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Investigation and implementation of Active Willis Metamaterials (AWM) have been done exclusively, in all the available literature, by approaches that do not rely on any solid control theory basis. When coupled with piezoelectric control elements, the available approaches have not included, from the first principles, the exact form of the constitutive relationship of the piezoelectric materials. Furthermore, in all these approaches, stability analysis, robustness, ability to accommodate uncertainty or parameter changes, or consideration of disturbance rejection has not been addressed at all. More importantly, the available formulations have always mixed the flow and effort variables of the AWM, resulting in a form that is totally incompatible for the use in generating, investigating, or even designing any appropriate sensing or control applications of the material. In this paper, the piezoelectric-based AWM is modeled, from the first principles, to develop a constitutive coupling form that enables its use in actuation, sensing, and as an integrated controller that can be analyzed, designed, and optimized using the classical, optimal, and robust control system theories. Lagrange dynamics formulation is used to generate the equations governing the Willis coupling, the piezoelectric coupling, as well as the active robust controller. With this developed controlled-based structure of the AWM, the inherent and powerful capabilities of the AWM that lie in its ability to robustly control the material properties themselves such as the compliance (or stiffness) and specific volume (or density) are demonstrated in great detail via several numerical examples. Controlling these properties enables the AWM to be used in numerous important and imaginative applications such as cloaking, beam shifting, beam focusing, as well as many other applications that are limited only by our imagination. [ABSTRACT FROM AUTHOR]

Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively. [ABSTRACT FROM AUTHOR]

In automated manufacturing systems (AMSs), because of unpredictable failures, resources can lose functions such that the deadlock control methods, in existence, are invalidated. In this paper, a robust deadlock control approach is proposed for AMSs with multiple unreliable resources. The considered AMSs modelled by Petri nets (PNs) allow to acquire different types of resources at each processing stage. In order to visualise the fact that resource failures occur in AMSs, recovery subnets are designed for the modelling AMSs to depict the failures and recoveries of resources. Based on a siphon detection method performed by a set of integer linear programming formulations, a control specification is proposed. Control places (monitors) with their control variables are designed for the detected unmarked siphons at a marking to guarantee that they are always marked even if some unreliable resources break down. Iteratively, all unmarked siphons are detected and controlled. Therefore, a robust deadlock supervisor is synthesised to ensure the controlled system's liveness no matter there exist resource failures or not. The theoretical analyses and proof are given to verify the correctness of the proposed method. Finally, the comparative studies are presented to expound the proposed method's effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

Motivated by the fully actuated system (FAS) approach, this paper proposes a direct robust control method for a type of uncertain multi‐order sub‐fully actuated systems (MOSFASs). Unlike numerous previous results, this paper broadens to a more general multi‐order model and the more challenging sub‐fully actuated case with the presence of singular problems. Firstly, a general uncertain MOSFAS model is presented, where the uncertainty merely needs to satisfy a common assumption. Secondly, a direct robust control method is proposed, giving a robust controller which only needs to satisfy very loose and basic requirements to ensure that the states ultimately converge into an arbitrarily small region. Simultaneously, by constraining the initial values of the states, it is perfectly guaranteed that the states always remain in a "safe" zone free of singular points, thus preserving the realizability of the controller. Finally, under certain conditions, a less conservative robust control scheme is introduced, which can relax the constraint of initial values easily. A simulation for a coarse‐fine angle system demonstrates the validity and value of the proposed robust control method. [ABSTRACT FROM AUTHOR]

This article investigates the stabilization problem of uncertain switched nonlinear systems. Uncertainty and saturated impulses are first considered together in switched nonlinear systems. It appears that the considered systems are robustly locally exponentially stable under the fast average dwell time method and the designed saturated impulsive controller even though subsystems are unstable. At the same time, our conclusions cover some previous results. A step‐by‐step strategy for optimizing multiple objectives is designed to estimate the basin of attraction of the systems as large as possible. At last, the efficacy of our conclusions is illustrated by two given examples. [ABSTRACT FROM AUTHOR]

Under the theoretical support of fuzzy sets theory and confidence index, the proposed approach involves the development of a high‐order robust control method that incorporates optimization techniques to address uncertain systems. First, the utilization of fuzzy sets theory is employed to establish a fuzzy dynamical model. Second, the design of a high‐order robust controller is performed. Third, the design parameters are optimized based on confidence index, and the values are found that minimize the control cost. The simulation results show that this high‐order robust control has significant advantages in dealing with uncertainty, as well as minimizing the control cost. It can be ensured the uniform boundedness and uniform ultimate boundedness. Thus, this proposed method offers the advantage of achieving both robustness and optimality simultaneously. [ABSTRACT FROM AUTHOR]

In this article, we deal with finite‐time optimal control of the Euler–Lagrange (E–L) multi‐body mechanism under: uncertain its kinematics and dynamics, displacement blocking of the damaged joint caused by the actuator failure, undesirable forces/torques exerted on the end‐effector and unknown friction forces originating from joints directly driven by the actuators, as well as completely unstructured forces arising from the kinematic singularities appearing on the mechanism trajectory. Based on the suitably defined task space non‐singular terminal sliding manifold and the Lyapunov stability theory, we propose a class of new fault tolerant estimated generalized Jacobian controllers, which seem to be effective in reducing (minimizing) the joint velocity jumps as well as in counteracting the unstructured forces/torques. On account of the fact, that the multi‐body mechanism is a redundant one, a useful criterion function (energy consumption +$$ + $$ manipulability measure) has been utilized in our controller to temporarily optimally track a desired trajectory. The proposed controllers' performance is demonstrated by computer simulations conducted on a redundant manipulator in conditions of unexpected actuator failure and the corresponding joint lock. Additionally, numerical comparisons are also provided with other representative controllers, found in the literature. [ABSTRACT FROM AUTHOR]

The enhanced model reference adaptive control (EMRAC) algorithm is an effective full‐state adaptive solution to control plants affected by nonlinear unmodelled dynamics and persistent disturbances. The EMRAC strategy improves the tracking performance by equipping the MRAC algorithm with adaptive switching and adaptive integral control actions. However, the need for the plant state prevents the applicability of the EMRAC algorithm to engineering control problems where only the plant output is measurable. To cover this gap and extend the range of plants controllable by EMRAC solutions, this article presents an output‐based EMRAC algorithm leveraging the closed‐loop (CL) MRAC formulation. The robustness of the closed‐loop control system is analytically analysed, not only with respect to plant parameter uncertainties and square measurable disturbances, but also to ℒ∞$$ {\mathcal{L}}_{\infty } $$ unmodelled terms and disturbances. The ultimate boundedness of the closed‐loop control system is assessed with respect to ℒ∞$$ {\mathcal{L}}_{\infty } $$ unknown nonlinear terms and disturbances, by using Lyapunov theory for Filippov systems, as the adaptive switching control action makes the closed‐loop system discontinuous. To assess the effectiveness of the CL‐EMRAC strategy to impose reference trajectories despite the unmodelled plant dynamics and persistent bounded disturbances, the problem of vehicles' direct yaw moment control is used as an engineering case study. The closed‐loop tracking performance is also quantitatively evaluated through a set of key performance indicators and compared to those provided by four benchmark controllers, that is, two LQ‐based strategies and two MRAC‐based control solutions. The CL‐EMRAC and benchmark controllers are implemented and tested in a co‐simulation environment based on a high‐fidelity IPG CarMaker vehicle model. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of robust adaptive safety control of a class of nonlinear systems with parametric uncertainties. Two novel definitions, that is, robust adaptive control Lyapunov function (RACLF) and robust adaptive control barrier function (RACBF) are introduced in this article. Also, an estimation of unknown parameters is obtained based on multiple identification models, state predictors and a logic switching mechanism. The switching mechanism plays a vital role in enhancing the transient properties of nonlinear systems. Meanwhile, a safe motion framework for differential robots is provided based on the existence of parametric uncertainties in RACLF and RACBF, and a safe and stable controller is obtained by solving quadratic programming. Finally, simulation results of differential robot capable of safe motion in space are presented to verify the validity of the design method. [ABSTRACT FROM AUTHOR]

The problem of fixed‐time formation control for a class of second‐order nonlinear multi‐agent systems is studied. For a class of such systems, a control algorithm is proposed to maintain the connections among the agents while avoiding collisions. Furthermore, a radial basis function neural network is used in the design to precisely approximate the nonlinear function for the nonlinear terms in the model. Then, a dynamic sliding mode control method is proposed to suppress the chattering phenomenon that may arise due to the sliding mode control. A sufficient condition for the system to achieve fixed‐time formation is obtained by using different methods, such as Lyapunov stability. Finally, the effectiveness of the proposed algorithm is verified by example. Simulation experiments reveal that the proposed method has faster error convergence and better robust control than conventional algorithms. [ABSTRACT FROM AUTHOR]

The control of quadrotor vehicles under state and parameter uncertainty is a well studied problem that is vitally important to the deployment of these systems under real world conditions. In this article, we propose a linearization‐based extension to nonlinear systems of the existing scenario model predictive control (MPC) framework, which quantifies the impact of uncertainty on the vehicle dynamics through repeated sampling of the uncertainty space. Given the computational costs of such an approach, we also propose two simplifications of the scenario MPC algorithm that are significantly more tractable. In order to evaluate the performance of the algorithms, the specific problem of the control of a bidirectionally actuated quadrotor vehicle is considered. Simulations are carried out for each scenario MPC scheme as well as for a reference deterministic MPC scheme. When a sufficiently large sample count is considered, each of the scenario MPC algorithms achieves safer performance than the deterministic formulation without sacrificing any optimality. Additionally, the approximate solution techniques conclusively outperform the original nonlinear scenario MPC formulation for the same computational cost. [ABSTRACT FROM AUTHOR]

This article addresses robust output regulation for systems affected by disturbances generated by an uncertain exosystem as well as matched external disturbances. The robustness of the feedback loop is achieved by combining internal model based control with sliding mode control, resulting in a structurally simple controller. The design of the proposed controller is presented first for the full information problem, that is, the disturbances generated by the exosystem and the state‐information is available for the control algorithm. This requirement is relaxed in the second step of the controller design, where the observer‐based robust output feedback‐loop structure is developed. Results from a comparative simulation study are presented to illustrate the advantages and the effectiveness of the proposed controller concept. [ABSTRACT FROM AUTHOR]

Path tracking plays a critical role in autonomous driving for autonomous ground vehicle (AGV). However, AGV faces challenges in accurate tracking and chatter reduction due to external disturbances, making it difficult to meet the tracking performance requirements. Currently, sliding mode control (SMC) and disturbances observer are primarily employed for disturbance estimation. However, ensuring finite‐time robust control remains a significant challenge. To ensure rapid convergence of tracking errors and effective disturbance rejection, this paper proposed a novel non‐singular fast terminal sliding mode (NFTSM) control scheme based on finite‐time disturbance observation (FDO). First, a novel NFTSM controller based on AGV dynamic model is developed to achieve fast convergence of tracking errors. Then, to mitigate disturbances effects and suppress chatter, an innovative FDO method is employed. Finally, based on FDO, the NFTSM‐FDO establishes a control scheme that enhances disturbances suppression and accelerates convergence. The simulation and experimental results demonstrate the innovation of the proposed method. Compared with other SMC methods, the results validate the effectiveness and advantages of the proposed approach, exhibiting fast convergence and superior tracking performance. [ABSTRACT FROM AUTHOR]

This article investigates the robust consensus problem for nonlinear multiagent systems against time‐varying false data injection attacks on actuators and sensors. First, the root‐mean‐square (RMS) theory is used to extend the assumption of the slow‐varying or constant attack signals to the case of time‐varying attack signals. Second, a novel distributed multivariate observer (DMO) is designed to estimate the followers' system states and the time‐varying attack signals on actuators and sensors. With the help of the outputs of DMO, a distributed robust consensus control arithmetic is proposed, which can compensate for actuator attacks and isolate sensor attacks so that exponential consensus and robust consensus are achieved. In particular, the robust performance of estimation errors and consensus errors is ensured by establishing the RMS gain index via linear matrix inequality, in which the zero initial conditions of estimation errors and consensus errors are not required. Finally, two simulation examples, including a network of four aircraft longitudinal dynamic systems, are given to verify the effectiveness of the proposed arithmetic. [ABSTRACT FROM AUTHOR]

This paper investigates the practical prescribed time tracking for a class of uncertain nonlinear systems based on neural networks and event‐triggered control. Introducing a time‐varying constraint function transforms the original practical prescribed time‐tracking control issue into a tracking error constraint problem. An event‐triggered adaptive control has been proposed, which can effectively reduce the communication burden between the controller and the actuator. Using neural networks to approximate unknown nonlinear functions avoids the differentiation of virtual controllers, thereby reducing the computational burden. In addition, users can independently choose preset time and tracking accuracy without changing the control structure, which remains independent of the initial conditions and any design parameters. Finally, the effectiveness of this method is verified through simulation examples. [ABSTRACT FROM AUTHOR]

This article is dedicated to event‐triggered anti‐disturbance control of networked control systems via a guaranteed cost triggering scheme. A distribution interconnected observer structure is built to estimate these unknown matched disturbances. A novel event triggered condition is constructed in terms of real‐time cost and averaged functions composed of observer states and the last successfully transmitted one. A composite control scheme is provided by an event‐triggered observer‐based state feedback controller and compensators for the matched disturbances. A sufficient condition in term of linear matrix inequality is supplied to ensure the asymptotic stability of the resultant closed‐loop system. A simulation is carried out to demonstrate the effectiveness of the proposed triggering control strategy. [ABSTRACT FROM AUTHOR]

Controlling variable wind speed turbine (VWT) system based on a doubly-fed induction generator (DFIG) is a challenging task. It requires a control law that is both adaptable and robust enough to handle the complex dynamics of the closed control loop system. Sliding mode control (SMC) is a robust control technology that has shown good performance when employed as a passive fault-tolerant control for wind energy systems. To improve the closed control loop of VWT based on DFIG with the aim of improving energy efficiency, even in presence of nonlinearities and a certain range of bounded parametric uncertainties, whether electrically or mechanically, an adaptive passive fault tolerant control (AP-FTC) based on a self-tuning fractional integral sliding mode control law (ST-FISMC) developed from a novel hyperbolic fractional surface is proposed in this paper. ST-FISMC introduces a nonlinear hyperbolic function into the sliding manifold for self-tuning adaptation of control law, while fractional integral of the control law smooths discontinuous sign function to reduce chattering. Additionally, this work introduces an adaptive observer, developed and proved based on a chosen Lyapunov function. This observer is designed to estimate variations in electrical parameters and stator flux, ensuring sensorless decoupling in indirect field-oriented control (SI-FOC) of DFIG. Lyapunov theory is also used to prove stability of states vectors in closed control loop with presence of bounded parameters uncertainties or external disturbances. Simulation results show that the proposed approach offers better performance in capturing optimal wind energy, as well as the ability to regulate active/reactive power and high resilience in presence of occurring parameter uncertainties or external disturbances. [ABSTRACT FROM AUTHOR]

This paper proposes a second-order terminal sliding mode (2TSM) approach to the trajectory tracking of the differential drive mobile robot (DDMR). Within this cascaded control scheme, the 2TSM dynamic controller, at the innermost loop, tracks the robot's velocity quantities while a kinematic controller, at the outermost loop, regulates the robot's positions. In this manner, chattering is greatly attenuated, and finite-time convergence is guaranteed by the second-order TSM manifold, which involves higher-order derivatives of the state variables, resulting in an inherently robust as well as fast and better tracking precision. The simulation results demonstrate the merit of the proposed control methods. [ABSTRACT FROM AUTHOR]

The literature on lottery gambling shows that players do not select numbers randomly, a phenomenon which is called conscious selection. Mainly, players prefer "small" numbers (less than thirty), either because of the existence of small lucky numbers or because they are victims of the so-called birthday-number effect. Because lotto games are parimutuel, such preferences result in poor ticket choices in terms of achieving below average returns. Using data from Belgium, where approximately 10% of the population plays lotto games every week, this paper extends prior literature by documenting the existence of a gender gap in the birthday-number effect, with women displaying a stronger birthday-number effect than men, as well as the non-persistence of the birthday-number effect (and consecutively of the gender gap) when participants are asked to fill in a second lotto ticket immediately after their first one. The disappearance of the birthday-number effect in sequential choices appears to be driven by response speed, with participants being twice as fast to fill in the second ticket compared to the first one. Moreover, we find that participants who bet on their birthday numbers take significantly more time to complete their ticket. Contrary to prior research, we find that the strength of the birthday-number effect is positively related to deliberative number choices, not intuitive and automatic number choices. Our results are robust to controlling for potential confounding effects including those related to participants' age, education, self-esteem, and superstitious beliefs. [ABSTRACT FROM AUTHOR]

This article addresses the problem of speed and steering control of unmanned sea surface vehicles operating under unknown ocean environments affected by complex nonlinearities and uncertain hydrodynamic coefficients. An inertial delay control (IDC)-based sliding mode control (SMC) is proposed. The proposed controller is robust against the system's nonlinearities, parametric uncertainties, external disturbances like a strong wind, complex disturbances due to wind-generated and ocean currents, etc. The proposed controller uses IDC to estimate these effects mentioned above, which makes the proposed SMC independent of the bound of uncertainties and disturbances, and provides chatter-free control. The effectiveness of the proposed controller is confirmed by considering the highly nonlinear model of Cypership-II using various performance indices. [ABSTRACT FROM AUTHOR]

In order to suppress the influence of uncertain disturbances on the trajectory tracking of hydraulic manipulator, a composite control strategy for the cutting electro-hydraulic driving system (CEHDS) of the tunneling robot is presented, which synthesizes the advantages of neural networks technique, recursive backstepping and adaptive control theory. The Lagrangian model with actuator dynamics is derived based on the practical tunneling robot. The back-stepping method is utilized for the strictly feedback state-space model. To address the matched and unmatched lumped uncertainties, the radial-basis-function neural networks (RBFNNs) are employed to approximate the unmatched term which contains the nonlinear friction torque and external cutting load in the mechanical subsystem. The nonlinear disturbance observer (NDOB) is utilized to estimate the matched lumped uncertainty in the hydraulic subsystem. Simultaneously, the adaptive robust mechanism is proposed to compensate the residual disturbances. Based on the Lyapunov theorem, the stability and the bounded tracking error of the CEHDS are obtained. The simulation and experimental results validate the effectiveness of the proposed method in comparison with the common backstepping and PID-controller approaches. [ABSTRACT FROM AUTHOR]

This article addresses the issue of collaborative wildfire monitoring using a group mobile mecanum‐wheeled omnidirectional vehicles (MWOVs) affected by nonlinear uncertainties and external disturbances. By integrating finite‐time extended state observers (FTESO) and backstepping nonsingular fast terminal sliding mode (BNFTSM) control method, an observer‐based finite‐time time‐varying elliptical formation control scheme is proposed for a group of MWOVs tasked with monitoring the propagation of wildfires in an elliptical pattern. First, the FTESO is employed to estimate the unavailable velocity system states and the lumped disturbances. Then, a novel nonsingular fast terminal sliding surface, enhanced with an exponential term, is introduced to improve the convergence rate. Through the Lyapunov theorem, the convergence of position and velocity cooperative tracking errors to zero in fast finite‐time is demonstrated. To showcase the effectiveness of the proposed control scheme, comparative simulation results are presented. [ABSTRACT FROM AUTHOR]

Macroscopic fundamental diagram (MFD)-based perimeter control has a potential to improve traffic throughput and relieve the overall congestion. In practice, not only the MFD but also the traffic demand suffers from a variety of inherent uncertainties. Hence, this paper aims to contrive a robust control technique to address the perimeter traffic flow control issue in the oversaturated region. To this end, an integral sliding mode control is proposed to drive the traffic state to the desirable condition. The developed strategy deals with practical issues such as finite time stability and range of uncertainty in both MFD and traffic demand. Theoretical analysis verifies that the developed integral sliding mode control approach can guarantee the finite time convergence of the traffic state to the desired one. The performance of the developed scheme is attested by considering various traffic scenarios with uncertain MFDs and traffic demand, in which a comparative performance study with the proportional and integral control method is conducted. It is indicated that the developed scheme can alleviate the congestion in the urban network and improve the throughput of the urban network. Practical Applications: The research presented in this article proposes a novel perimeter control technique designed to enhance traffic flow management in densely populated urban road networks, particularly during peak congestion times. By leveraging the macroscopic fundamental diagram (MFD) and integral sliding mode control theory, the method significantly boosts traffic throughput and alleviates the impact of congestion. This advancement can be seamlessly integrated into current urban traffic management systems, leading to more efficient and convenient urban commutes. Additionally, it addresses the rise in vehicle emissions due to heavy traffic, aiding in the reduction of pollution and supporting sustainable development initiatives. The technique also curtails vehicle fuel consumption and cuts down on costs associated with congestion-related delays, thereby fostering resource optimization and economic growth within urban environments. Moreover, the method is designed to be resilient, taking into account the variability of traffic demand and ensuring the robustness of the traffic control strategy. Overall, the article demonstrates the practical application of advanced control technologies to address real-world traffic challenges, providing a scalable and robust solution adaptable to realistic situations with the uncertainties of urban traffic demand. [ABSTRACT FROM AUTHOR]

This paper presents a modal analysis‐based impact analysis of the change in system inertia due to the integration of the large‐scale doubly fed induction generator (DFIG)‐based wind turbine system (WTS) on the power system damping in inter‐area oscillation modes. The impact of replacement of a synchronous generator by WTS of same MVA capacity on system dynamics such as emergence of new critical modes of inter‐area oscillations affecting system stability is studied. Further, a double‐channel H∞ scheme‐based wide‐area damping controller (WADC) is proposed for WTS, which provides sufficient damping of prominent oscillation modes and enhanced stability margin to alleviate the negative impact of reduction in system inertia. The comparative assessment of the proposed controller with a PSS‐based WADC on a modified New England 10‐machine system validates the performance and is found to be more effective in mitigating inter‐area oscillation in the system. The real‐time feasibility of the proposed double‐channel H∞ WADC is evaluated on the Real‐Time Digital Simulator (RTDS) platform. The simulation results show that the proposed WADC can successfully mitigate various inter‐area modes simultaneously. Furthermore, it provides robust performance for a variety of contingencies, time delays in feedback signals, and uncertainties associated with different operating scenarios of WTS. [ABSTRACT FROM AUTHOR]

Summary: The unstable operation of a direct‐drive permanent magnet synchronous generator (DPMSG) is exacerbated by periodic oscillation, having a significant impact on the safe and stable functioning of wind energy generation systems. This paper proposes an approximate solution method for analyzing the periodic oscillation of the Hopf bifurcation and a method for suppressing its bifurcation through H∞ robust control. Firstly, a three‐dimensional nonlinear dynamic model of the DPMSG is constructed. Secondly, the Hopf bifurcation of the system with changes in internal parameters is solved using the time domain and frequency domain methods, and the harmonic balancing method is used to approximate the periodic solution at the point of Hopf bifurcation. The order of the Hopf bifurcation neighborhood is then decreased using the central manifold theorem. Finally, this study suggests a H∞ output feedback control employing bifurcation parameters. The Nyquist criteria are used for evaluating small signal stability and convergence speed of the response system in DPMSG before and after dimensionality reduction. The simulation results suggest that the proposed strategy helps to tackle the periodic solution expression and instability difficulties caused by Hopf bifurcation. This paper provides theoretical suggestions for the future reliable operation of new energy generation systems. [ABSTRACT FROM AUTHOR]

As the share of renewable energy sources in the power system keeps growing, a new issue with frequency stability – diminishing and changing inertia – has emerged. Estimating power system inertia has received a lot of attention lately in order to market design of synthetic inertia as an additional service and implement timely corrective steps for robust frequency control. Curve fitting technique has emerged as one of the promising techniques for estimation of power system inertia, however, many challenging aspects need to be addressed for its practical applications. This study aims to systematically assess the effectiveness of the curve fitting method under a range of operational parameters and conditions, such as the curve fitting order, the length of data to be used for curve fitting after an event begins, and the length of the moving average filter applied to the frequency data to remove oscillatory and noise from the frequency transient. The simulation studies have been performed on DIgSILENT and MATLAB platforms. The results show that very high and very low order curve fitting results are high errors and the 5th order model with mean error in estimated value of inertia less than 1% has outperformed others. The analysis on various window width of moving average filter found that increasing the window width results in more error. For IEEE-9 bus system, a filter up to 850 ms width has a mean percentage error below 1%. The analysis also revealed that the duration of the data used for curve fitting is not significant. For variation of the duration of the data used for the curve fitting from 50 ms to 500 ms, the estimated inertia values are found to be in a close range of 2.4881 s to 2.5262 s, for the single machine system with H = 2.5 s. The analysis presented in this study will be useful for effective application of curve fitting method in inertia estimation. [ABSTRACT FROM AUTHOR]

This article considers the following problems for a parametric uncertain (affine) linear time-invariant system. The first problem is: Let a feedback gain matrix be designed such that the states of the closed loop system satisfy the specified transient performance bounds. Then, compute a ball in the uncertain parameter space such that for all parameter perturbations within it, the state response continues to satisfy the same transient performance bounds. The second problem is on the synthesis of a robust static state feedback control, which i) minimises the norm of the gain matrix, ii) maximises the radius of the ball in the uncertain parameter space, and iii) ensures achieving specified transient performance in the closed loop. For this, a sub-optimal linear matrix inequality optimisation is formulated. The developed results are demonstrated with numerical examples. It also highlights how the proposed methodology can be applied to design robust static state feedback control for a polytopic uncertain system. [ABSTRACT FROM AUTHOR]

This paper proposes a systematic approach for optimizing the distribution of local models in multi-model control systems (MMCS) to enhance overall robustness. While existing literature discusses this method for linear parameter varying (LPV) and uncertain linear time-invariant (LTI) systems, significant limitations persist in addressing nonlinear dynamic systems. Robust control tools like the gap metric and generalized stability margin (GSM) have limited effectiveness in analyzing the robustness of nonlinear feedback systems. To address these challenges, novel concepts of the gap metric and GSM are introduced to determine central operating points (COPs) within local operating areas (LOAs) across the total operating area (TOA). These COPs guide the extraction of affine disturbance local models (ADLMs). Additionally, an optimization problem based on the s-gap metric and GSM is presented to optimize COPs placement and LOAs boundaries. Challenges such as non-monotonic behavior of the cost function and complexity arising from the s-gap metric formulation necessitate novel solution methods. To address these, constraints are applied to the cost function, and a novel discrete optimization approach is introduced. Finally, theoretical findings are applied to the Duffing system, pH neutralization process, and continuous stirred tank reactor (CSTR) plant to evaluate the proposed method's effectiveness. This comprehensive validation across different systems underscores the versatility and practical utility of the proposed approach. • We provide a systematic solution for addressing multi-model control systems (MMCS) for nonlinear dynamic systems. • Our approach stands out for its versatility, extending its applicability to a broad spectrum of nonlinear dynamical systems. • The solution is achieved through the utilization of s-gap metric concepts. • We tackle the optimization problem in a discrete form, introducing a novel clustering-based optimization approach. • The non-monotonic behavior of the s-gap metric is addressed by incorporating constraints into the problem formulation. [ABSTRACT FROM AUTHOR]

In this paper, for macro–micro composite motion platform with piezoelectric hysteresis, an finite-time adaptive robust control method based on extended hysteresis observer is proposed. The dynamic model of macro–micro system is constructed at first. An extended hysteresis observer was designed to estimate the actual displacement and speed of motion system. Then, an adaptive robust control law is designed to eliminate the uncertain hysteresis model parameters. After this, exponential convergence result of the proposed control method is given and proved. By setting the expected bandwidth of macro–micro system, the gain adjustment process of the control method can be reduced in computation. The effectiveness of the proposed control method is demonstrated by comparison with other control methods in simulation, and the proposed control method has more stable tracking effect and smaller tracking error. • Finite-time adaptive robust controller for Macro–micro composite platform. • Design and implementation of extended state observer for piezoelectric hysteresis. • Design of gain adjustment process to simplify calculation. [ABSTRACT FROM AUTHOR]

This article proposes a preview-based robust path-tracking control technique for maintaining lateral stability and tracking performance of autonomous vehicles, particularly in the presence of external disturbances and modeling uncertainties. First, a vehicle-road dynamic model with tire norm-bounded uncertainty is developed, which includes time-varying velocities and preview distances. The lateral and yaw dynamic characteristics are also analyzed in the frequency domain. Subsequently, an optimal preview model corresponding to sideslip-yaw rate states and longitudinal velocities is formulated employing a fuzzy logic model, and the sideslip angle is estimated using a sliding mode observer. Furthermore, a linear parameter-varying (LPV)/ H ∞ path-tracking controller that satisfies the pole placement and performance constraint is constructed to guarantee robustness and lateral stability across the whole parameters space with the coexistence of external disturbances and parametric uncertainties. Finally, the simulation results demonstrate that the proposed controller substantially enhances tracking performance while also maintaining excellent lateral stability. • A vehicle-road dynamic model with norm-bounded uncertainty for path-tracking controller design is built and analyzed. • An optimal-preview model is innovatively produced by utilizing velocity and the sideslip-yaw rate state of the vehicle. • An LPV/ H ∞ path-tracking control structure integrated optimal-preview model is proposed to improve tracking performance. [ABSTRACT FROM AUTHOR]

Nowadays, the demand for high-precision devices is becoming more intense, thanks to the growing complexity and sophistication of modern technology and applications, including microscopy, nanomeasurement and analysis instruments. However, challenges arise because environmental factors such as vibration negatively affect their performance. An active vibration isolation system (AVIS) is one of the most recent solutions for that, but the high degree-of-freedom (DoF) nature results in it strongly suffering from unwanted interactions. Hence, in this paper, a robust decoupling controller is designed to handle the mentioned disadvantages. The system model is first presented, followed by the proposed decoupling techniques, and then, a feedback controller is designed by applying the mixed-sensitivity H ∞ control framework. Experimental studies are conducted to investigate the effectiveness of the proposed AVIS and compare it with other systems, namely, a passive vibration isolation system, a proportional–derivative (PD)-controlled AVIS, and a robust controlled AVIS. The robustness and decoupling performance of the proposed controller are guaranteed by suppressing external vibrations and isolating interactions, and, therefore, stabilizing the system. [ABSTRACT FROM AUTHOR]

Featured Application: Featured Application: Automatic control of electrical motors and robotic systems actuated with electrical motors are the main featured applications of this study but are not the limit. Any closed-loop automatic control system with known plant dynamics can be a featured application of this study. In this study, a novel approach of designing automatic control systems with the help of AI tools is proposed. Given plant dynamics, expected references, and expected disturbances, the design of an optimal neural network-based controller is performed automatically. Several common reference types are studied including step, square, sine, sawtooth, and trapezoid functions. Expected reference–disturbance pairs are used to train the system for finding optimal neural network controller parameters. A separate test set is used to test the system for unexpected reference–disturbance pairs to show the generalization performance of the proposed system. Parameters of a real DC motor are used to test the proposed approach. The real DC motor's parameters are estimated using a particle swarm optimization (PSO) algorithm. Initially, a proportional–integral (PI) controller is designed using a PSO algorithm to find the simple controller's parameters optimally and automatically. Starting with the neural network equivalent of the optimal PI controller, the optimal neural network controller is designed using a PSO algorithm for training again. Simulations are conducted with estimated parameters for a diverse set of training and test patterns. The results are compared with the optimal PI controller's performance and reported in the corresponding section. Encouraging results are obtained, suggesting further research in the proposed direction. For low-disturbance scenarios, even simple controllers can have acceptable performance, but the real quality of a proposed controller should be shown under high-amplitude and difficult disturbances, which is the case in this study. The proposed controller shows higher performance, especially under high disturbances, with an 8.6% reduction in error rate on average compared with the optimal PI controller, and under high-amplitude disturbances, the performance difference is of more than 2.5 folds. [ABSTRACT FROM AUTHOR]

PI-PD controllers have superior performance compared to traditional PID controllers, especially for controlling unstable and integrating industrial processes with time delays. However, computing the four tuning parameters of this type of controller is not an easy task. Recently, there has been significant interest in determining the tuning rules for PI-PD controllers that utilize the stability region. Currently, most tuning rules for the PI-PD controller are presented graphically, which can be time-consuming and act as a barrier to their industrial application. There is a lack of analytical tuning guidelines in the literature to address this shortfall. However, the existing analytical tuning guidelines do not consider a rigorous design approach. This work proposes new robust analytical tuning criteria based on predefined gain and phase margin bounds, as well as the centroid of the stability region. The proposed method has been tested using various simulation studies related to a DC–DC buck converter, a DC motor, and a heat exchanger. The results indicate that the proposed tuning rules exhibit strong performance against parameter uncertainty with minimal overshoots. Furthermore, the suggested technique for simultaneous control of yaw and pitch angles has been tested in a real-time application using the twin rotor multi-input multi-output system (TRMS). Real-time results indicate that, compared to other methods under investigation, the suggested approach provides nearly minimal overshoots. [ABSTRACT FROM AUTHOR]

Aiming at the attitude cooperative control problem of multi-spacecraft system, the attitude estimation of the spacecraft is estimated by invariant extended Kalman filter (InEKF), and the attitude estimation of the spacecraft is made independent of the transfer matrix. Then, the multi-spacecraft special orthogonal group (SO(3)) attitude model is constructed by combining the undirected communication topology, and the attitude coordination error on SO (3) is deduced. Among them, an attitude coordination control algorithm based on the consistency theory is proposed based on the special orthogonal group SO(3). The radial basis function neural network is used to tit and compensate virtual disturbances. The proposed algorithm considers spatial disturbances to ensure that the collaborative controller is applicable to the entire attitude space. Multi-satellite attitude collaboration, tracking desired attitude, and collaboration under the constraints of actuator capabilities are realized. The system is analyzed based on LaSalle invariant set theory, proving that the system has global asymptotic stability. Finally, the effectiveness of the proposed attitude collaborative control algorithm is verified by using a six-satellite spacecraft system. [ABSTRACT FROM AUTHOR]

This article presents an extremum‐seeking control (ESC) algorithm for unmodeled nonlinear systems with known steady‐state gain and generally non‐convex cost functions with bounded curvature. The main contribution of this article is a novel gradient estimator, which uses a polyhedral set that characterizes all gradient estimates consistent with the collected data. The gradient estimator is posed as a quadratic program, which selects the gradient estimate that provides the best worst‐case convergence of the closed‐loop Lyapunov function. We show that the polyhedral‐based gradient estimator ensures the stability of the closed‐loop system formed by the plant and optimization algorithm. Furthermore, the estimated gradient provably produces the optimal robust convergence. We demonstrate our ESC controller through three benchmark examples and one practical example, which shows our ESC has fast and robust convergence to the optimal equilibrium. [ABSTRACT FROM AUTHOR]

Quantum systems are exceedingly difficult to engineer because they are sensitive to various types of noises. In particular, time-dependent noises are frequently encountered in experiments but how to overcome them remains a challenging problem. In this work, we propose a flexible robust control technique to resist time-dependent noises based on inverse geometric optimization working in the filter-function formalism. The basic idea is to parameterize the control filter function geometrically and minimize its overlap with the noise spectral density. This then effectively reduces the noise susceptibility of the controlled system evolution. We show that the proposed method can produce high-quality robust pulses for realizing desired quantum evolutions under realistic noise models. Also, we demonstrate this method in examples including dynamical decoupling and quantum sensing protocols to enhance their performances. [ABSTRACT FROM AUTHOR]

This article develops an event-triggered cooperative robust formation control scheme for nonlinear multi-agent systems with dynamic uncertainties via reinforcement learning. By formulating a modified value function for each agent, the cooperative robust formation control problem of uncertain multi-agent systems is transformed into a cooperative optimal formation control problem of its nominal plant. To save communication and computing resources, a novel triggering condition is developed for each agent, and the controller is renovated only when an event occurs. Subsequently, the event-triggered optimal formation control law of each agent is derived by solving the coupled Hamilton-Jacobi-Bellman equation via single-critic structure. Furthermore, theoretical analysis indicates that the developed event-triggered cooperative robust formation control approach ensures the asymptotic stability of the formation error for each uncertain agent. Eventually, two simulation cases are adopted to confirm the effectiveness of the developed control approach. [ABSTRACT FROM AUTHOR]

Momentum stocks are exposed to aggregate volatility risk. This paper estimates an exponential generalized autoregressive conditional heteroskedastic model of market volatility to introduce a new volatility risk factor. Winners have negative loadings on this factor, whereas losers have positive loadings. Because volatility risk carries a negative price of risk, the new factor explains 73% of momentum profits. The paper rationalizes the volatility risks of momentum portfolios using growth option arguments and explains why momentum profits are short‐lived, depend on market states, and concentrate among firms with high idiosyncratic volatility. Results are robust to controlling for other risk factors and using alternative estimation procedures. [ABSTRACT FROM AUTHOR]

The past two decades have seen growing calls for the “tobacco endgame.” Its advocates are united by their commitment to two ideas. First, tobacco‐related harms represent a catastrophic health emergency, and second, current tobacco‐control approaches are an inadequate response to the scale of that emergency. To endgame advocates, tobacco policy should have more ambitious goals than merely “controlling” tobacco. Instead, it should aim to bring about a smoke‐free world. While a range of different policies are included under the umbrella of the “tobacco endgame,” the most radical proposal is for a complete ban on tobacco. Its advocates argue that in addition to improving global public health, an effective ban on tobacco would also promote overall autonomy and would have important egalitarian benefits. This article critically examines these arguments for a tobacco ban. I argue that they rely on idealizing assumptions about the likely effects of a ban. Because an effective ban would require robust enforcement to control the illegal market in tobacco, it would be more likely to undermine autonomy and equality than it would be to promote them. By relying on idealizing assumptions and ignoring the likely consequences of a tobacco ban, advocates of a ban obscure, rather than clarify, both the policy debate and the ethical stakes. I conclude by considering the ways that idealizing assumptions should—and should not—play a role in debates about ethical issues in public policy. [ABSTRACT FROM AUTHOR]

Robust control charts are getting vital importance in statistical process control theory as they are insensitive to the departure from normality. Therefore, the main objective of current work is to determine the effects of non‐normal process on the Exponentially Weighted Moving Average (EWMA) control chart. To achieve this goal, the sensitivity and reliability comparisons are made under the non‐normal process by comparing five robust M‐scale estimators, suggested in literature to modify the EWMA control limits for monitoring process mean and on the basis of percentile bootstrap estimator. The paper addresses the run length (RL) distribution of a robust EWMA control chart under the non‐normal process for which the exponential distribution is used as non‐normal process. The standard deviation of RL, out‐of‐control average run length (ARL), and shift detection probabilities are examined to assess the sensitivity and reliability of robust EWMA control charts for mean of monitoring process. The results of this research indicate that the classical EWMA control chart's performance is substantially impacted by the non‐normal distribution and the proposed EWMA control charts show higher sensitivity than classical one in terms of having smaller values of out‐of‐control ARLs. A real‐life example from the medical sciences field is provided the practical usage of the proposed control charts. The simulation analysis and practical example have shown that the suggested control charts are effective in quickly monitoring the out‐of‐control process. [ABSTRACT FROM AUTHOR]

This work introduces a new actuator fault estimation approach coupled with a fault‐tolerant control (FTC) strategy for uncertain systems in an output feedback framework. The proposed method involves constructing a Multi‐Layer Neural Network (MLNN) observer‐based fault estimation unit to accurately predict system states and potential faults in the actuator channel. An online control allocation (CA) scheme is then developed, utilizing the derived estimates to actively reconfigure the virtual control signals among the healthy redundant actuators in the event of actuator malfunction. Furthermore, an adaptive neural network‐based output integral sliding mode control scheme is designed based on the virtual control. This integration enhances the overall system's robustness and significantly reduces the chattering effect. The stability analysis of the proposed fault estimations scheme is initially performed using MLNN structure, followed by a comprehensive closed‐loop stability analysis to establish the stability of the entire system. Finally, the effectiveness of the proposed method is validated on a nonlinear six‐degree‐of‐freedom model of multirotor unmanned aerial vehicle aircraft. Numerical simulations under different fault and failure scenarios validate the efficacy of the proposed method. The comparative analysis of the proposed scheme is conducted with the static output feedback control allocations and adaptive allocation strategy. This analysis focuses on evaluating performance using metrics such as root mean square error and mean square deviation, particularly in the presence of faults and failures. The results demonstrate the superior performance of the proposed scheme in fault/failure conditions. [ABSTRACT FROM AUTHOR]

The traditional Nussbaum‐type functions encounter challenges when extended to systems with multiple unknown control directions, as the coupling between the Nussbaum‐type function and Nussbaum‐type gain may lead to mutual elimination. To address this issue, a novel Nussbaum‐type function is introduced to handle multiple unknown control directions for stochastic systems. The stability of the proposed Nussbaum‐based design can be guaranteed using the Lyapunov analysis. To conserve computational resources, a static composite event‐triggered mechanism is integrated with intermittent feedback in the Nussbaum‐based design. In contrast to conventional event‐triggering mechanisms that depend solely on control signals, the presented design incorporates tracking errors into the event‐triggering conditions. Moreover, to further alleviate computational burdens, we further develop a dynamic composite event‐triggered mechanism. With the overall design scheme, bounded tracking errors and reduced computational burden can be ensured. Simulation examples validate the efficacy of the proposed adaptive Nussbaum composite event‐based robust control design. [ABSTRACT FROM AUTHOR]

This research is dedicated to developing a min–max robust control strategy for a dynamic game involving pursuers, evaders, and defenders in a multiple-missile scenario. The approach employs neural dynamic programming, utilizing multiple continuous differential neural networks (DNNs). The competitive controller devised addresses the robust optimization of a joint cost function that relies on the trajectories of the pursuer–evader–defender system, accommodating an uncertain mathematical model while adhering to control restrictions. The dynamic programming min–max formulation facilitates robust control by accounting for bounded modeling uncertainties and external disturbances for each game component. The value function of the Hamilton–Jacobi–Bellman (HJB) equation is approximated by a DNN, enabling the estimation of the closed-loop formulation for the joint dynamic game with state restrictions. The controller’s design is grounded in estimating the state trajectory under the worst possible uncertainties and perturbations, providing a robustness factor through the robust neural controller. The learning law class for the time-varying weights in the DNN is generated by studying the HJB partial differential equation for the missile motion for each player in the dynamic game. The controller incorporates the solution of the obtained learning laws and a time-varying Riccati equation, offering an online solution to the control implementation. A recurrent algorithm, based on the Kiefer–Wolfowitz method, adjusts the initial conditions for the weights to satisfy the final condition of the given cost function for the dynamic game. A numerical example is presented to validate the proposed robust control methodology, confirming the optimization solution based on the DNN approximation for Bellman’s value function. [ABSTRACT FROM AUTHOR]

This study presents a predefined-time control strategy for rigid spacecraft, employing dynamic predictive techniques to achieve robust and precise attitude tracking within predefined time constraints. Advanced predictive algorithms are used to effectively mitigate system uncertainties and environmental disturbances. The main contributions of this work are introducing adaptive global optimization for period updates, which relaxes the original restrictive conditions; ensuring easier parameter adjustments in predefined-time control, providing a nonconservative upper bound on system stability; and developing a continuous, robust control law through terminal sliding mode control and predictive methods. Extensive simulations confirm the control scheme reduces attitude tracking errors to less than 0.01 degrees at steady state, demonstrating the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Robust regulation is predictively investigated in time-delay models including uncertainties, non-zero reference, and disturbance. Hence, to handle the complexities induced because of the time-delays, disturbances, and uncertainties, enhancing the transient performance would be a main control goal. To this purpose, the required transient and steady-state specifications are achieved through an integral control structure with adjustable gains. The constraints on the signals and aims of the control algorithm are also described by some linear matrix inequalities. Guaranteeing the stability, a minimisation procedure is found to specify the predictive controller. Several simulations are performed to establish the effectiveness of the introduced plan in comparison with the similar strategy. [ABSTRACT FROM AUTHOR]

In this paper, the model‐free robust control problem is investigated for nonlinear systems with a relaxed condition of initial admissible control. An advanced integral reinforcement learning method is developed, which merges the adaptive network‐based fuzzy inference system (ANFIS) and pre‐training of the initial weights. To loose the condition for choosing the initial control law, pre‐training of initial weights is established by utilizing the ANFIS to provide the information corresponding to the system model, which is applicable to the model‐free issue. Based on the actor‐critic structure, the approximate optimal control law is obtained by employing adaptive dynamic programming. Redesigning the obtained control law, the robust controller can be derived to stabilize the system with the uncertain term. Eventually, two examples are utilized to verify the effectiveness of the constructed algorithm. [ABSTRACT FROM AUTHOR]

Lunar-based equipment undertakes the task of movement and transportation in the construction of unmanned lunar base. In the process of moving, the mechanical legs of the equipment are influenced by the lunar soil with special mechanical properties. In order to avoid these uncertainties caused by the lunar soil and other lunar environmental conditions affecting the safety during the mission, a new robust control method with the form of sectionalized expression is proposed based on the dynamic model of the leg-soil system. Lyapunov second method is introduced to demonstrate that the proposed control method can maintain the stability of the leg-soil system successfully. In order to clarify the contact force in the dynamics model, CAS-1 lunar soil simulant that can accurately simulate real lunar soil is used in the calibration test to obtain the precise mechanical parameters. Simulation and experiment are also carried out to verify the proposed control method and the traditional control methods are introduced to make a comparison. Both the simulation and experiment results show that the proposed control method has a better control effect than traditional methods. The proposed method improves the accuracy by an average of 75.7% and 55.9% compared to the traditional methods and the error is limited to 0.2%. By maintaining the stability and accuracy of the leg-soil system, the stability of the lunar-based equipment is improved when performing construction tasks. This study lays the foundation for the construction of unmanned lunar base in advance. [ABSTRACT FROM AUTHOR]

• The 6-DOF attitude-orbit coupled model of SFF is established. The model has no redundant state and can be achieved globally without singularity. • A FxTDO is developed to estimate the external disturbance. Any prior knowledge of the disturbance is not required. The estimation error of the disturbance can converge to zero in fixed time regardless of the initial states. • A composite control scheme which consists of the NFFTSM surface and a feed-forward term based on the FxTDO is proposed such that each follower spacecraft can track the desired positions and attitudes in fixed time. This paper presents a distributed fixed-time control protocol for 6-DOF(degree-of-freedom) attitude-orbit coupled spacecraft formation flying with external disturbances. Firstly, the 6-DOF attitude-orbit coupled dynamics is established. The communication topology between the spacecraft in the formation is described by a directed graph. Secondly, a fixed-time disturbance observer (FxTDO) is designed to ensure that the estimation errors of the unknown external disturbances can converge to zero in fixed time. Thirdly, based on non-singular fixed-time terminal sliding mode (NFFTSM) surface, the fixed-time coordination control protocol is proposed combined with the fixed-time disturbance observer, which can guarantee that each spacecraft can track their desirable positions and attitudes in fixed time. The stability of the closed-loop system is proved through Lyapunuov method. Finally, simulation results for a formation with one virtual leader and five followers demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Investigating a long-standing conceptual question in bacterial physiology, we examine why DnaA, the bacterial master replication initiator protein, exists in both ATP and ADP forms, despite only the ATP form being essential for initiation. We engineered the Δ4 Escherichia coli strain, devoid of all known external elements facilitating the DnaA-ATP/ADP conversion and found that these cells display nearly wild-type behaviors under nonoverlapping replication cycles. However, during rapid growth with overlapping cycles, Δ4 cells exhibit initiation instability. This aligns with our model predictions, suggesting that the intrinsic ATPase activity of DnaA alone is sufficient for robust initiation control in E. coli and the DnaA-ATP/ADP conversion regulatory elements extend the robustness to multifork replication, indicating an evolutionary adaptation. Moreover, our experiments revealed constant DnaA concentrations during steady-state cell elongation in both wild-type and Δ4 cells. These insights not only advance our understanding of bacterial cell-cycle regulation and DnaA but also highlight a fundamental divergence from eukaryotic cell-cycle controls, emphasizing protein copy-number sensing in bacteria versus programmed protein concentration oscillations in eukaryotes. [ABSTRACT FROM AUTHOR]