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Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the global minima of the cost function describing the coupled oscillator system and the ground state of the Ising Hamiltonian. However, the properties of the oscillator Ising machine (OIM) from a nonlinear control viewpoint, such as the stability of the OIM solutions, remain unexplored. Therefore, in this work, using nonlinear control-theoretic analysis, we (i) identify the conditions required to ensure the functionality of the coupled oscillators as an Ising machine, (ii) show that all globally optimal phase configurations may not always be stable, resulting in some configurations being more favored over others and, thus, creating a biased OIM, and (iii) elucidate the impact of the stability of locally optimal phase configurations on the quality of the solution computed by the system. Our work, fostered through the unique convergence between nonlinear control theory and analog systems for computing, provides a new toolbox for the design and implementation of dynamical system-based computing platforms. [ABSTRACT FROM AUTHOR]

In response to the challenges posed by large-scale, uncoordinated electric vehicle charging on the power grid, Vehicle-to-Grid (V2G) technology has been developed. This technology seeks to synchronize electric vehicles with the power grid, improving the stability of their connections and fostering positive energy exchanges between them. The key component for implementing V2G technology is the bidirectional AC/DC converter. This study concentrates on the non-isolated bidirectional AC/DC converter, providing a detailed analysis of its two-stage operation and creating a mathematical model. A dual closed-loop control structure for voltage and current is designed based on nonlinear control theory, along with a constant current charge–discharge control strategy. Furthermore, midpoint potential balance is achieved through zero-sequence voltage injection control, and power signals for the switching devices are generated using Space Vector Pulse Width Modulation (SVPWM) technology. A simulation model of the V2G system is then constructed in MATLAB/Simulink for analysis and validation. The findings demonstrate that the control strategy proposed in this paper improves the system's robustness, dynamic performance, and resistance to interference, thus reducing the effects of large-scale, uncoordinated electric vehicle charging on the power grid. [ABSTRACT FROM AUTHOR]

Nonlinear control theory applied to unmanned aeronautical vehicles is an engineering topic that has received higher and higher popularity during the last decade. Model-based control approaches have shown increased performance in flight control accuracy and robustness compared to model-free proposals based on parameter adaptation and estimation. However, model-based structures need more computational efforts in terms of spatial and temporal variables. To avoid these constraints, the latest drone flight controls are based on quaternion models, ensuring more advanced computational performances. To this aim, this paper deals with a flight control algorithm of a quadrotor, in which the mathematics model of the plant is defined in terms of quaternions. Additionally, when aerial vehicles are used in specific applications such as slung load transportation and agriculture fields, among others, the variation of the mass receives high importance since it could make the entire system unstable. In the same line of ideas, this paper presents a H ∞ strategy, combined with a Super-Twisting Sliding-Mode Control, ensuring the control objective of the mass variations identification, and trajectory tracking, to be solved. The stability analysis of the proposed control approach is also discussed, and the quality and performances of the presented control strategy are tested by simulations, in an interesting case in which mass variations and external perturbations cannot be negligible. [ABSTRACT FROM AUTHOR]

The article discusses the importance of research in the field of flight dynamics, control, and simulation for advancing aeronautical sciences. It emphasizes the need for a deep understanding of flight dynamics to enhance aircraft performance, safety, and efficiency. The integration of advanced control strategies and the use of simulation play a crucial role in optimizing aircraft behavior and reducing costs. The article also provides an overview of 14 papers published in a special issue of the Aerospace journal, covering various topics such as hybrid electric propulsion, aerodynamic parameter identification, and autonomous flare control. The research presented in the papers contributes to the development of new technologies and innovations in aviation. [Extracted from the article]

This paper analyses the evolution of nonlinear oscillation control methods and presents an innovative approach known as analytical design of aggregated oscillation controllers (ADACO). This method is based on the principles of synergetic control theory and focuses on the integration of selforganization and control processes to synthesize energy-efficient control laws for nonlinear oscillating systems. The authors elaborate on the theoretical foundations of ADACO, which extends the previous analytical design of aggregated controllers (ADAC) method by incorporating energy invariants and integrals of motion into the synthesis of control laws. This approach demonstrates significant advantages over traditional methods, offering a versatile framework for the design of energy-efficient control systems for a wide range of nonlinear oscillating systems in various fields such as aerospace, robotics, vibromechanical systems, and objects with chaotic dynamics. The aim of the paper is to establish a unified approach to the control of nonlinear oscillations, solving both the problems of generation of stable oscillations and suppression of unwanted perturbations. The application of synergetic control principles in the framework of ADACO opens prospects for further development of nonlinear control theory. [ABSTRACT FROM AUTHOR]

Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris–Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of spacing control between adjacent trains in train formation and proposes a distributed train-formation speed-convergence cooperative-control algorithm based on barrier Lyapunov function. Considering practical limitations such as communication distance and bandwidth constraints during operation, not all trains can directly communicate with the leader and obtain the expected trajectory it sends, making it difficult to maintain formation consistency as per the predetermined ideal state. Furthermore, to address the challenge of unknown external disturbances encountered by trains during operation, this paper designs a distributed observer deployed on each train in the formation. This observer can estimate and dynamically compensate for unknown reference trajectories and disturbances solely based on the states of adjacent trains. Additionally, to ensure that the spacing between adjacent trains remains within a predefined range, a safety hard constraint, this paper encodes the spacing hard constraint using barrier Lyapunov function. By integrating nonlinear adaptive control theory to handle model parameter uncertainties, a barrier Lyapunov function-based adaptive control method is proposed, which enables all trains to track the reference trajectory while ensuring that the spacing between them remains within the preset interval, therefore guaranteeing the asymptotic stability of the closed-loop system. Finally, a practical example using data from the Guangzhou Metro Line 22, specifically the route from Shiguang Road Station to Chentougang Station over three stations and two sections, is utilized to validate the effectiveness and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The main objective of this research is to expand right coprime factorization based on operator theory in nonlinear systems. A novel method for right coprime factorization is proposed by introducing an operator that can deform the system's response into an arbitrary shape. This enables the design of control systems that are highly effective against noise. As an application, we use a pneumatic stage. The effectiveness of this method is verified through simulations and real-world experiments. [ABSTRACT FROM AUTHOR]

High-quality identification schemes are essential for controller design of nonlinear systems in the field of automatic control. In control communities, the prescribed performance technology has received wide attention as a promising methodology because of its quantitative description of the steady-state and transient performance of system control over the past several years. The improved transient performance of the parameter estimation is widely known to enable simplified controller design, reduce system regulation time, and prevent system divergence. However, in system identification communities, few studies on the transient performance of parameter identification have been published because of the difficulties in designing an error variable that reflects the transient performance of parameter identification. To address this problem, this study provides a solution by integrating the prescribed performance technique into the estimator design. In this study, we introduced an adaptively prescribed performance parameter identification for nonlinear sandwich systems subjected to quantitative observations. First, a low-pass filter and forcing variables are developed to construct an identification error expression. Subsequently, an improved prescribed performance function that characterises the error bound of parameter estimation is introduced. Second, the error transformation concept is used to obtain a new system by transforming the raw system such that constraint conditions are avoided. A novel adaptive law is proposed to guarantee original parameter identification using the prescribed performance. Finally, simulation and process examples are presented to illustrate finding results. [ABSTRACT FROM AUTHOR]

Fuzzy-based control systems have demonstrated a remarkable ability to control nonlinear processes, a characteristic commonly observed in power systems, particularly in the context of power quality enhancement. Despite this, an updated and comprehensive literature review on the applications of fuzzy logic in the domain of power quality control has been lacking. To address this gap, this study critically examines published research on the effective and efficient use of fuzzy logic in resolving quality issues within power systems. Data sources included the Web of Science and academic journal databases, followed by an evaluation of target articles based on predefined criteria. The information was then classified into seven categories, including control system type, features of the fuzzy logic controller, fuzzy logic inference strategy, power quality issue, control device, implementation methodology (efficacy testing), and efficiency improvement. Our study revealed that fuzzy-based control systems have evolved from simple type-1 fuzzy controllers to advanced control systems (type-2 fuzzy and hybrid) capable of effectively addressing complex power quality issues. We believe that the insights gained from this study will be useful to both experienced and inexperienced researchers and industry engineers seeking to leverage fuzzy logic to enhance power quality control. [ABSTRACT FROM AUTHOR]

This study numerically investigates mixed convective cooling in a two‐dimensional horizontal channel containing periodically heated blocks by applying proportional (P), proportional‐integral (PI), and proportional‐integral‐derivative (PID) controllers. Three different controller configurations regulate the amount of cold air entering the chamber. The air's non‐dimensional temperature is continuously monitored at the set point to compare the controllers' performance, and the percentage of overshoot and the steady‐state error are analysed. The investigated chamber comprises one inlet and two exit ports, a temperature sensor, and two heated blocks that are isotherm heat sources. The Galerkin finite element approach computationally solves the equations of continuity, momentum, and energy to analyse the thermo‐fluid phenomena occurring within the chamber. Parametric simulation is carried for different values of the proportional gain (Kp = 0.005, 0.010, 0.050 m s−1 K−1), the integral gain (Ki = 0.05, 0.10, 0.15 m s−2 K−1), the derivative gain (Kd = 10−5, 10−4, 10−3 m K−1) to achieve a consistent and expeditious response. Variations of Reynolds, Richardson, and mean Nusselt numbers with time are plotted to compare the system's performance. The investigation indicates that the PI controller produces a comparable level of performance with the PID controller, reducing the necessity to add a derivative controller. [ABSTRACT FROM AUTHOR]

This paper studies a class of input-saturated nonlinear systems with Lipschitz condition. We combine the fully actuated system approach with anti-windup control to design control system. The proposed control method has the advantages of both fully actuated system approach and anti-windup control. The main advantages are: (1) establishing a fully actuated system approach control framework based on anti-windup control. The controller of the nonlinear system can be written out immediately when a fully actuated system (FAS) model or a group of FAS models of the system is derived, simplifying the steps of control system analysis and design; (2) many actual systems are FAS models, and there is no need to convert the system into a state space model; (3) the anti-windup compensator works only when the actuator saturation occurs to ensure the stability of the control system. In fact, most of the time, the system operates in an unsaturated state, which means that in most cases, the system performance is not affected. A numerical simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

To solve the delay problem of a unified power quality conditioner (UPQC) system during the separation of the fundamental positive-order components and to better filter out the DC and harmonic components to realize accurate phase locking, a mixed second-and third-order generalized integrator phase-locked loop (MSTOGI-PLL) has been designed to replace the traditional synchronous reference frame phase-locked loop (SRF-PLL). Under the premise of adopting the new phase-locking device of MSTOGI-PLL, the active disturbance rejection control (ADRC) controller or the super-twisting algorithm (STA) sliding mode controller is used in the DC voltage control module instead of the traditional PI controller, and the suitability of the two nonlinear controllers with the MSTOGI-PLL device is investigated. First, the new MSTOGI-PLL device is designed, and the new phase-locking method is applied to make the UPQC realize accurate phase locking under the non-ideal situation of the grid voltage containing unbalance, DC component, harmonics, and so on. Based on the above foundation, the ADRC or STA controller is independently adopted to replace the PI controller to construct the UPQC system with the ADRC + MSTOGI phase-locking device and the second-order STA + MSTOGI phase-locking device. Finally, a simulation comparison is carried out in a Simulink simulation platform regarding the UPQC system under different phase-locking devices, and the simulation results demonstrate that MSTOGI-PLL can successfully filter out the DC component and resolve the phase-locking process delay issue. Additionally, the UPQC system with ADRC + MSTOGI-PLL exhibits superior immunity and response speed to the PI controller and the second-order STA controller. [ABSTRACT FROM AUTHOR]

In this paper, we propose a class of predator-prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings. [ABSTRACT FROM AUTHOR]

UAVs are commonly used in transportation, especially in the express delivery of light cargo parcels. However, controlling UAVs is difficult because of their complex structure and wide range of operations in space. The research contribution is proposed a cascade control structure using six PID controllers for the 6-DOF UAV quadcopter, that ensures the altitude angulars positions control at the desired values and maintains flight balance stability for the 6-DOF UAV quadcopter. First, the mathematical dynamic models for the 6-DOF UAV quadcopter have been researched and developed, including the translational dynamic mathematical model and the rotational dynamic mathematical model of the 6-DOF UAV quadcopter. This is a complex object with strong nonlinearity and difficult control. And then, the article introduces the method of designing six PID controllers for 6-DOF UAV quadcopter to meet the requirements, based on applying the Ziegler-Nichols experimental method. Applying the Ziegler-Nichols experimental method makes the process of designing a UAV quadcopter control system simple, straightforward and heuristics with fast controller parameters tuning. Next, the article presents the results of modeling and simulation of the 6-DOF UAV quadcopter control system on Matlab/Simulink. The simulation results show that the six proposed PID controllers have ensured the flight balance stability at the desired altitude and angular positions with overshoot less than 20%, steady-state error less than 1%. This shows the prospect of applying the proposed PID control method to physical UAVs, easily adjusting PID parameters to suit the flight environment. [ABSTRACT FROM AUTHOR]

This paper aims to establish a new event-triggered model predictive control (MPC) strategy for perturbed nonlinear systems working in a networked environment, which can effectively save the computation and communication resources while ensuring control performance. The core of the framework is a new event-triggered mechanism, which is built by combining the differential and integral (D-I) information of the error between the optimal state and the actual state in a pre-specified time horizon. Based on such a triggering mechanism, a D-I based event-triggered robust MPC algorithm is proposed to stabilise the system and reduce the computation/communication resource consumption. In addition, sufficient conditions to ensure the feasibility and stability of the proposed MPC algorithm and avoid Zeno behaviour are obtained through rigorous theoretical analysis. Finally, the proposed control framework is implemented in the nonlinear cart-damper-spring and autonomous underwater vehicle systems to verify its effectiveness. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii's fixed point theorem, the theory of evolution family and the resolvent operator. In particular, the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results. [ABSTRACT FROM AUTHOR]

This study examines stability improvement of the power system which includes Double Feed Induction Generators (DFIGs) and Static Series Synchronous Compensator (SSSC). The proposed nonlinear controller is designed based on the terminal sliding mode control theory. A sliding mode observer is also developed to remove the need to access the information of all the state variables. The final closedloop of the power system modeling is robust against parameter variations and uncertainties. The limitations of the control signals in the process of controller design are also considered. The application of such a method increases the stability margins and results in higher robustness degrees. A comparison with other nonlinear approaches such as back-stepping and feedback linearization approaches is carried out. The results show the faster and more reliable convergence rate of the power system-controlled trajectories to reach back to the equilibrium point after occurring a sudden fault. The results are obtained by performing a simulation on the standard 39-Bus, 10 machines NEW ENGLAND power system. [ABSTRACT FROM AUTHOR]

This article discusses the development and application of an event-triggered distributed observer for a leader-following consensus problem in multiple rigid body systems. The authors present a design framework called the distributed observer based approach, which involves designing control laws and a distributed observer to estimate the state of the leader. The main result of the article is the existence of upper bounds for certain variables in the system. The article also discusses the convergence of the system and presents a lemma and theorem to prove the convergence. Additionally, the article applies the event-triggered distributed observer to the leader-following adaptive consensus problem of multiple uncertain rigid body systems and provides a numerical example to illustrate the result. The paper concludes by acknowledging support received and suggesting future directions for improvement. [Extracted from the article]

The study of soft pneumatic actuator control techniques is an important research topic in soft robotics. However, much of the research has concentrated on upper-level control algorithms, with little attention paid to the bottom-level pneumatic controller. This work aims to develop a simple, low cost, and quick-response pressure controller for soft pneumatic actuators. The controller is designed based on an on/off valve-driven pneumatic supply system, which is high speed, economical, and easy to set up. Using the actual pneumatic properties of a controlled object to estimate the switching time of the valves, the controller avoids complex nonlinear pneumatic computation and can achieve a high control frequency. Experiments demonstrate that the controller performs well in terms of speed and precision, having practical value in the control of soft actuators. [ABSTRACT FROM AUTHOR]

This paper presents a novel input channel gain adaptive active disturbance rejection control (ICGA‐ADRC) framework for the nonlinear control system with large load variation. This paper first introduces the design of ICGA‐ADRC and proves its stability through the rigorous Lyapunov approach. Subsequently, the proposed controller is simulated by subjecting it to a nonlinear mass‐spring‐damping system characterized by significant load variations. Furthermore, the position‐tracking performance of the controller is tested experimentally by using a motor‐driven pendulum system with various loads. Finally, the results of both simulations and experiments show that the ICGA‐ADRC is capable of compensating for system model uncertainty and external perturbation while accurately estimating the system input channel gain in real‐time. The innovation of this paper is that the robustness of active disturbance rejection control (ADRC) to the system load variation is significantly strengthened by integrating robust adaptive finite‐time parameter estimation method into the conventional ADRC control architecture. [ABSTRACT FROM AUTHOR]

This article concentrates on the challenging adaptive tracking problem of multi‐input and multi‐output (MIMO) nonlinear systems with unknown nonlinear dynamics, for which a novel optimization‐based data‐driven adaptive control (ODDAC) equipped with an extended dynamic linearization method is developed. Through considering MIMO nonlinear systems in the fully‐actuated case and over‐actuated case separately, the ODDAC is proposed consisting of a parameter updating algorithm and an adaptive control law. A new design of parameter updating algorithm is presented such that the estimation can be guaranteed to be bounded by a strict contraction process. By leveraging properties of the nonnegative matrix, a grouping‐based contraction mapping (GCM) analysis method is proposed for the convergence of tracking error. Notably, the GCM does not require the contraction mapping condition to hold at all time instants. The proposed ODDAC is data‐based, avoiding reliance on model information, and its validity is verified through simulations. [ABSTRACT FROM AUTHOR]

We consider a two-mass drive with a flexible joint with a nonlinear characteristic of the transmitted torque as a function of the torsion angle. We propose a new, nonlinear, adaptive position-tracking controller, taking this nonlinearity of stiffness into account. The derivation of the controller is based on nonlinear adaptive control theory, incorporates several non-standard mathematical techniques and provides a proof of the uniform ultimate boundedness of tracking errors. As the result, we present a controller that solves the position tracking problem, attenuates dangerous tortional oscillations in the shaft and operates correctly in the presence of unknown torques acting on both sides of the joint, even if all plant parameters are unknown. We demonstrate experimentally that using some materials indeed introduces a nonlinear characteristic of the joint. We prove via real plant experiments that the proposed control algorithm is easily implementable with a DSP controller in real-world applications. [ABSTRACT FROM AUTHOR]

New approaches are proposed in the problem of constructing equivalent scalar differential equations for multidimensional nonlinear systems of control theory, as well as in the problem of constructing equivalent Hamiltonian systems for nonlinear Lurie equations (scalar differential equations containing derivatives of only even orders). The conditions for the solvability of the corresponding problems are studied, and new formulas for the transition to equivalent equations and systems are proposed. For the Lurie equations, the proposed approaches are based on the transition from the linear part to the normal forms of the corresponding Hamiltonian systems with a subsequent transformation of the resulting system. Calculation formulas and algorithms are obtained, and their efficiency is illustrated by examples. [ABSTRACT FROM AUTHOR]

Quasi-parametric chirped-pulse amplification (QPCPA), which features a theoretical peak power much higher than those obtained with Ti:sapphire laser or optical parametric chirped-pulse amplification, is promising for future ultra-intense lasers. The doped rare-earth ion used for idler dissipation is critical for effective QPCPA, but is usually not compatible with traditional crystals. Thus far, only one dissipative crystal of Sm3+-doped yttrium calcium oxyborate has been grown and applied. Here we introduce optical means to modify traditional crystals for QPCPA applications. We theoretically demonstrate two dissipation schemes by idler frequency doubling and sum-frequency generation with an additional laser. In contrast to absorption dissipation, the proposed nonlinear dissipations ensure not only high signal efficiency but also high small-signal gain. The demonstrated ability to optically modify crystals will facilitate the wide application of QPCPA. [ABSTRACT FROM AUTHOR]

For controlling nonlinear processes represented by state‐space models, a state observer is needed to estimate the states from the trajectories of measured variables. While model‐based observer synthesis is traditionally challenging due to the difficulty of solving pertinent partial differential equations, this article proposes an efficient model‐free, data‐driven approach for state observation, which is suitable for data‐driven nonlinear control without accurate nonlinear models. Specifically, by using a Chen–Fliess series representation of the observer dynamics, state observation is endowed with an online least squares regression formulation that can be solved by gradient flow with performance guarantees. When the target state trajectories for regression are unavailable, by exploiting the Kazantzis–Kravaris/Luenberger observer structure, state observation is reduced to a dimensionality reduction problem amenable to an online implementation of kernel principal component analysis. The proposed approach is demonstrated by a limit cycle dynamics and a chaotic system. [ABSTRACT FROM AUTHOR]

This article discusses the challenges and research priorities related to traffic mixed with connected and automated vehicles (CAVs). The article highlights the need to understand how different types of vehicles operate and interact in heterogeneous traffic flow, as well as the evolution mechanism of mixed traffic. The special issue of the journal includes papers on driving behavior modeling, optimization, and traffic flow modeling. The papers cover topics such as simulation platforms for hybrid transportation systems, trajectory reconstruction methods, lane management strategies, fuel consumption modeling, deadlock detection and recovery methods, crash analysis, traffic flow prediction, and gantry positioning methods. The authors conclude that there is still room for future research in areas such as the relationship between the cyber and physical network of transportation systems, driving characteristics of regular vehicles, and macro-level traffic prediction and control. [Extracted from the article]

To overcome the difficulty of propagating the stochastic uncertainties through a nonlinear model for successful online implementation of the stochastic nonlinear model predictive control (SNMPC) framework, this paper proposes the utilisation of Gaussian processes (GPs) in the context of SNMPC for the stochastic multivariable nonlinear systems to track a given trajectory in the presence of stochastic uncertainties and system constraints. Taking advantage of the GP regression which not only provides predictions, but also uncertainty quantification in the function estimation, the proposed GP-SNMPC architecture exploits the probability distribution of stochastic uncertainties and utilises the predictions provided by the GPs to formulate the model cost and constraint functions, which yields a tractable framework for handling nonlinear constrained control problems with Gaussian parametric uncertainties. By employing a cancellation strategy, the control law consists of two components, that is, tracking control law and disturbance rejection control law. Theoretical results regarding the performance bounds of the closed-loop system are derived. Numerical examples are provided to verify the effectiveness of the proposed GP-SNMPC scheme. [ABSTRACT FROM AUTHOR]

This paper presents a new method to calculate the inversion of the controlled linear/nonlinear dynamic plants which are described by input–output differential equation models. This new U-model-based inverter (U-inverter), cancels both system dynamics and nonlinearities, can be used directly to facilitate the control system design, which the design of U-model-based control (U-control) systems is selected for demonstration in this study. The most important advantage of this U-inverter is that it does not require system state variables, only uses the input/output measurements from the controlled plants. A nonlinear disturbance observer is introduced into the U-control design framework to increase its robustness. The analysis explains the properties of this developed the disturbance observer-based U-control (DOBUC) method and its design procedures. Finally, a wind energy conversion system is simulated to illustrate the design of this DOBUC and the corresponding performance. [ABSTRACT FROM AUTHOR]

One of the most important branches of nonlinear control theory of dynamical systems is the so-called sliding mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface. Here, dynamics become completely independent of the model parameters and can be tuned accordingly to the desired target. In this paper we study this problem when the feedback law is subject to strong structural constraints. In particular, we assume that the control input may take values only over two bounded and disjoint sets. Such sets could be also not perfectly known a priori. An example is a control input allowed to switch only between two values. Under these peculiarities, we derive the necessary and sufficient conditions that guarantee sliding-mode control effectiveness for a class of time-varying continuoustime linear systems that includes all the stationary state-space linear models. Our analysis covers several scientific fields. It is only apparently confined to the linear setting and also allows one study an important set of nonlinear models. We describe fundamental examples related to epidemiology where the control input is the level of contact rate among people and the sliding surface permits to control the number of infected. We prove the global convergence of epidemic sliding-mode control schemes applied to two popular dynamical systems used in epidemiology, i.e., SEIR and SAIR, and based on the introduction of severe restrictions like lockdowns. Results obtained in the literature regarding control of many other epidemiological models are also generalized by casting them within a general sliding-mode theory. [ABSTRACT FROM AUTHOR]

Twin‐roll strip casting is a near‐net‐shape casting technology that can produce thin steel strips directly from molten steel. Stably controlling the molten steel level is regarded as an important issue to ensure strip quality and casting process stability. As the control of the molten steel level is a time‐varying, nonlinear, and multidisturbance complex system, it is difficult to establish an accurate process model for designing a model‐based controller. Top side‐pouring twin‐roll casting is a new kind of twin‐roll strip casting technology. This study introduces the control system of the top side‐pouring twin‐roll casting process. A fuzzy logic controller (FLC) with its fuzzy rules optimized by particle swarm optimization (PSO) is developed to regulate the molten steel level. Simulation results show that the performance of the FLC can be improved while its fuzzy rules are optimized by PSO. The objective function of PSO has a great influence on the optimization of the fuzzy rules. The top side‐pouring twin‐roll casting experiments are carried out using the FLC with its fuzzy rules optimized by PSO; the results show that strip quality and casting process stability are guaranteed. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of generalized nonlinear hyperbolic partial differential equations of the Hunter-Saxton-Calogero type, which arise in the theory of control of liquid crystals and in the control of unsteady gas flows. We found such conditions that the original equation can be reduced to linear one by contact transformations. The general exact multivalued solutions of the Hunter-Saxton-Calogero equation are found. The obtained solutions are visualized. [ABSTRACT FROM AUTHOR]

In this paper, the problem of existence-uniqueness and global exponential stability of periodic solution (i.e., stationary oscillation) for a class of nonlinear delay systems with impulses was studied. Some new sufficient conditions ensuring the existence of stationary oscillation for the addressed equations were derived by using the inequality technique that has been reported in recent publications. Our proposed method, which is different with the existing results in the literature, shows that nonlinear delay systems may admit a stationary oscillation using proper impulsive control strategies even if it was originally unstable or divergent. As an application, we considered the single species logarithmic population model and established a new criterion to guarantee the existence of positive stationary oscillation. Some numerical examples and their computer simulations were also given at the end of this paper to show the effectiveness of our development control method. [ABSTRACT FROM AUTHOR]

This paper provides a new method to nonlinear control theory, which is developed from the eigenvalue assignment method. The main purpose of this method is to locate the pointwise eigenvalues of the linear-like structure built by freezing the nonlinear systems at a given time instant in a desired disk region. Since the control requirements for the transient response characteristics are the major constraints on the selection of the disk centre and radius, two different update algorithms are also developed to reshape the disk region by changing the disk centre and radius at each time step. The effectiveness of the proposed methods is tested in both simulations and experiments. A validated three-DOF laboratory helicopter is used for experiments. [ABSTRACT FROM AUTHOR]

The effective motion control task is highly influencing the final drive performance in wide-range motor drives applications such as electric vehicles (EVs), washing machines, compressors, elevators and lathe machines. Recently, permanent magnet synchronous motor (PMSM) drive has been widely employed in these applications to achieve desired performances such as high efficiency, high torque requirements with minimum size "occupancy". The PMSM drive features combining with these modern drive applications are highly nonlinear and the desired operation requirements demand high-performance control schemes with fast system response and robustness features. Linear control schemes are usually implemented to drive the PMSM that entail tradeoffs between drive performance and simplicity in control implementation. Therefore, this paper presents the nonlinear control technique based on augmented finite control set (AFCS) model predictive control (MPC) scheme (AFCS-MPC). The proposed AFCSMPC scheme enhances the standard MPC design by augmenting the nonlinear characteristics of the PMSM drive to achieve wide speed range drive performance under both steady-state and dynamic operating conditions. Comparative performance studies have been conducted and presented to confirm the efficacy of the proposed scheme. [ABSTRACT FROM AUTHOR]

This contribution presents a gain adaptation, which allows us to tune a robust asymptotic feedback linearization (RAFL). The gain adaptation allows the RAFL to attenuate the measurement noise sensitivity. The RAFL is considered here because it ensures tracking without prior information about the system's nonlinearities and parameter bounds. Also, the RAFL only has the system output available for feedback. In this work, the robust tracking problem is faced considering: modeling errors, parametric variations, external perturbations, and noisy output measurement. On one side, the RAFL control faces modeling errors, parametric variations, and external perturbations through an observer that estimates uncertainties using an extra state, which lumps all the unknown nonlinearities and uncertainties. On the other hand, the proposed adaptive gain function allows the observer's high gain to vary to have a fast observer's convergence while simultaneously avoiding amplifying the measurement noise in the steady-state. The adaptive gain function provides the RAFL control robustness against noisy measurement. Thereby, the RAFL control with adaptive gain function becomes a robust feedback linearizing against to measurement noise. Finally, the RAFL controller with the adaptive gain function is illustrated by a numerical simulation of a tracking problem for a DC-motor and a chemical oxygen demand regulation in an anaerobic digestion process. [ABSTRACT FROM AUTHOR]

Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides its classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws such as the well-known policy iteration. In this manuscript, the focus is on the Lyapunov function of a nonlinear autonomous finite-dimensional dynamical system which will be rewritten as an infinite-dimensional linear system using the Koopman or composition operator. Since this infinite-dimensional system has the structure of a weak-* continuous semigroup, in a specially weighted Lp-space one can establish a connection between the solution of an operator Lyapunov equation and the desired Lyapunov function. It will be shown that the solution to this operator equation attains a rapid eigenvalue decay which justifies finite rank approximations with numerical methods. The potential benefit for numerical computations will be demonstrated with two short examples. [ABSTRACT FROM AUTHOR]

Synchronization of chaotic systems is usually investigated for structurally equivalent systems typically coupled through linear diffusive functions. Here, we focus on a particular type of coupling borrowed from a nonlinear control theory and based on the optimal placement of a sensor—a device measuring the chosen variable—and an actuator—a device applying the actuating (control) signal to a variable's derivative—in the response system, leading to the so-called flat control law. We aim to investigate the dynamics produced by a response system that is flat coupled to a drive system and to determine the degree of generalized synchronization between them using statistical and topological arguments. The general use of a flat control law for getting generalized synchronization is discussed. [ABSTRACT FROM AUTHOR]

In this study, the adaptive backstepping control of a class of multi‐input multi‐output nonlinear systems with immeasurable states, structural uncertainties and periodic perturbations is researched using neural network (NN) based nonlinear observer. Firstly, a series of harmonic components obtained from Fourier series expansion (FSE) are employed to estimate the unknown periodic perturbations. Then treating the estimated perturbations as inputs, a radial basis function‐based neural network (RBFNN) is constructed as a component of the observer, and the observer is proved to be uniformly ultimately bounded (UUB) in estimating the immeasurable system states with the negative‐gradient adaptive laws of NN parameters. Subsequently, the adaptive backstepping control is designed to track reference signals at the outputs of system based on the FSE‐RBFNN observer, and the stability of the closed‐loop system is proved on a finite set of system states. Finally, the proposed methods are applied to a triangular tethered satellite formation model to test the stability of the observer and control, and the effect of FSE in estimating perturbations is comparatively tested as well. [ABSTRACT FROM AUTHOR]

Recent results on the passivity analysis and control of physical systems, based on the balance of dissipated and internally generated energy, are generalised to nonlinear systems represented by bond graphs. For linear systems, the internally generated energy associated with modulated sources can be coupled with the dissipative field, so that if external energy sources are excluded, then the system is passive (or dissipative) if the resulting composite multiport field is passive. Such a result for linear systems was previously conveniently expressed in terms of a characteristic matrix being positive semi-definite. Parasitic elements of previous works are no longer required, which allows working on the original bond graph of lower dimension than the augmented bond graph and for no-linear systems avoid inverting the dissipative nonlinear constitutive relations. For nonlinear systems, passivity is now considered through the explicit difference between the dissipated and the internally generated energy. If this energy difference is positive, the system is passive. For control systems, the current work proposes that the controller is designed to have a structure similar to the plant (linear or nonlinear), and its parameters are chosen to assure that in closed-loop the difference between the dissipated and the internally generated energy is positive. In particular, the control parameters can be chosen to assign a desired dissipated energy or to cancel by feedback the internally generated energy and to add damping, therefore achieving sufficient conditions for the passivity of the closed-loop system. [ABSTRACT FROM AUTHOR]

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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]

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]

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]

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]

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]