applied problems, where the existence of a solution is not known a priori. After this study, some numerical tests are developed to apply the semilocal convergence theoretical results obtained. Finally, mediating the dynamic planes generated by the different numerical methods that compose the family, we study the symmetry of the basins of attraction generated by each solution, the shape of these basins, and the convergence to each root of a polynomial function. [ABSTRACT FROM AUTHOR]

The training method for deep neural networks mainly adopts the gradient descent (GD) method. These methods, however, are very sensitive to initialization and hyperparameters. In this paper, an enhanced gradient descent method guided by the trajectory-based method for training deep neural networks, termed the Trajectory Unified Framework (TJU) method, is presented. From a theoretical viewpoint, the robustness of the TJU-based method is supported by an analytical basis presented in the paper. From a computational viewpoint, a TJU methodology consisting of a Block-Diagonal-Pseudo-Transient-Continuation method and a gradient descent method, termed the TJU-GD method, for training deep neural networks is added to obtain high-quality results. Furthermore, to resolve the issue of imbalanced classification, a TJU-Focal-GD method is developed and evaluated. Experimental numerical evaluation of the proposed TJU-GD on various public datasets reveals that the proposed method can achieve great improvements over baseline methods. Specifically, the proposed TJU-Focal-GD also possesses several advantages over other methods for a class of imbalanced datasets from the homemade power line inspection dataset (PLID). [ABSTRACT FROM AUTHOR]

Electro-hydraulic servo systems (EHSSs) are nonlinear and uncertain due to their inappropriate fluid levels, air temperature, friction, and leakage. The finite-time tracking control is difficult with the use of a proportional, integral, and derivative (PID) controller, which no longer provides adequate and achievable control performance over the whole operating range. This has led to the idea of an iterative learning controller (ILC). An intelligent and memory-based learning control approach that attempts to imitate the human way of thinking. The proposed ILC has an additional learning gain, learning filter, and robustness filter to enhance the finite-time tracking performance and stability improvement. This study is focused on the design of the ILC to regulate the servo spool valve of an EHSS, which in turn controls the displacement of a hydraulic cylinder. In simulation and experimentation, vital parameters such as overshoot and settling time in the varieties of tests, the ILC has shown better results when compared to conventional PID controllers. In step input tracking at different operating points over 0-250 mm, the ILC has 40% less overshoot and settles 12-15 s faster than the PID controller. In sinewave tracking and disturbance rejection, the PID controller performs better than the ILC in integral square error and integral absolute error as the error indices are not considered as the objective function in the design of the controller. During a robustness test, the ILC rejects the uncertainty, which evidences the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This article aims to design a low gain feedback controller for a class of discrete‐time feedforward nonlinear systems (DFNSs) with unknown input saturation. Although the design of the low gain feedback control can be converted into the choosing of a parameter, it is difficult to design the control due to the inherent nonlinear dynamics and the unknown input constants. To solve this problem, we first show that the low gain feedback control can be found to stabilize the DFNSs when the saturation is known. Then, by analyzing the dynamics of DFNSs under the saturating input, the relation is built between the parameter and the system state. Finally, we introduce a technology to update the parameter based on different performance, whose effectiveness is illustrated through considering a numerical example. [ABSTRACT FROM AUTHOR]

n this paper, we present a family of iterative schemes for solving nonlinear systems with 3 real parameters. If we do not fix values for the parameters this family has order 2, but if we fix two of them we obtain order 5. Starting from the fifth-order family, we study different ways of introducing memory, thus obtaining 6 order methods. We also analyze the efficiency indices of the family and of the methods with memory obtained from it, and we compare them with each other, as well as compare them with other known classes of iterative methods with order 5 and 6. Several numerical experiments are carried out to see the behaviour of the discussed methods, including dynamical planes to compare the stability of the different iterative schemes. [ABSTRACT FROM AUTHOR]

This paper focuses on the three-body confrontation problem of a Target–Defender team against an Attacker possessing greater maneuverability. Based on the input-to-state stability approach, a cooperative robust line-of-sight guidance law is proposed for the Target–Defender team to ensure that the Attacker has a certain tolerance range on the unavailable guidance information. In addition, the optimal evasion strategy is developed for the Target to maximize the terminal distance between the Target and Attacker. A key feature of the proposed guidance law is that the interception of the Attacker can be guaranteed as long as the uncertainty generated by the Attacker's maneuver is bounded. Furthermore, by using the optimal control technique, the control input of the Target–Defender team is minimized. Simulation examples are given to illustrate the effectiveness of the proposed guidance law. • Disturbance is considered in the second-order nonlinear LOS dynamics. • The guidance law is input-to-state stable. • The static optimization is used to minimize the accelerations of vehicles. • The special case is considered to derive the optimal evasion strategy. • An optimal evasion strategy is developed to maximize the terminal distance. [ABSTRACT FROM AUTHOR]

In the presence of external disturbances, a backstepping control scheme based a genetic algorithm (GA) is built with the objective of tracking a desired trajectory of robot manipulators. The nonlinear-coupled higher order dynamic model of an n-link robot manipulator is first briefly presented. Then, a traditional backstepping control system (BSC) creates a two-link robotic manipulator position tracking control. Furthermore, a mix of nonlinear control and artificial intelligence is suggested for manipulator robot control. To determine the optimal control parameters, the backstepping controller is combined with the genetic algorithm, a metaheuristics-based optimization technique. The effectiveness of the suggested optimal control strategy based on backstepping approach and GA in trajectory tracking problems, such as a good angle tracking and a good disturbance rejection capability, is demonstrated by numerical simulations using the dynamic model of a two-link planar rigid robot manipulator. [ABSTRACT FROM AUTHOR]

Chaotic systems are suitable for protecting digital images due to many of their own characteristics. However, many chaos-based image colour encryption algorithms exhibit many disadvantages such as the lack of randomness of the chaotic map, the separate encryption of three colour planes and the inability to transmit the key over a public channel. The main significances of this paper are as follows: Firstly, we propose a chaotic logistic-sine coupling map (2D-CLSM), which exhibits better chaotic performance and randomness than some existing chaotic systems. Secondly, based on 2D-CLSM, we have designed a cross-plane colour image encryption algorithm (CLSM-CCIE). The image pixel values are diffused and scrambled across the planes of the red, green and blue components. The experimental results show that CLSM-CCIE is highly secure and can resist common attacks. Finally, the sensitive data of the symmetric encryption algorithm cannot be transmitted over the common channel. In order to make CLSM-CCIE more applicable in practice, we have further implemented CLSM-CCIE in the elliptic curve integrate encrypt scheme (ECIES) framework in public key Systems. Therefore, it is more convenient and secure to transmit CLSM-CCIE keys and other sensitive data over the public channel. [ABSTRACT FROM AUTHOR]

The hunting phenomenon is an intrinsic swaying motion appearing in railway vehicles due to the vehicle's forward speed and the wheel–rail contact forces. Hunting motion consists of wheelset and other vehicle's components oscillations that arise above a certain vehicle's speed known as critical or hunting speed. These oscillations are of unstable nature and represent a safety hazard as they could lead to the vehicle's derailment. This article analyses the stability of a bogie nonlinear model for a Spanish high-speed train when this is travelling at speeds near the hunting speed. The vehicle's stability is studied by means of root loci methods, and the value of the critical speed is found. In addition to this, the behaviour of the vehicle is studied in both stable and unstable regions and the existence of limit cycles is discussed in this work. Finally, a sensitivity analysis of the axle load and suspension parameters is performed. The results show that the axle load, the vertical stiffness of the primary suspension and the lateral damping of the secondary suspension have a significant influence on the value of the critical speed. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications 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.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications 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.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications 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.)

The aim of this paper is to find numerical solutions of nonlinear boundary value problems (BVPs). First, the nonlinear system is transformed into linear system using the Quasi-Newton's method, and the convergence of the method is verified. Second, we defined Hilbert space W (2 , 2) and constructed a set of multiscale orthonormal basis in W (2 , 2) . By solving the ε - approximation solution of the linear systems, the numerical solution of linear systems is obtained. Furthermore the feasibility and effectiveness of the proposed method are verified by three numerical experiments. [ABSTRACT FROM AUTHOR]

This paper provides an inverse-model-based iterative learning control (ILC) for the unknown multi-input multi-output (MIMO) nonlinear system with neural network (NN), where a novel gradient adaptive law is used to update the NN weights both hidden and output layers such a faster convergence can be achieved. First, a three-layer NN structure is introduced to observe the MIMO nonlinear system with input–output data, and a new gradient algorithm is proposed to update the unknown parameters of both hidden and output layers. Then, the input dynamic can be obtained with the NN observer, and the inversion-model-based control is designed. Moreover, the ideal inversion control can be obtained based on the reference signal, and the inverse ILC is designed. The stability of the NN observer and the convergence of the inverse-model-based control are analyzed. Finally, a SCARA manipulator MIMO model is simulated to illustrate the correctness of the proposed methods. [ABSTRACT FROM AUTHOR]

A design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed‐loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling‐hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed‐loop system. The effectiveness of the proposed method is illustrated through a chemical process example. [ABSTRACT FROM AUTHOR]

The fixed-time stability on uncertain neural networks with adaptive coupling strength is addressed in this paper. To beign with, a new time-varying coupling strength is introduced, which is based on the projective transform of quantized error systems. Next, to address various disturbances in master-slave systems, inhomogeneous uncertainty is taken into consideration. Then, a multi-quantized fixed-time controller is put forward to ensure that the systems reach to a prescribed trajectory in the settling time. Afterward, sufficient synchronization criteria are derived on the strength of the Lyapunov stability theorem. Finally, simulation examples are given to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Factors such as changes in the external atmospheric environment, volatility in the external radiation, convective heat transfer, and radiation between the internal surfaces of the airship skin will cause a series of changes in the motion model of an airship. The adaptive control method of the characteristic model is proposed to extract the relationship between input and output in the original system, without relying on an accurate dynamic model, and solves the problem of inaccurate modeling. This paper analyzes the variables needed for two-dimensional path tracking and combines the guidance theory and the method of wind field state conversion to determine specific control targets. Through the research results, under the interference of wind, the PD control method and the reinforcement learning-based method are compared with a characteristic model control method. The response speed of the characteristic model control method surpasses the PD control method, and it reaches a steady state earlier than the PD control method does. The overshoot of the characteristic model control method is smaller than that of the PD control method. Using the control method of the characteristic model, the process of an airship flying to a target point will be more stable under the influence of an external environment. The modeling of the characteristic model adaptive control method does not rely on a precise model of the system, and it automatically adjusts when the parameters change to maintain a consistent performance in the system, thus reflecting the robustness and adaptability of the characteristic model adaptive control method in contrast with reinforcement learning. [ABSTRACT FROM AUTHOR]

Here, we prove the Haraux-Weissler equation has no solution on a domain which is strictly starshped with respect to 0. Finally, we present some questions. [ABSTRACT FROM AUTHOR]

Summary: In control engineering, the disturbance is a major problem that deteriorates system robustness. To address this problem, a disturbance observer (DOB) has been proposed and developed. In particular, a general method of estimating high‐order disturbance, expressed as a time series expansion, was studied (H‐DOB). However, systems to which H‐DOB are applicable are limited to those in which disturbance gain is constant. This constraint degrades the generality of H‐DOB because applicable systems are limited. Therefore, by expanding to a system with a time‐varying disturbance gain, we propose a more general H‐DOB. The DOB proposed in this paper redesigns the dynamics of the observer based on the structure of the H‐DOB. The proposed DOB is applicable even if the system is highly nonlinear. This paper verifies the convergence of the proposed DOB through proof. Using this proof, the same characteristic error dynamics can be obtained, so the same design method can be applied. The simulation for the verification of the proposed method performs disturbance estimation of the extension system. This simulation proves that, compared to H‐DOB, the proposed DOB has good disturbance estimation performance. [ABSTRACT FROM AUTHOR]

The Neural Networks (NN) model which is incorporated in the control system design has been studied, and the results show better performance than the mathematical model approach. However, some studies consider that only offline NN model learning and does not use the online NN model learning directly on the control system. As a result, the controller's performance decreases due to changes in the system environment from time to time. The Reinforcement Learning (RL) method has been investigated intensively, especially Model-based RL (Mb-RL) to predict system dynamics. It has been investigated and performs well in making the system more robust to environmental changes by enabling online learning. This paper proposes online learning of local dynamics using the Mb-RL method by utilizing Long Short-Term Memory (LSTM) model. We consider Model Predictive Control (MPC) scheme as an agent of the Mb-RL method to control the regulatory trajectory objectives with a random shooting policy to search for the minimum objective function. A nonlinear Mass Spring Damper (NMSD) system with parameter-varying linear inertia is used to demonstrate the effectiveness of the proposed method. The simulation results show that the system can effectively control high-oscillating nonlinear systems with good performance. [ABSTRACT FROM AUTHOR]

Summary: This article considers the identification problems of nonlinear systems with scarce measurements by using the instrumental variable technique. When the product of the instrumental matrix and the information matrix is a nonsingular matrix and the weak persistent excitation condition about the instrumental vector is true, the obtained parameter estimates can be unbiased consistent estimates. The key is how to choose the instrumental variables. Difficulty arises in that the system outputs are unavailable. By applying the negative gradient search, a recursive instrumental variable‐based gradient algorithm is derived to estimate the parameters of the nonlinear systems with missing observed data. Moreover, the multi‐innovation identification theory is introduced to further improve the parameter estimation accuracy. The simulation results illustrate that the proposed methods are effective. [ABSTRACT FROM AUTHOR]

In this paper, a new algorithm developing to solve optimization problems with many nonlinear factors in ultra-precision machining by magnetic liquid mixture. The presented algorithm is a collective global search inspired by artificial intelligence based on the coordination of nonlinear systems occurring in machining processes. Combining multiple nonlinear systems is established to coordinate various nonlinear objects based on simple physical techniques during machining. The ultimate aim is to create a robust optimization algorithm based on the optimization collaborative of multiple nonlinear systems (OCMNO) with the same flexibility and high convergence established in optimizing surface quality and material removal rate (MRR) when polishing the SKD61-coated Ni-P material. The benchmark functions analyzing and the established optimization polishing process SKD61-coated Ni-P material to show the effectiveness of the proposed OCMNO algorithm. Polishing experiments demonstrate the optimal technological parameters based on a new algorithm and rotary magnetic polishing method to give the best-machined surface quality. From the analysis and experiment results when polishing magnetic SKD 61 coated Ni-P materials in a rotating magnetic field when using a Magnetic Compound Fluid (MCF). The technological parameters according to the OCMNO algorithm for ultra-smooth surface quality with Ra = 1.137 nm without leaving any scratches on the after-polishing surface. The study aims to provide an excellent reference value in optimizing the surface polishing of difficult-to-machine materials, such as SKD 61 coated Ni-P material, materials in the mould industry, and magnetized materials. [ABSTRACT FROM AUTHOR]

Even if a system has only one stable equilibrium point, its dynamics can still be complicated. In the case of the equilibrium point with a complicated boundary of the attraction basin, it is probably difficult to predict the long-term behavior of the trajectory starting from a point outside but near the boundary. The exploration of such systems is helpful for deepening our understanding of the dynamics of complex systems. This paper studies a class of three-dimensional polynomial systems with a nonelementary singularity. With parameters satisfying some conditions, the asymptotic stability of the origin is proved and the complexity of the attraction basin is investigated. It is demonstrated that the boundary of the attraction basin of the origin has a fractal structure in the following sense: An invariant set homeomorphic to the well-known Lorenz strange attractor is contained in the basin boundary. Based on the non-negative function we constructed, how fast a trajectory of the system tends to the asymptotically stable nonelementary singularity is measured. [ABSTRACT FROM AUTHOR]

In the present paper, a hybrid deep learning diagonal recurrent neural network controller (HDL-DRNNC) is proposed for nonlinear systems. The proposed HDL-DRNNC structure consists of a diagonal recurrent neural network (DRNN), whose initial values can be obtained through deep learning (DL). The DL algorithm, which is used in this study, is a hybrid algorithm that is based on a self-organizing map of the Kohonen procedure and restricted Boltzmann machine. The updating weights of the DRNN of the proposed algorithm are developed using the Lyapunov stability criterion. In this concern, simulation tasks such as disturbance signals and parameter variations are performed on mathematical and physical systems to improve the performance and the robustness of the proposed controller. It is clear from the results that the performance of the proposed controller is better than other existent controllers. [ABSTRACT FROM AUTHOR]

We consider the construction of a feedback according to the Kalman algorithm for a continuous nonlinear control system on a finite time interval with control constraints where the right-hand side of the dynamics equations is linear in control and linearizable in the vicinity of the zero equilibrium position. The solution of an auxiliary optimal control problem with a quadratic functional is used for this task by analogy with the SDRE approach. Because this approach is used in the literature to find suboptimal synthesis in optimal control problems with a quadratic functional with formally linear systems where all coefficient matrices in differential equations and criteria can contain state variables, on a finite time interval it becomes necessary to solve a complicated matrix differential Riccati equations with state-dependent coefficient matrices. Due to the nonlinearity of the system this issue significantly increases the number of calculations for obtaining the coefficients of the gain matrix in the feedback and for obtaining synthesis with a given accuracy in comparison with the Kalman algorithm for linear-quadratic problems. The proposed synthesis construction algorithm is constructed using the extension principle proposed by V.F. Krotov and developed by V.I. Gurman and allows one not only to expand the scope of the SDRE approach to nonlinear control problems with control constraints in the form of closed inequalities, but also to propose a more efficient computational algorithm for finding the matrix of feedback gains in control problems on a finite interval. This article establishes the correctness of the application of the extension principle by introducing analogs of the Lagrange multipliers, which depend on the state and time, and also derives a formula for the suboptimal value of the quality criterion. The presented theoretical results are illustrated by calculating suboptimal feedbacks in the problems of managing three-sector economic systems. [ABSTRACT FROM AUTHOR]

A scheme of attitude control based on three-track moving mass-actuated mechanism is proposed for the problem that overcomplicated rotor components and low reliability of the coaxial dual-rotor unmanned aerial vehicle（UAV）. The motion model and the aerodynamic model of the moving mass-actuated ducted coaxial dual-rotor UAV are derived. The dynamic characteristics of moving mass-actuated UAV（MAUAV） with different slider positions and mass ratios are analyzed. The state equation of the attitude control system for MAUAV is established. Aiming at the nonlinearity and uncertainty of the system，the attitude controller based on the backstepping sliding mode control is designed. Simulation results show that the designed controller can effectively complete the attitude tracking task under the condition of external disturbances，and has good anti-interference ability. [ABSTRACT FROM AUTHOR]

In this article, the problem of tracking control for nonlinear system with unknown gain and disturbance is studied. First, to compensate for the adverse effects of disturbance, a disturbance observer via sliding‐mode is designed to estimate the disturbance, and the finite‐time convergence of estimation error is ensured under certain conditions. Then, an event‐triggered neural networks controller based on estimated disturbance is presented to achieve tracking control. Among which, the Nussbaum technique is employed to deal with the unknown gain, and the super‐twisting estimator is introduced to estimate the derivative of virtual control input. Then a time‐varying event‐triggered strategy is designed to reduce communication load. Furthermore, the stability analysis shows that the close‐loop signals are bounded, the tracking error converges to a small compact set, and no Zeno phenomenon occurs. Finally, two examples are provided to illustrate the effectiveness of the proposed new design schemes. [ABSTRACT FROM AUTHOR]

The state-norm estimation problem for the switched nonlinear system under a more generalized type of switching signals is investigated in this paper. The component subsystems consist of input/output-to-state stability (IOSS) and non-IOSS continuous systems simultaneously, whose activation time is lower and upper bounded by mode-dependent time-varying functions, respectively. The considered switching signals satisfy mode-dependent time-varying constraints, whose switching number can grow faster than those with constant average dwell time condition. Then based on multiple IOSS Lyapunov functions method, the existence condition and design method for the switched state-norm estimator are proposed. The obtained results present extensions compared with the existing results, which are applicable for the more general situations. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

A novel technique to building an adaptable fuzzy model predictive control (AFMPC) is suggested in this study, based on the algorithm Particle Swarm Optimization-Cuckoo Search (PSOCS). This technique combines the particle swarm optimization (PSO) algorithm's iterative scheme with the Cuckoo Search (CS) algorithm's searching approach. To identify the system parameters at each time step, an on-line adaptive fuzzy identification is used. Based on a predictive technique, these factors are utilized to generate the goal function. The PSOCS method is then used to solve the optimization issue and select the best control signal. The suggested controller's utility is demonstrated using an experimental communicating three-tank system, in which the proposed approach-based PSOCS algorithm outperforms both the approach-based CS and the approach-based PSO algorithms. • Formulate a PSOCS algorithm and analyzes its performance by numerical computing. • The PSOCS is applied to calculate the predictive control of a nonlinear system. • The PSOCS is able to handle a nonlinear system manipulated under hard constraints. • The WRLS is used to adapt the consequent parameters in a recursive way. [ABSTRACT FROM AUTHOR]

This work investigates the observer-based asynchronous control of discrete-time nonlinear systems with network-induced communication constraints. To avoid the data collisions and side effects in a constrained communication channel, a novel dynamic event-based weighted try-once-discard (DEWTOD) protocol is proposed. In contrast to the existing protocols, the DEWTOD scheduling regulates whether the sampling instant to release and which node to transmit the sampling instant simultaneously. In light of a hidden Markov model, the time-varying detection probability matrix is characterized by a polytopic set. By resorting to the polytopic-structured Lyapunov functional, sufficient conditions are derived such that the closed-loop dynamic is mean-square exponentially stable, and the observer-based controller is designed. In the end, two numerical examples are provided to explicate the validity of the attained methodology. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive fixed-time fault-tolerant control (FTC) problem is investigated for a class of uncertain multi-input multi-output (MIMO) nonlinear systems. By utilizing the radial basis function neural networks (NNs), a state observer is designed to estimate the unmeasured states. Then, an observer-based adaptive fixed-time FTC scheme is proposed, which is capable to deal with the unknown actuator faults, asymmetric time-varying state constraints and input saturation simultaneously. It is shown that the boundedness of all the closed-loop signals can be guaranteed, and system output tracks the desired signal to a bounded compact set in fixed time, while the asymmetric time-varying state constraint requirements are not violated. Moreover, the bound of the settling time is independent of the initial states and related to the designed parameters only. Simulation results on a dynamic mechanical system demonstrate the effectiveness of the proposed FTC scheme. [ABSTRACT FROM AUTHOR]

When high-dimensional chaotic systems are applied to many practical applications, they are required to have robust and complex hyperchaotic behaviors. In this article, we propose a novel $n$ D chaotic system construction method using the Pascal-matrix theory. First, a parametric Pascal matrix is constructed. Then, an $n$ D chaotic system can be generated by using the parametric Pascal matrix as the parameter matrix of the system. Theoretical analysis shows that the generated $n$ D chaotic systems have robust and complex chaotic behaviors, and they become $n$ D Arnold Cat maps by fixing the parameters as some special values. Performance evaluations demonstrate that the $n$ D chaotic systems have more complex chaotic behaviors and better distribution of outputs compared with existing HD chaotic systems. A 4-D Arnold Cat map and a 4-D chaotic map with hyperchaotic behaviors are generated as two examples. The two chaotic maps are then simulated on a microcontroller-based hardware platform and the chaotic sequences are tested to show good randomness. [ABSTRACT FROM AUTHOR]

In this article, an adaptive fuzzy predefined time and accuracy tracking control scheme is proposed for strict-feedback nonlinear systems. A sufficient condition that can be used to determine whether the tracking error converges to a predefined region within a predefined time is first derived based on the definition of predefined time stability. Under the proposed stability criterion, an adaptive fuzzy controller is developed by applying the backstepping technique, and the stability time and convergence accuracy of the tracking error can be set previously, which facilitates the engineering application with requirements for convergence time and accuracy. Especially, to reduce chattering and decrease energy consumptions on the premise of ensuring the stability of the system, an inequality is introduced to construct a continuous term which can replace the sign function. Finally, a practical example is presented to illustrate the feasibility of main results. [ABSTRACT FROM AUTHOR]

This paper considers the parameter identification problems of a Volterra nonlinear system. In order to overcome the excessive calculation amount of the Volterra systems, a hierarchical least squares algorithm is proposed through combining the hierarchical identification principle. The key is to decompose the Volterra systems into three subsystems with a smaller number of parameters and to estimates the parameters of each subsystem, respectively. The calculation analysis indicates that the proposed algorithm has less computational cost than the recursive least squares algorithm. Finally, the simulation results indicate that the proposed algorithm are effective for identifying Volterra systems. [ABSTRACT FROM AUTHOR]

The development of a robust control system for a variable speed wind turbine (VSWT) is presented in this paper. The proposed controller is designed for torque and pitch control of VSWT operation based on the uncertainty estimator and output feedback for the extraction of utmost power from the wind. A suitable reference model has been obtained for smooth tracking of rotor speed and estimating the uncertainty. The simulation study has been made to show the efficacy of the robust controller designed for VSWT. The performance of the proposed controller has been analyzed by a comparative evaluation with the standard controllers of the wind turbines in terms of the degree of rotor speed tracking, elimination of the effect of uncertainties, maximum power extraction, etc. It is found that the performance of the VSWT operation using the proposed control scheme has been improved significantly in comparison to a few existing control schemes. [ABSTRACT FROM AUTHOR]

Abstract It is a difficult task to root the cause of the failure of a gas face seal because different causes may result in similar observations. In the work being presented, the discrimination of multiple types of abnormities in a spiral groove gas face seal is studied. A dynamic model is employed to analyze groups of cases in order to uncover the dynamic behaviors when the face contact is induced by different mixtures of abnormities, whose discriminative features when motion and contact are monitored are studied and uncovered. A circumferential-pattern-related oscillation phenomenon is discovered, which is extracted from contact information and implies the relative magnitude of the moment on stator and the rotor tilt. The experimental observation shows consistent results. It means that the grooves (or other circumferential patterns) generate useful informative features for monitoring. These results provide guidance for designing a monitored gas face seal system.