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To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

This paper investigates the data-driven consensus tracking problem for heterogeneous multi-agent systems. All of the heterogeneous dynamics, disturbances and measurement noises are considered for the output tracking consensus of nonlinear multi-agent network under a data-driven scheme. A dynamic linearisation method is introduced to deal with the nonlinear nonaffine structures of the agents and a heterogeneous linear data model for the agent is obtained due to the heterogeneous dynamics of the agent itself. On this basis, a distributed model-free adaptive predictive control (DMFAPC) algorithm is constructed by the use of consensus errors and the robustness analysis is conducted in the presence of disturbances. Further, the results are modified by using measured outputs to replace the system outputs, and thus a measured output-based DMFAPC is presented to deal with the omnipresent measurement noises in practical applications. The two proposed DMFAPC methods are data driven since no mechanistic model information is required wherein. And thus, no unmodelled dynamics affects the consensus performance. Instead, they can improve the control performance by utilising additional predictive information. The two proposed DMFAPC methods are verified using numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is devoted to the terrain aided navigation (TAN) systems based on the state estimation algorithms. In particular, the emphasis is laid on the design of the Bayesian Rao–Blackwellized point-mass filter for nonlinear state-space models of a specific structure typically used in the terrain aided navigation. The proposed filter preserves advantages of the point-mass filter, including the high estimation accuracy, robust initialization, deterministic nature of the algorithm, and predictable computational complexity, while the computational complexity is significantly reduced. The performance of the Rao–Blackwellized point-mass filter is illustrated using a simulated numerical example and a TAN system based on the real data. [ABSTRACT FROM AUTHOR]

This paper concerns the input-to-state stability (ISS) problems for a class of discrete-time nonlinear input-saturated switched descriptor systems (SDSs). An ISS criterion that only partial subsystems are exponentially stable is provided based on average dwell time method and discrete-time iterative algorithm. The proof difficulty is greatly decreased, and the switching controllers for the subsystems of the closed-loop SDSs are much simple and viable. Furthermore, the cost of the controllers is also greatly reduced. Finally, extensive simulation results are presented to illustrate the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

Precise positioning of a robot plays an very important role in advanced industrial applications, and this paper presents a new kinematic calibration method based on the extended Kalman filter (EKF) and particle filter (PF) algorithm that can significantly improves the positioning accuracy of the robot. Kinematic and its error models of a robot are established, and its kinematic parameters are identified by using the EKF algorithm first. But the EKF algorithm has a kind of linear truncation error and it is useful for the Gauss noise system in general, so its identified accuracy will be affected for the highly nonlinear robot kinematic system with a non-Gauss noise system. The PF algorithm can solve this with non-Gauss noise and a high nonlinear problem well, but its calibration accuracy and efficiency are affected by the prior distribution of the initial values. Therefore, this paper proposes to use the calibration value of the EKF algorithm as the prior value of the PF algorithm, and then, the PF algorithm is used further to calibrate the kinematic parameters of the robot. Enough experiments have been carried out, and the experimental results validated the viability of the proposed method with the robot positioning accuracy improved significantly. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for estimating the instantaneous fundamental frequency of a noisy non-stationary periodic signal whose components are harmonically related. To this end, the authors' propose a harmonic state-space model for the input signal and use it to derive an extended Kalman filter (EKF), an unscented Kalman filter (UKF) and a particle filter (PF). In this model, the input signal is characterised by a time-varying fundamental frequency and amplitude which is a practical assumption for real-world periodic signals. In contrast to most of existing methods such as short-time Fourier transform, the proposed algorithm does not use any windowing technique. Therefore the trade-off between time and frequency resolutions is less controversial and so can be used for real-time frequency tracking. It also reveals some fine and continuous variations in signal pitch such as Vibrato and Glissando. Simulation results show that the proposed algorithm performs well even when most of the signal energy is contained in the higher-order harmonics. The performance of the proposed algorithm using EKF, UKF and PF is also evaluated and the results are compared in diverse conditions. [ABSTRACT FROM AUTHOR]

This article discusses the issue of robust adaptive neural network (NN) consensus tracking control for nonlinear strict-feedback multi-agent systems with quantised input. By combining the neural network approach with robust techniques, a novel switching function is introduced to guarantee the tracking performance of this system. To estimate the unmeasured state, an NN-based adaptive state observer is developed. Based on backstepping dynamic surface control algorithms, a robust output feedback controller is constructed to guarantee that all signals in the closed-loop system remain globally uniformly ultimately bounded. Finally, numerical simulations are carried out to demonstrate the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]

This paper presents the mathematical modeling of a multivariable process used in level control, under the assumptions that all pipes are filled with fluid and the inertial effects caused by flow variations, in case of small accelerations, are neglected. Because of the way the two tanks are interconnected and interact with each other, the resulting mathematical model is nonlinear. In the paper it is proposed a robust control algorithm for this plant developed based on H-infinity loop shaping procedure. The required computations and the study of the behavior of the system are done in the Matlab simulation environment. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed receding horizon control (RHC) problem of a vehicle platoon with nonlinear dynamics and subject to system constraints, where each vehicle can communicate with its immediate predecessor and follower. A novel optimization problem and detailed distributed RHC algorithm are designed in order to keep a platoon formation, and further to ensure neighbor γ -gain stability (which is a new notion proposed in this paper and generalizes the string stability). The sufficient conditions on ensuring closed-loop stability and neighbor γ -gain stability are established, respectively. Finally, simulation studies are provided to verify the theoretical results. It is shown that it is possible to achieve certain control performance (i.e., γ -gain stability) and keep a formation simultaneously for the nonlinear vehicle platoon using distributed RHC. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of tracking a moving target by means of a network of geographically dispersed nodes with Doppler sensing, communication, and processing capabilities. The problem is addressed both in a hierarchical setting, i.e., in the presence of a fusion center that can fuse data from all the local nodes, and in a peer-to-peer setting wherein each node (peer) has to locally estimate the target kinematic state only on the grounds of local measurements and of data received from its neighbors. A suitable nonlinear observability decomposition is introduced in order to single out state coordinates that can be fully observed from a single Doppler sensor. Based on such a decomposition, a novel dual-stage filtering approach to distributed Doppler-only tracking is developed. In particular, it is shown how the proposed approach can be adopted both in the presence of a fusion center by means of covariance intersection and in the peer-to-peer case by exploiting consensus algorithms. The effectiveness of the proposed algorithms is evaluated via computer simulations. [ABSTRACT FROM AUTHOR]

SUMMARY Recently, the passivity results for linear time-invariant systems were successfully extended to nonlinear and nonstationary systems, thus guaranteeing stability of adaptive control of nonlinear square systems. Based on this theoretical development, this paper presents the development of a new class of direct adaptive controllers, which employ a new decentralized adaptation law mechanism that is developed from the simple adaptive control technique. The resulting direct adaptive control methodology is referred to as decentralized simple adaptive control. A simplification of this new control algorithm, referred to as decentralized modified simple adaptive control, is also presented. In addition, it is shown that both control methodologies can be modified to avoid divergence in practical situations, where the trajectory tracking errors cannot reach zero. Using Lyapunov direct method and Lasalle's invariance principle for nonautonomous systems, the formal proof of stability is established. As well, a numerical simulation study for a trajectory tracking problem by a rigid-joint manipulator is presented to illustrate the new adaptive control approaches. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The problem of Mittag–Leffler stabilization (MLS) is studied for a class of nonlinear non-integer order systems. The stabilizer is constructed by using the Lyapunov function and backstepping algorithm. The continuous controller is designed to ensure that the state of the nonlinear fractional-order closed-loop system converges to the equilibrium. Two simulation examples are given to illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the adaptive consensus problem of multi-agent nonlinear systems with odd impulsive sequence. To reduce the required information transmitted among the nodes, the distributed impulsive control protocol is designed. Considering the unknown system parameters in real system, the adaptive control technique is also used and some novel sufficient consensus conditions are derived to achieve the consensus of multi-agent nonlinear systems. The proposed odd impulsive control can obtain larger control region than the common impulsive consensus method with fixed impulsive instants, which is more flexible and reliable in practical application. Finally, two simulations are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear model predictive control (NMPC) has been used to control an induction motor (IM). The IM model that is used in the control is third or fifth order model that is based in the vector analysis of the IM. In the third order model, the rotor speed and fluxes are considered as system states where the source frequency and the stator currents are control variables. In the fifth order, the state variables involve stator currents, rotor speed and fluxes where the control variables are stator voltages and source frequency. The formulated nonlinear optimal control problems that are used in the NMPC frameworks are not based on the field ordination technique, however, the input frequency is computed by the MPC optimizer. Moreover, the convergence or stability of the motor speed is guaranteed using stability auxiliary constraint. Simulation studies show the performance of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This paper was aimed at using an adaptive control to develop a backstepping method for a special class of nonlinear systems, which requires no information on the upper bound of parametric uncertainty or disturbance. In this research, a novel control approach, including a developed backstepping method and an adaptive controlling method, is introduced as an adaptive generalized backstepping method (AGBM). Compared to the standard backstepping method, AGBM is far more efficient because the standard method is applicable in strictly feedback systems, but AGBM expands this class of systems. Another advantage of AGBM is that it can be applied to a special class of nonlinear systems with unmatched uncertainty as well as unknown upper bound disturbance. In this method, an adaptive controlling method is used to compensate uncertainty and parametric uncertainty besides stabilizing the controller against disturbances applied to the system. Finally, numerical simulation results demonstrate the advantages and feasibility of the presented algorithm, showing that the AGBM controller guarantees robustness and system stability in the presence of disturbance and uncertainty. [ABSTRACT FROM AUTHOR]

Pore network construction provides the ability to characterize and study the pore space of inhomogeneous and geometrically complex granular media in a range of scientific and engineering applications. Various approaches to the construction have been proposed, however subtle implementational details are frequently omitted, open access to source code is limited, and few studies compare multiple algorithms in the context of a specific application. This study presents, in detail, a new pore network construction algorithm, and provides a comprehensive comparison with two other, well-established Delaunay triangulation-based pore network construction methods. Source code is provided to encourage further development. The proposed algorithm avoids the expensive non-linear optimization procedure in existing Delaunay approaches, and is robust in the presence of polydispersity. Algorithms are compared in terms of structural, geometrical and advanced connectivity parameters, focusing on the application of fluid flow characteristics. Sensitivity of the various networks to permeability is assessed through network (Stokes) simulations and finite-element (Navier-Stokes) simulations. Results highlight strong dependencies of pore volume, pore connectivity, throat geometry and fluid conductance on the degree of tetrahedra merging and the specific characteristics of the throats targeted by the merging algorithm. The paper concludes with practical recommendations on the applicability of the three investigated algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for an optimal systematic determination of models' base for multimodel identification. This method is based on the neural classification of data set picked out on a considered nonlinear system. The obtained cluster centers are exploited to provide the weighting functions and to deduce the corresponding dispersions and their models' base. A simulation example and an experimental validation on a chemical reactor are presented to evaluate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This study presents a novel framework, namely, the fusion of a conventional controller and a linear model predictive controller, for the position control of a tilt‐rotor tricopter. While the conventional controller in the outer loop is responsible for the position control, the inner‐loop model predictive control–based controller handles the angular dynamics and vertical body velocity. Furthermore, a novel control allocation algorithm for the proposed controller is introduced. In addition, this study also covers mathematical modeling and trim analysis of the tilt‐rotor tricopter dynamics. An evaluation of the designed control system is accomplished with a nonlinear 6‐degree‐of‐freedom simulation model of the tilt‐rotor tricopter in which realistic actuator limitations are considered. The efficiency of the proposed control algorithm is elaborated for a trajectory tracking problem where basic surveillance operation is considered. The simulation results show that the proposed model predictive controller is able to provide a satisfactory trajectory tracking performance under the realistic actuator limits. [ABSTRACT FROM AUTHOR]

In this paper, a self-organizing fuzzy neural network with adaptive gradient algorithm (SOFNN-AGA) is proposed for nonlinear systems modeling. First, a potentiality of fuzzy rules (PFR) method is introduced by using the output of normalized layer and the error reduction ratio (ERR) in the training process. And a structure learning approach is developed to determine the network size based on PFR. Second, a novel adaptive gradient algorithm (AGA) with adaptive learning rate is designed to adjust the parameters of SOFNN-AGA. Moreover, a theoretical analysis on the convergence of SOFNN-AGA is given to show the efficiency in both fixed structure and self-organizing structure cases. Finally, to demonstrate the merits of SOFNN-AGA, simulation and experimental results of several benchmark problems and a real world application are examined for nonlinear systems modeling with comparisons against other existing methods. Some promising results are reported in this study, indicating that the proposed SOFNN-AGA performs better favorably in terms of both convergence speed and modeling accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a tracking control strategy for nonlinear systems without needing a prior knowledge of the reference trajectory. The proposed method consists of a set of local controllers with appropriate overlaps in their stability regions and an on-line switching strategy which implements these controllers and uses some augmented intermediate controllers to ensure steering the system states to the desired set points without needing to redesign the controller for each value of set point changes. The proposed approach provides smooth transient responses despite switching among the local controllers. It should be mentioned that the stability regions of the proposed controllers could be estimated off-line for a range of set-point changes. The efficiencies of the proposed algorithm are illustrated via two example simulations. [ABSTRACT FROM AUTHOR]

This paper proposes a state estimation method for a sampled-data descriptor system by the Kalman filtering method. The sampled-data descriptor system is firstly discretized to obtain a discrete-time nonsingular model. Based on the discretized nonsingular system, a strong tracking unscented Kalman filter (STUKF) algorithm is designed for the state estimation. Then, a defined suboptimal fading factor is proposed and added to the prediction covariance for decreasing the weight of the prior knowledge on the conventional UKF filtering solution. Finally, a simulation example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the coordination of nonlinear multi-agent systems with multiple leaders and stochastic disturbance. Two impulsive control algorithms are proposed to make all agents to track the convex set determined by the multiple leaders under both fixed and switching topologies. Based on Lyapunov function and comparison principle of impulsive systems, some results on the convergence of the controlled systems are obtained. Finally, some numerical simulations demonstrate the validity of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

In this paper, an optimal nonlinear feedback guidance algorithm with complex state and control constraints is developed for Mars powered decent. The analysis of the optimal control problem for Mars powered descent is undertaken firstly. Then based on the real-time sampling optimal feedback control theory, the Mars powered descent guidance (PDG) algorithm is designed and analysed. A practical method is also proposed to solve the problem of the initialization of the PDG algorithm. Numerical simulations are performed to evaluate the effectiveness of the proposed PDG algorithm. The effects of the sampling period and the prediction errors on landing errors are studied in the numerical simulations. The fuel consumption performances of the proposed PDG algorithm and the Apollo guidance algorithm are also studied and compared. The simulation results show that the less fuel consumption is obtained with the proposed PDG algorithm. Monte Carlo simulation verifies the high landing precision of the proposed PDG algorithm. [ABSTRACT FROM AUTHOR]

This paper utilizes the super-twisting algorithm (STA) to obtain a traction controller for road vehicles. The control objective is to operate the vehicles such that a desired wheel slip ratio is achieved. The controller comprises a STA-based sliding-mode control law and a nonlinearity observer. Simulation and experimental studies illustrate the success of the controller. The controller successfully drove the vehicle to operate at the desired wheel slip ratio and efficiently handled the sudden changes of tire–road frictions. The results are compared to those obtained with a conventional sliding-mode controller. It is shown that the STA-based controller yields better control performance. [ABSTRACT FROM AUTHOR]

The purpose of this work is to estimate target coordinates and velocity. Target tracking is performed by an autonomous underwater vehicle (AUV). The observer is equipped with the direction finder that measures the azimuth and elevation angles of the target and the target range. Such problems are normally solved with the aid of non-linear filters due to nonlinearity of measurements. However, most filters produce estimations with unknown bias in the absence of estimations of accuracy. An important problem is related to unobservability of the target. A pseudomeasurement method is proposed to transform the problem of estimation into a linear problem. Such an approach makes possible to estimate coordinates and velocity of a moving target and solve the problem of unobservability. Results of computer simulation prove efficiency of the proposed algorithm in the problem of passive target tracking when only angles are measured. [ABSTRACT FROM AUTHOR]

In the variational data assimilation (VarDA), the typical way for gradient computation is using the adjoint method. However, the adjoint method has many problems, such as low accuracy, difficult implementation and considerable complexity, for high-dimensional models. To overcome these shortcomings, a new data assimilation method based on dual number automatic differentiation (AD) is proposed. The important advantages of the method lies in that the coding of the tangent-linear/adjoint model is no longer necessary and that the value of the cost function and its corresponding gradient vector can be obtained simultaneously through only one forward computation in dual number space. The numerical simulations for data assimilation are implemented for a typical nonlinear advection equation and a parabolic equation. The results demonstrate that the new method can reconstruct the initial conditions of the high-dimensional nonlinear dynamical system conveniently and accurately. Additionally, the estimated initial values can converge to the true values quickly, even if noise is present in the observations. [ABSTRACT FROM AUTHOR]

State estimation of nonlinear systems is a challenging task, especially when the Gaussian approximation fails. The unscented Kalman filter was proposed to deal with state estimation of nonlinear systems. We modify the traditional unscented Kalman filter to capture the third-order moment (skewness) of the state vector. Methods are also proposed to reduce the computation time of the suggested approach, and showing that the proposed algorithm is as fast as the unscented Kalman filter. Simulation results confirm that the method is better than, or at least as good as, the unscented Kalman filter. [ABSTRACT FROM AUTHOR]

Our work here is to propose a novel technique by which chaos complete and phase synchronizations can be accomplished via a low-cost scheme. We call the proposed technique a "single-state feedback track synchronization control algorithm". A single-state feedback track synchronization control algorithm is designed so that both complete and phase synchronizations can be accomplished using the same controller. Complete synchronization between two chaotic systems means complete symmetry between them, but phase synchronization means complete symmetry with a phase shift. In addition, the proposed method is applied to the synchronization of two identical chaotic Lorenz models. The effectiveness and robustness of the proposed algorithm is well illustrated via exhaustive numerical simulation experiments based on the Matlab toolbox of the powerful genetic algorithm. The robustness of the proposed algorithm motivated us to apply this method of synchronization in a secure communication application. [ABSTRACT FROM AUTHOR]