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Copyright of Journal of Graduate School of Natural & Applied Sciences of Mehmet Akif Ersoy University / Mehmet Akif Ersoy Üniversitesi Fen Bilimleri Enstitüsü Dergisi is the property of Burdur Mehmet Akif Ersoy University 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 work develops a transfer learning (TL) framework for modeling and predictive control of nonlinear systems using recurrent neural networks (RNNs) with the knowledge obtained in modeling one process transferred to another. Specifically, transfer learning uses a pretrained model developed based on a source domain as the starting point, and adapts the model to a target process with similar configurations. The generalization error for TL‐based RNN (TL‐RNN) is first derived to demonstrate the generalization capability on the target process. The theoretical error bound that depends on model capacity and the discrepancy between source and target domains is then utilized to guide the development of pretrained models for improved model transferability. Subsequently, the TL‐RNN model is utilized as the prediction model in model predictive controller (MPC) for the target process. Finally, the simulation study of chemical reactors via Aspen Plus Dynamics is used to demonstrate the benefits of transfer learning. [ABSTRACT FROM AUTHOR]

The purpose of this work is to provide a novel approach for studying the chaos control of hybrid nanoparticles in a porous medium under feedback control and quasiperiodic gravity sinusoidal modulation. We use the powerful tool of Fourier modes to convert the governing flow model PDEs into ordinary ones. Under the combined effect, the properties of hybrid nanofluids a silver–magnesium oxide/water can be used to suppress heat transfer in a variety of industrial applications, i.e., cooling nuclear components. Numerical data comparison with the results presented in the previous literature shows a significant agreement with the present study. On the basis of nonlinear control theory and chaotic dynamics, the equilibrium points of the system are analyzed along with the local stability. As part of the article, different aspects of hybrid nanofluids (Ag–MgO/ H 2 O ) stability are discussed, starting from the preliminary stages to the practical application of hybrid nanofluids. It has been specifically focused on preventing nonlinear conditions from being aggravated by hybrid nanofluids. A pitchfork and inverted bifurcation can occur at various control gain and frequency or amplitude parameters. As a consequence of chaos, the paper proposes the implications of feedback control combined with quasi-gravity modulation to effectively control the chaotic system. [ABSTRACT FROM AUTHOR]

Formal power series products appear in nonlinear control theory when systems modeled by Chen–Fliess series are interconnected to form new systems. In fields like adaptive control and learning systems, the coefficients of these formal power series are estimated sequentially with real-time data. The main goal is to prove the continuity and analyticity of such products with respect to several natural (locally convex) topologies on spaces of locally convergent formal power series in order to establish foundational properties behind these technologies. In addition, it is shown that a transformation group central to describing the output feedback connection is in fact an analytic Lie group in this setting with certain regularity properties. [ABSTRACT FROM AUTHOR]

We propose a design of data-driven Model Predictive Control (MPC) using a suboptimal trajectory and the linear time-varying (LTV) models from data-driven trajectory optimisation that achieves offset-free tracking. Data-driven constrained differential dynamic programming (CDDP) is exploited to improve the trajectory iteratively without the knowledge of the nonlinear model. A trajectory is divided to the transient and steady state regions, controlled by the Linear time-varying MPC (LTVMPC) and the offset-free linear MPC (LMPC), respectively. We prove the feasibility of the proposed LTVMPC in the transient region, and the offset-free tracking property of LMPC. The proposed scheme is validated to a continuous stirred tank reactor (CSTR) process. Simulation studies show that the suboptimal trajectory and LTV models are generated by CDDP, and the proposed MPC achieves offset-free tracking and disturbance rejection for a set of initial conditions and set points in the operating region. [ABSTRACT FROM AUTHOR]

This works aims to develop a new and improved GWO (Grey Wolf Optimizer), the so-called Robotic GWO (RGWO). First, to improve GWO's update formula position with an optimal learning strategy, we adapt the algorithm to real mobile environments, including robots, so that tracking robots can move prey toward targets. Then, the nonlinear active suspension (AS) control system is linearized by a neural network (NN) based linear differential inclusion (LDI) using feedback and feedforward linearization. In theory, it is found that the general SM (Sliding Mode) optimal control cannot provide sudden optimal results for the active linearized suspension system, so a method is proposed to improve the shortcomings of the active linearized suspension system. By constructing an extended SM-optimal manifold function, an improved SM-optimal controller is designed, which incorporates information on the entire structure and the expected performance of the suspension. For comparison purposes, the performance of three kinds of controls: SM optimal refinement control, logic-fuzzy SM control, and PS (passive suspension), shows the proposed controller's advantages . Finally, our improved SM optimal control for nonlinear AS systems, in general, can achieve the actual nominal optimal suspension performance, as confirmed by the simulation results. The results also show that the improved SM optimal control method provides better robustness even when the operating conditions or parameters of the structure vary. [ABSTRACT FROM AUTHOR]

This paper focuses on the implementation of a nonlinear control technique called control by state feedback for regulating the speed of a three-phase asynchronous motor. The unique aspect of this approach is the utilization of nonlinear state feedback, resulting in an interconnected mathematical structure. The main advantage of this control technique is its ability to ensure robustness against abrupt parametric variations in the motor, particularly during full load or prolonged traction tasks. To demonstrate the effectiveness of the proposed control, a series of simulations were conducted using the MATLAB-SIMULINK environment. These simulations highlighted the robustness, stability, and reliability of the control strategy. Overall, the study showcases the application of nonlinear control by state feedback as a viable solution for controlling the speed of three-phase asynchronous motors, offering enhanced resilience in the face of varying operational conditions. [ABSTRACT FROM AUTHOR]

The inverted pendulum is controlled in this article by using the nonlinear control theory. From classical analytical mechanics, its substructure equation of motion is derived. Because of the inclusion of the restoring forces, the Taylor expansion is employed to facilitate the analysis. An estimated satisfactory periodic solution is obtained with the aid of the modified Homotopy perturbation method. A numerical technique based on the fourth-order Runge–Kutta method is employed to justify the previous solution. On the other hand, a positive position feedback control is developed to dampen the vibrations of an IP system subjected to multi-excitation forces. The multiple time scale perturbation technique of the second order is introduced as a mathematical method to solve a two-degree-of-freedom system that simulates the IP with the PPF at primary and 1:1 internal resonance. The stability of these solutions is checked with the aid of the Routh–Hurwitz criterion. A set of graphs, based on the frequency response equations resulting from the MSPT method, is incorporated. Additionally, a numerical simulation is set up with RK-4 to confirm the overall controlled performance of the studied model. The quality of the solution is confirmed by the match between the approximate solution and the numerical simulation. Numerous other nonlinear systems can be controlled using the provided control method. Illustrations are offered that pertain to implications in design and pedagogy. The linearized stability of IP near the fixed points as well as the phase portraits is depicted for the autonomous and non-autonomous cases. Because of the static stability of the IP, it is found that its instability can be suppressed by the increase of both the generalized force as well as the torsional constant stiffness of the spring. Additionally, the presence of the magnetic field enhances the stability of IP. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization of nonlinear systems with external disturbances, which are both bounded and unbounded. Firstly, the stabilization problem of the nominal nonlinear system is realized, and the corresponding stabilization controllers are designed. Then, three suitable filters are proposed and applied to asymptotically estimate the corresponding disturbances, and the disturbance estimators are presented and used to exactly eliminate the corresponding disturbances. Then, the disturbance estimator (DE)-based controllers are proposed to stabilize such nonlinear systems. It should be pointed out the unbounded disturbances are exactly estimated by suitable filters, which has advantages over the existing results. Finally, two illustrative examples, which have certain symmetrical properties, are taken, and the related numerical simulations are carried out to verify the effectiveness and correctness of the proposed results. [ABSTRACT FROM AUTHOR]

Wind speed measurement depends on the efficiency of the anemometer sensors. In fact, the anemometer wind speed sensors, mounted on top of the wind turbine nacelle, give the wind speed measurements to the controller devices. These measurements obtained from the anemometers represent the turbulent wind speed and cannot represent the wind speed upstream of the rotor blades. For that, Effective Wind Speed (EWS) will be estimated by applying linear and nonlinear Kalman Filter methods to Wind Turbines System (WTS). In this study, the variable wind speed is computed numerically based on the estimation values obtained from the linear KF, while it is directly estimated from the nonlinear KF. Furthermore, Backward Euler Approximation is used to perform the discretization of the continuous-time state space model of WTS based on KF estimators. In this paper, the efficiency of each filter is investigated on a wind turbine using a two-mass drive train interconnected by a common spring and damper. The comparative studies show that the two estimators have high accuracy estimates at the steady-state with greater than 95% similarity between the estimated and measured wind speeds. However, the nonlinear KF has better performance than linear KF at the transient-state due to its very small time response. These results achieved are justified by computing the covariance and the Correlation Coefficient (CC) between the measured and estimated wind speeds for each 5 ms. The covariance curves obtained are positive, while the CC curves are close to one at the steady-state for both estimators. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered dynamic surface controller is proposed for strict-feedback nonlinear networked systems with mismatched uncertainties. Towards this aim and first of all, an event-based dynamic surface control law is designed. Then, the closed-loop error dynamics is derived and rewritten as a linear dynamics with nonlinear perturbation terms. Next, these terms are classified into vanishing and nonvanishing perturbations. Finally, by imposing some constraints on the nonvanishing terms, an event-triggering mechanism is constructed. By formulating the imposed constraints in the form of linear matrix inequalities (LMIs) and using the ultimate boundedness theory, the ultimate error boundedness and quadratic tracking objectives are addressed in the framework of convex optimisation. The absence of the Zeno behaviour, which is an important feature of any event-triggered methodology, is also proven. The validity of the theoretical results is illustrated by applying the proposed method to a remotely operated underwater vehicle in a simulation study as well as an experimental implementation on a magnetic levitation system. [ABSTRACT FROM AUTHOR]

In this paper, passivity is used to investigate the formation control problem for second-order multi-agent systems (MASs) with linear or nonlinear coupling. Firstly, the passivity of a single agent is studied by selecting appropriate adaptive state feedback controllers. Moreover, in order to ensure that MASs with nonlinear intrinsic dynamics and linear/nonlinear coupling can converge to a predefined formation, some appropriate control schemes are designed based on the passivity of a single agent. In addition, the passivity-based formation problem for the MASs with double-integrator dynamics is also studied. Finally, the effectiveness of the proposed formation control strategies is demonstrated through two numerical examples. [ABSTRACT FROM AUTHOR]

In this work, a novel nonlinear control theory design for first-order systems is developed, contributing to the improvement of the existing theory. The theory will allow a design of the open loop and closed-loop controllers that ensure the tracking of any reference, constant, or variant in time with a free initial condition where the Laplace transform was used to find all the analytical solutions, avoiding the transfer function theory. Moreover, the closed-loop control will be the best option to speed up or slow down the reference convergence rate in the desired finite time. Then, an algorithm indicating the steps for designing a closed-loop controller and achieving proper tuning for a real-time application is shown. Finally, this manuscript presents the results and discussions of the theory implemented in a prototype tank of a liquid temperature control system, where the effectiveness of the applied temperature control can be seen. [ABSTRACT FROM AUTHOR]

The shaking table has been used extensively in the structure test field to verify the structure's performance against various vibrations, for example earthquakes. In order to replicate the vibrations, which are measured by the acceleration signal, the model of the shaking table should be thoroughly constructed to design the controller. However, parametric uncertainty and strong nonlinearity, such as the nonlinear friction, make it an obstacle to obtaining an accurate model. A neural network‐based controller, specifically a long short‐term memory neural network‐based neural network controller, is designed in this paper to address this issue. The nonlinear systems are estimated by the neural network's universal approximation characteristics, and a long short‐term memory neural network is utilized to optimize the time‐series‐related errors. Furthermore, a robust sliding mode controller is utilized to compensate for the residual error of the neural network and other uncertainties. The semi‐global asymptotic stability of the controller is proved by Lyapunov analysis. Comparative experimental results indicate the superiority of the proposed controller. [ABSTRACT FROM AUTHOR]

In this study, a fault-tolerant super-twisting sliding mode controller with a control allocation system for a quadrotor aircraft is proposed. Super twisting sliding mode control is a robust control technique that handles a system with a relative degree equal to one. A super-twisting sliding mode controller is proposed because of its robustness to uncertainties and perturbations. It increases accuracy and reduces chattering. A control allocation algorithm is developed to cope with the actuator fault. Firstly, a nonlinear model of the quadrotor unmanned aerial vehicle (UAV) is presented. Then, the controller design and type of the actuator fault are explained. The control allocation algorithm is used to optimize the trajectory tracking performance of the quadrotor in the presence of an actuator fault. A control allocation algorithm is an effective approach to implementing fault-tolerant control. When actuator faults are identified, they can be modeled as changes in the B matrix of constraints. Various simulations have been made for situations with and without actuator failure. In normal conditions, the quadrotor can accurately track altitude, roll, pitch and yaw references. In faulty conditions, the quadrotor can follow the references with a small error. Simulations prove the effectiveness of the control allocation algorithm, which stabilizes the quadrotor in case of an actuator fault. Overall, this paper presents a novel fault-tolerant controller design for quadrotor aircraft that effectively addresses actuator faults using a super-twisting sliding mode controller and control allocation algorithm. [ABSTRACT FROM AUTHOR]

The design of active robust controller based on delay state compensation for a class of flexible air-breathing hypersonic vehicles with input delays is described in this paper. Due to high dynamic characteristics of hypersonic vehicle, the strong uncertainties, high nonlinearity, strong coupling and control input time delays are challenging problems in the design of its control system. Therefore, it is necessary to design a control method that can handle input time delays. Finally, in this paper, the mathematical expression of the altitude nonlinear control theory problem of an aircraft with input time delay is given. Secondly, based on the backstepping method, the time delay compensation controller is designed. Thirdly, the backstepping method and dynamic control surface are used to design altitude angle control law. The stability and time delay compensation effect are proved. Finally, simulation results show that the suggested method can improve the stability and disturbance rejection performance for the system effectively, which has certain actual application value. [ABSTRACT FROM AUTHOR]

Chaotic systems arise everywhere in control theory and nonlinear vibration. This paper uses a high-precision numerical approach for capturing chaotic attractors of the fractional EI Ni ñ o chaotic systems. The numerical results indicate that some of the chaotic attractors of fractional-order systems are topologically equivalent to those discovered in the integer-order systems, and some unusual attractors of fractional EI Ni ñ o chaotic systems are found by using the present method. [ABSTRACT FROM AUTHOR]

The dynamics model of the unmanned underwater vehicle (UUV) system is highly nonlinear, multi-degree-of-freedom, strongly coupled, and time-varying. Its motion control has been a complex problem due to the unknown information about and the uncertainty of the working environment. To improve the performance and reliability of UUV trajectory tracking control, a trajectory tracking method based on nonlinear model predictive control is designed, and an improved gray wolf optimization (IGWO) is proposed for the optimization of nonlinear model predictive control. The convergence factor of IGWO is designed as a nonlinear attenuation function, and the memory function is added to the position update equation to enhance the effect of trajectory tracking control. Through the simulation in the ROS environment, the influence of the convergence factor on the convergence rate of trajectory tracking error and tracking control performance is obtained. By comparing the tracking effects of several groups of reference trajectories, it is shown that the proposed method is universally applicable and effective to the trajectory tracking control of UUV. Compared with traditional gray wolf optimization (GWO), SQP, and other optimization algorithms, the reliability of the proposed method for UUV trajectory tracking control is demonstrated. [ABSTRACT FROM AUTHOR]

This paper focuses on the synchronous vibration suppression of an active magnetic bearing (AMB) system without a rotating speed sensor. One of the most intractable problems with AMB systems is the synchronous vibration caused by the mass imbalance of the rotor. Moreover, practically all existing unbalance control algorithms require the rotating speed sensor to determine rotation speed. However, in some unique applications, it is impossible to install and use the rotating speed sensor as intended. This study provided a nonlinear adaptive control (NAC) algorithm and a modified frequency estimator to address the above issues. The proposed approach can suppress current and displacement vibrations by regulating the control structure. The frequency estimator calculates the rotating speed based on the position of the rotor at different moments, which has a quick response time, high precision, and effective tracking. The NAC algorithm can achieve unbalanced control based on the period iteration strategy. Additionally, the Lyapunov method is used to demonstrate the stability of the NAC algorithm. Finally, the experimental and simulation results also confirm the effectiveness and reliability of the overall control scheme. The results from simulations and experiments indicate that the novel frequency estimator can track the speed accurately and that its error can be regulated to within ± 0.05 Hz. The overall control schema can reduce the displacement vibration's amplitude by 72.2% and the current vibration's amplitude by 65.6%. [ABSTRACT FROM AUTHOR]

35458980 5 Tian L., Zhang Z., Zheng C., Tian Y., Zhao Y., Wang Z., Qin Y. An Improved Rapidly-Exploring Random Trees Algorithm Combining Parent Point Priority Determination Strategy and Real-Time Optimization Strategy for Path Planning. HT

In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed in general. Additionally, we also apply the aforementioned main inequality in order to investigate the null controllability of two nonlinear parabolic systems. The first application is concerned a global null controllability result obtained for some semilinear equations, relying on a fixed point argument. In the second one, a local null controllability for some equations with nonlocal terms is also achieved, by using an inverse function theorem. [ABSTRACT FROM AUTHOR]

In this research, a new method named d to solve non-linear constrained and un constrained optimal control problems for trajectory optimization was proposed. The main objective of this method was defined as solving optimal control problems by the combination of the orthogonal functions, the heuristic optimization techniques, and the principles of optimal control theory. Three orthogonal functions Fourier, Chebyshev, and Legendre were considered to approximate the control variables. Also, GA-PSO and imperialist competition algorithms were considered as heuristic optimization techniques. Moreover, the motivation of the mentioned method belonged to a novel combination of zero Hamiltonian in the optimal control theory, optimality conditions, and newly proposed criteria. Furthermore, lunar landing, asteroid rendezvous, and low-thrust orbital transfer with respect to minimumtime and minimum-fuel criteria were investigated to show the ability of the proposed method in regard to constrained and un constrained optimal control problems. Results demonstrated that the d method has high accuracy in the optimal control theory for non-linear problems. Hence, the d method allows space trajectory and mission designers to solve optimal control problems with a simple and precise method for future works and studies. [ABSTRACT FROM AUTHOR]

In this paper, the problem of simultaneous stabilization of a collection of nonlinear systems is proposed by using the Takagi-Sugeno (TS) fuzzy modeling and synthesis approach. In practice, due to the uncertainty in the system model, failure modes, or different operating points, we often encounter the problem of simultaneous stabilization. The TS fuzzy model has been considered for the controller design of complex nonlinear systems as it provides a simple and effective concept. This problem refers to the stabilization of some nonlinear systems by utilizing a single nonlinear controller. Both state feedback and output feedback controllers are designed based on the PDC concept and by solving some linear matrix inequalities (LMIs). Moreover, to reduce the conservatisms related to using the common Lyapunov function and restrictive equality conditions in the design method, Finsler's lemma has been employed. Finally, three numerical examples are provided to show that the proposed controllers stabilize well-considered nonlinear systems. [ABSTRACT FROM AUTHOR]

In this article, committed to extending the robust integral of the sign of the error (RISE) feedback control to the working condition of output feedback, a novel output feedback controller with a continuously bounded control input which combines the adaptive control and integral robust feedback will be proposed for trajectory tracking of a family of nonlinear systems subject to modeling uncertainties. A novel adaptive state observer (ASO) with disturbance rejection performance is creatively constructed to derive real‐time estimation of the unmeasured state signals. Moreover, a projection‐type adaption law is integrated to handle parameter uncertainties and an integral robust term is employed to deal with external disturbances. It is shown that asymptotic estimation performance and meanwhile asymptotic tracking result can eventually be derived. Simulation validations are implemented to demonstrate the high tracking performance of the presented controller. Notably, the synthesized control algorithm can be readily extended to the Euler–Lagrange systems. Typically, it can be extended to practical electromechanical equipment such as three‐dimensional vector forming robots to improve the real‐time forming accuracy. [ABSTRACT FROM AUTHOR]

This work investigates simultaneous prescribed performance tracking control and mismatched disturbance rejection problems for a class of strict‐feedback nonlinear systems. A novel control scheme combining prescribed performance control, disturbance observer technique, and backstepping method is proposed. The disturbance estimations are introduced into the design of virtual control law design in each step to compensate the mismatched disturbances. To further improve the control performance, a prescribed performance function characterizing the error convergence rate, maximum overshoot, and steady‐state error is used to construct the composite controller. The proposed controller guarantees transient and steady‐state performance specifications of tracking error and provides much better disturbance attenuation ability simultaneously. Rigorous stability analysis for the closed‐loop system is established by direct Lyapunov function method. It is shown that all the states in the resulting closed‐loop system are stable, and the tracking error evolves within the prescribed performance boundaries and asymptotically converges to zero even in the presence of mismatched external disturbances. Finally, theoretical results are illustrated and demonstrated by two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, a new strategy for developing effective control policies suitable for guiding the motion of articulated mechanical systems that are described within the framework of multibody system dynamics is proposed. In particular, a scissor lift table having a pantograph topology is analytically modeled as a rigid multibody system by using a Lagrangian formulation. An operational approach is thus introduced in this investigation to design the control system that commands the motion of the lift table. In this vein, two dynamical models are developed in this investigation, namely a minimal coordinate multibody model and a redundant coordinate multibody model. While the minimal coordinate multibody model is used in the paper for the proper design of a high-performing nonlinear controller, the redundant coordinate multibody model is employed to verify both the efficiency and the effectiveness of the control approach adopted in this work, as well as for the refinement of the feedback controller parameters. More specifically, the nonlinear control system devised in this paper is based on the combination of an open-loop control architecture with a closed-loop control strategy. The open-loop control policy is determined by using a nonlinear quasi-static feedforward controller, whereas the closed-loop control action is obtained considering an error-based proportional-derivative feedback controller. With the use of the analytical models of the pantograph scissor lift system developed in this work, several numerical experiments were carried out by employing three multibody programs based on the computational environments relying on MATLAB and SIMSCAPE MULTIBODY, thereby demonstrating the readiness and the effectiveness of the control methodology proposed in this investigation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the convolution closure problem for the class of strong subexponential distributions, denoted as ... are equivalent. Then, using examples constructed by Klüppelberg and Villasenor [The full solution of the convolution closure problem for convolution-equivalent distributions, J. Math. Anal. Appl., 41:79-92, 1991], we show that S-is not closed under convolution. [ABSTRACT FROM AUTHOR]

This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound the range of the nonlinear function and associates with each vertex an auxiliary linear system. Provided controls associated with the linear systems can be generated to satisfy an ordering constraint, the nonlinear control is computable by the interpolation of controls obtained by convex optimization. This theoretical result leads to two numerical approaches for solving the nonlinear constrained problem: one requires solving a single convex optimization problem and the other requires solving a sequence of convex optimization problems. The approaches are applied to two practical problems in aerospace engineering: a constrained relative orbital motion problem and an attitude control problem. The solve times for both problems and approaches are on the order of seconds. It is concluded that these techniques are rigorous and of practical use in solving nonlinear trajectory design and control problems. [ABSTRACT FROM AUTHOR]

A continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein's model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem. [ABSTRACT FROM AUTHOR]

This paper is devoted to design an event-triggered data-driven control for a class of disturbed nonlinear systems with quantized input. A uniform quantizer reconstructed with decreasing quantization intervals is employed to reduce the quantization error. A neural network-based estimation strategy is proposed to estimate both the pseudo partial derivative and disturbances. Consequently, an input triggering rule for single-input single-output systems is provided by incorporating the estimated disturbances, the quantization error bound and tracking errors. Resorting to the Lyapunov method, sufficient conditions for synthesized error systems to be uniformly ultimately bounded are presented. The validity of the proposed scheme is demonstrated via a simulation example. [ABSTRACT FROM AUTHOR]

The outcome of this paper is to suggest an efficient energy-management strategy (EMS) for a direct-current (DC) microgrid (MG). The typical MG is composed of two renewable energy sources [photovoltaic (PV) systems and fuel cells (FCs)] and two energy-storage elements (lithium-ion battery and supercapacitor). An EMS was proposed to ensure optimal bus voltage with a power-sharing arrangement between the load and the sources. As a result, in the suggested DC MG, non-linear flatness control theory was used instead of the traditional proportional-integral control approach. The suggested EMS is intended to supply high power quality to the load under varying load conditions with fluctuating solar irradiation while considering the FC status. To validate and prove the effectiveness of the proposed EMS, a MATLAB® environment was used. In addition, the output power of the PV system was maximized using the particle swarm optimization algorithm as a maximum power point tracking (MPPT) technique to track the MPP of the 3000-W PV system under different irradiance conditions. The results show that the suggested EMS delivers a stable and smooth DC bus voltage with minimum overshoot value (0.1%) and improved ripple content (0.1%). As a result, the performance of the DC MG was enhanced by employing the flatness control theory, which provides higher power quality by stabilizing the bus voltage. [ABSTRACT FROM AUTHOR]

The present document outlines a non-linear control theory, based on the PID regulation scheme, to synchronize two second-order dynamical systems insisting on a Riemannian manifold. The devised extended PID scheme, referred to as M-PID, includes an unconventional component, termed 'canceling component', whose purpose is to cancel the natural dynamics of a system and to replace it with a desired dynamics. In addition, this document presents numerical recipes to implement such systems, as well as the devised control scheme, on a computing platform and a large number of numerical simulation results focused on the synchronization of Duffing-like non-linear oscillators on the unit sphere. Detailed numerical evaluations show that the canceling contribution of the M-PID control scheme is not critical to the synchronization of two oscillators, however, it possesses the beneficial effect of speeding up their synchronization. Simulation results obtained in non-ideal conditions, namely in the presence of additive disturbances and delays, reveal that the devised synchronization scheme is robust against high-frequency additive disturbances as well as against observation delays. [ABSTRACT FROM AUTHOR]

A new method is presented for evaluating the performance of a nonlinear control allocation system within a linear control loop. To that end, a worst‐case gain analysis problem is formulated that can be readily solved by means of well‐established methods from robustness analysis using integral quadratic constraints (IQCs). It exploits the fact that control allocation systems are in general memoryless mappings that can be bounded by IQCs. A data‐driven approach is used to find an optimal bound of the input/output mapping of the control allocation. Additionally, an iterative procedure based on local IQCs is introduced to determine meaningful sampling limits for less conservative yet accurate results. The effectiveness of the proposed data‐driven performance analysis is shown at the example of an actively controlled flexible wing in a wind tunnel. [ABSTRACT FROM AUTHOR]

Persistence, excitability and stability properties are considered for a class of nonlinear, forced, positive discrete-time systems with delays. As will be illustrated, these equations arise in a number of biological and ecological contexts. Novel sufficient conditions for persistence, excitability and stability are presented. Further, similarities and differences between the delayed equations considered presently and their corresponding undelayed versions are explored, and some striking differences are noted. It is shown that recent results for a corresponding class of positive, nonlinear delay-differential (continuous-time) systems do not carry over to the discrete-time setting. Detailed discussion of three examples from population dynamics is provided. • Qualitative properties of nonlinear delayed difference equations are studied. • The class of equations considered find relevance in mathematical biology/ecology. • Conditions for boundedness, persistence, excitability, stability are provided. • Striking differences between previous works are observed and described. • Our rigorous results use tools from positive systems and nonlinear control theory. [ABSTRACT FROM AUTHOR]

In this article, we address the problem of asymptotic output tracking control with prescribed transient performance for a class of nonlinear systems in the presence of unknown dynamics. By fusing the funnel control approach and the tool of barrier Lyapunov function, a smooth adaptive tracking control strategy is developed in a recursive manner. In the proposed design, a new barrier Lyapunov function is adopted to eliminate the effects of unknown nonlinear dynamics, ensuring the prescribed transient behavior of the output tracking. The distinctive characteristic of the proposed method is that the designed control algorithm can guarantee not only prescribed output tracking performance but also global asymptotic stability without incorporating any prior knowledge of nonlinear dynamics or even corresponding bounding functions. Three illustrative examples are provided to testify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This work presents a nonlinear model predictive control scheme with a novel structure of observers aiming to create a methodology that allows feasible implementations in industrial anaerobic reactors. In this way, a new step-by-step procedure scheme has been proposed and tested by solving two specific drawbacks reported in the literature responsible for the inefficiencies of those systems in real environments. Firstly, the implementation of control structures based on modeling depends on microorganisms' concentration measurements; the technology that achieves this is not cost-effective nor viable. Secondly, the reaction rates cannot be considered static because, in the extended anaerobic digestion model (EAM2), the large fluctuation of parameters is unavoidable. To face these two drawbacks, the concentration of acidogens and methanogens, and the values of the two reaction rates considered have been estimated by a structure of two observers using data collected by sensors. After 90 days of operation, the error in convergence was lower than 5% for both observers. Four model predictive controller (MPC) configurations are used to test all the previous information trying to maximize the volume of methane and demonstrate a satisfactory operation in a wide range of scenarios. The results demonstrate an increase in efficiency, ranging from 17.4% to 24.4%, using as a reference an open loop configuration. Finally, the operational robustness of the MPC is compared with simulations performed by traditional alternatives used in industry, the proportional-integral-derivative (PID) controllers, where some simple operational scenarios to manage for an MPC are longer sufficient to disrupt a normal operation in a PID controller. For this controller, the simulation shows an error close to the 100% of the reference value. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system. [ABSTRACT FROM AUTHOR]

We solve the Kapitza pendulum equation analytically and numerically. In the latter solution, we use the fourth-order Runge-Kutta (RK4) numerical method. The proposed methodology is beneficial in the study of nonlinear phenomena and control theory. [ABSTRACT FROM AUTHOR]

Flight control design of unmanned aerial vehicles UAVs is becoming increasingly important due to advances in computational power of computers with lower cost. The control algorithms are mainly employed for the attitude and position control of the UAVs. In the past decades, quadrotors have become the most popular UAVs, their adaptability and small size. They are employed to carry out tasks such as delivery, exploration, fumigation, mapping, surveillance, rescue mission, traffic monitoring, and so on. While carrying out these tasks, quadrotor UAVs face various challenges, such as environmental disturbances, obstacles, and parametric and non-parametric perturbations. Therefore, they require robust and effective control to stabilize them and enhance their performance. This paper provides a survey of recent developments in control algorithms applied to attitude and position loops of quadrotor UAVs. In addition, the limitations of the previous control approaches are presented. In order to overcome the relative drawbacks of the previous control techniques and enhance the performance of the quadrotor, researchers are combining various control approaches to obtain the hybrid control architecture. In this study, a review of the recent hybrid control schemes is presented. [ABSTRACT FROM AUTHOR]

This article is dedicated to studying realization issues of the stability performance-based nonlinear fault-tolerant control framework via Takagi–Sugeno (T–S)fuzzy models. To this end, the nonlinear fault-tolerant control strategy with an online fault detection system monitoring the system stability performance degradation induced by faults is first introduced by means of the stable image and kernel representations. On this basis, the T–S fuzzy models are applied to approximate the nonlinear system, and a design approach of the fuzzy observer-based controller is proposed for the system stabilization via the iterative linear matrix inequality method. With the controller gains, the fuzzy-model-based nominal stable image representation of the system is formulated, which leads to the generation of the input and output error signals. Then, with the reference signal and system input and output error signal data, a data-driven algorithm is given to online estimate the evaluation function defined in terms of system uncertainties and faults. By virtue of the $L_{2}$ input–output stability of the controller stable kernel representation, a threshold calculation method is presented and, thus, the stability performance-based fault detection system based on fuzzy models is realized. Furthermore, for fault-tolerant purpose, the fault-tolerant controller design is discussed, which aims to retain the system stability. Two examples are provided in the end to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

This paper deals with an approach to study nonlinear chatter analysis, which is based on the synthesis of linear theory for different turning conditions. Mainly, contact nonlinearities play a crucial role in the behavior of the machine tool and the stability of turning operation. However, the analysis of nonlinear systems is challenging because nonlinear system analyzes are often limited to a linearized solution, which may be insufficient to reveal the stability lobe diagram. The presented study proposes a theoretical approach which is based on a synthesis of linearization in the operating point. This approach provides several solutions of stability lobe diagrams which are strongly depending on the loading conditions of the nonlinear system and all solutions are integrated to the final stability lobe diagram. The presented method is applied to a simplified 2D structure between two supports with nonlinear contact stiffness. Resulted analysis of the lobe diagram are compared with results of the time-domine simulations and it shows a good match. This paper shows that the presented approach offers an effective solution for refining the stability estimate for nonlinear mechanical systems. [ABSTRACT FROM AUTHOR]

The conventional method for finding the location of turn-to-turn stator fault on the stator winding of the induction motor is spectral analysis. Using the harmonics method, the current spectrum can show the location of the fault. In this paper, it is shown that the chaos phenomenon could occur when fault arises on the motor. The spectrum of chaotic system has a wide range of harmonics. Consequently, spectral analysis is confused in this state. For this reason, first inductances of an induction machine with a turn-to-turn fault in stator winding are determined by the winding function theory. Using the nonlinear control theory, a first-order Poincare's map of the induction machine is computed and a new extended Poincare's map is drawn for the induction machines. In addition, the characteristic multipliers and the largest Poincare's exponents are calculated with this map. The new map is capable of modeling electrical machines in nonlinear and unbalanced cases for stability, bifurcation, and chaos analysis. The characteristic multiplier and Poincare's exponents of the extended map show the condition of a system. Chaos phenomena are observable in the condition of machines with a fault. In such cases, spectral analysis shows that the machine's current spectrum is varied in each period by a continuous spectrum of chaotic systems; consequently, identification of the location of an internal fault is not easily possible with conventional methods such as the Fourier spectrum or harmonics identification on a machine's terminal current. The experimental results supported the chaotic manner of the faulty induction motor. [ABSTRACT FROM AUTHOR]