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This article introduces a new technique for stabilizing autonomous underwater vehicles in the descriptor model. Autonomous underwater vehicle stabilization is limited by several constraints, including time-variable uncertainty, time delay, and disturbances. The interaction of descriptor system requirements and the issues mentioned above adds complexities. This study outlines the delay-dependent [Formula: see text] robust stability achieved through memory-less and memory state feedback. Furthermore, a less conservative sufficient condition is obtained for admissibility using a new delay-dependent linear matrices inequality. Autonomous underwater vehicle is regular, impulse-free, and stable under all permissible conditions and satisfies prescribed [Formula: see text] performance conditions via a Lyapunov functional approach. The method applies to neutral and retarded dynamics with discrete and distributed time delays.

This paper considers the stability problem of a class of uncertain fractional reset control systems that undergo the ${L}_2$ gain performance improvement via the conformable fractional calculus. To remove the Zeno phenomenon in the system’s response, a new reset law based on the time regularization technique is designed. By developing a theory to design a new reset control, the stability of the proposed fractional order (FO) linear system with model uncertainties and bounded exogenous input is proved via an extended quadratic Lyapunov function and some efficient linear matrix inequalities. Likewise, the impulsive effect in the control input is removed by employing an appropriate low-pass filter (LPF). In the end, two numerical examples show that when the plant is modelled by the FO differential equations, by utilizing the constructive role of fractional reset controller, the robustness of FO reset system can also be attained.

This article proposes an event-triggered control framework to satisfy the tracking formation performance for a group of uncertain non-linear n-link robotic manipulators. The robotic manipulators are configured as a multi-agent system and they communicate over a directed graph (digraph). Furthermore, the non-linear robotic manipulator-multi-agent systems are subject to stochastic environmental loads. By introducing extra virtual controllers in the final step of the backstepping design, a total number of n event-triggering mechanisms are introduced independently for each link of all the robotic manipulator agents to update the control inputs in a fully distributed manner. More precisely, the actuator of each link of a particular agent is capable of being updated independent of other link actuator updates. A rigorous proof of the convergence of all the closed-loop signals in probability is then given and the Zeno phenomenon is excluded for the control event-triggered architectures. The simulation experiments finally quantify the effectiveness of proposed approach in terms of reducing the number of control updates and handling the stochastic environmental loads.

In this paper, a novel fractional-order adaptive controller is presented for a class of nonlinear systems with unknown dynamics. The dynamics of the system is considered to be fully unknown. The mu...

Kalman filter and its different variants are commonly used as optimal methods for fault detection in various types of system components. In this paper, a newly introduced type of aforementioned filters, called modal Kalman filter, is extended and utilized in order to estimate the states of nonlinear systems, for sensor fault detection purposes, in a class of nonlinear certain systems. This method, in contrast to the extended Kalman filter, which employs only the linear term of Taylor expansion, retains higher-order terms; as a result, the estimation error will reduce accordingly. Practicality and effectivity of this method, and its superiority over Kalman filter, in terms of accuracy and promptness of sensor fault detection, are also verified with simulation results.

This study presents a novel fractional-order nonlinear sliding mode controller (FONSMC) based on an extended nonlinear disturbance observer (ENDOB) for a class of fractional order systems with matched and mismatched disturbances. Firstly, an ENDOB is introduced to estimate both the matched and mismatched disturbances. Then, the fractional-order nonlinear sliding surface is designed to satisfy the sliding condition in finite time. Accordingly, the corresponding FONSMC is proposed using the Lyapunov stability theorem. The proposed method shows an impressive disturbances rejection and also guarantees finite-time stability of closed-loop systems. Finally, the effectiveness of the proposed FONSMC-ENDOB structure is illustrated via numerical simulation. The simulation results exhibit the superiority of the proposed controlling method.

In this study a novel type-2 fuzzy control approach on basis of the adaptive immersion and invariance (I&I) control method is proposed to control of brushless DC motors (BLDCMs). The parameters of the mathematical model of the BLDCM are considered to be unknown and furthermore the dynamics of BLDCM are disturbed by changes of some variables such load torque and phases resistance. The stability is analyzed based on the adaptive I&I theorem and some tuning laws are derived for uncertain parameters. Furthermore, the approximation error is tackled by the proposed fuzzy compensator. The parameters of the fuzzy compensator are tuned through the Lyapunov stability method. The reference signal tracking performance of the suggested control technique is examined in three cases. In the first case the load torque and phases resistance are constant, in the second case the phases resistance is considered to be time-varying and the load torque is abruptly changed and finally in the third case, a comparison with some other well-known control techniques is taken to account. It is shown that the proposed controller results in desired performance.

SUMMARYThis paper proposes an adaptive robust impedance control for a single-link flexible arm when it encounters an environment at an unknown intermediate point. First, the intermediate collision point is estimated using a collision detection algorithm. The controller, then, switches from free to constrained motion mode. In the unconstrained motion mode, the exerted force to environment is nearly zero. Thus, the reference trajectory is a prescribed desired trajectory in position control. In the constrained motion mode, the reference trajectory is determined by the desired target dynamic impedance. The simulation results demonstrate the efficiency of proposed control scheme.

In this paper, based on Modal series, a new filter is proposed for a nonlinear system state estimation. Modal series is a new method to obtain a closed-form approximate solution of a nonlinear differential equation. Up to now, this series is only obtained in the neighborhood of an equilibrium point. In the proposed method, this series is attained in the neighborhood of the current estimated state vector that is named as Stochastic Extended Modal Series (SEMS). Based on SEMS and proper approximations, the proposed nonlinear filter is converted to a series of linear filters, and the extracted filter is named as Extended Modal Kalman Filter (EMKF). The performance of EMKF is analytically compared with that of Extended Kalman Filter (EKF), and its applicability presented with some simulations. Finally, it is proved that the EKF is a special case of EMKF.

SUMMARYThis paper presents a fractional-order sliding mode control scheme equipped with a disturbance observer for robust impedance control of a single-link flexible robot arm when it comes into contact with an unknown environment. In this research, the impedance control problem is studied for both unconstrained and constrained maneuvers. The proposed control strategy is robust with respect to the changes of the environment parameters (such as stiffness and damping coefficient), the unknown Coulomb friction disturbances, payload, and viscous friction variations. The proposed control scheme is also valid for both unconstrained and constrained motions. Our novel approach automatically switches from the free to the constrained motion mode using a simple algorithm of contact detection. In this regard, an impedance control scheme is proposed with the inner loop position control. This means that in the free motion, the applied force to the environment is zero and the reference trajectory for the inner loop position control is the desired trajectory. However, in the constrained motion the reference trajectory for the inner loop is determined by the desired impedance dynamics. Stability of the closed loop control system is proved by Lyapunov theory. Several numerical simulations are carried out to indicate the capability and the effectiveness of the proposed control scheme.

This study is about the identification problem of continuous-time switched linear systems from low-rate sampled data. The main problem in the identification of such systems, when the sampling rate is low, is that the sampling instances do not coincide with the switching times. Therefore, some of the measured samples are generated from more than one subsystem. This problem was first observed during the sampling of a step-up DC–DC converter at the rate of 100 kHz. The current study aims to explain the theoretical aspects of the identification problem of continuous-time switched linear systems, and to offer a new method for estimating of subsystem parameters plus the switching times. The proposed method accurately determines the switching times which might be between two consecutive sampling instances. The results obtained from the proposed method are used to determine the switching times and parameters of an experimental DC–DC boost converter.

The distributed finite-time control problem through adaptive neural identifier for a group of nonlinear agents with strict-feedback structure is assessed here. The main considered and assessed technical problems in this proposed control strategy are that followers’ states are not fully available for control design, and at the same time, each follower is represented by uncertain nonlinear switched dynamics. Due to the structure of the proposed followers here, a switched linear state observer is constructed to estimate the unavailable states. To finite convergence time guarantee, the backstepping design and finite-time approach are adopted in the distributed control design in a simultaneous manner. The control architecture is chosen to guarantee graph stability through multiple Lyapunov functions. It is revealed that the followers’ outputs are forced to follow the leader output in the finite time, and all signals in the overall closed-loop network system are assured to be bounded. Two simulation examples are presented to further demonstrate the validity of this proposed method.

This paper deals with sub-optimal control of a fuzzy linear dynamical system. The aim is to keep the state variables of the fuzzy linear dynamical system close to zero in an optimal manner. In the fuzzy dynamical system, the fuzzy derivative is considered as the granular derivative; and all the coefficients and initial conditions can be uncertain. The criterion for assessing the optimality is regarded as a granular integral whose integrand is a quadratic function of the state variables and control inputs. Using the relative-distance-measure (RDM) fuzzy interval arithmetic and calculus of variations, the optimal control law is presented as the fuzzy state variables feedback. Since the optimal feedback gains are obtained as fuzzy functions, they need to be defuzzified. This will result in the sub-optimal control law. This paper also sheds light on the restrictions imposed by the approaches which are based on fuzzy standard interval arithmetic (FSIA), and use strongly generalized Hukuhara and generalized Hukuhara differentiability concepts for obtaining the optimal control law. The granular eigenvalues notion is also defined. Using an RLC circuit mathematical model, it is shown that, due to their unnatural behavior in the modeling phenomenon, the FSIA-based approaches may obtain some eigenvalues sets that might be different from the inherent eigenvalues set of the fuzzy dynamical system. This is, however, not the case with the approach proposed in this study. The notions of granular controllability and granular stabilizability of the fuzzy linear dynamical system are also presented in this paper. Moreover, a sub-optimal control for regulating a Boeing 747 in longitudinal direction with uncertain initial conditions and parameters is gained. In addition, an uncertain suspension system of one of the four wheels of a bus is regulated using the sub-optimal control introduced in this paper.

In this paper, using the concept of horizontal membership functions, a new definition of fuzzy derivative called granular derivative is proposed based on granular difference. Moreover, a new definition of fuzzy integral called granular integral is defined, and its relation with the granular derivative is given. A new definition of a metric—granular metric—on the space of type-1 fuzzy numbers, and a concept of continuous fuzzy functions are also presented. Restrictions associated to previous approaches—Hukuhara differentiability, strongly generalized Hukuhara differentiability, generalized Hukuhara differentiability, generalized differentiability, Zadeh's extension principle, and fuzzy differential inclusions—dealing with fuzzy differential equations (FDEs) are expressed. It is shown that the proposed approach does not have the drawbacks of the previous approaches. It is also demonstrated how this approach enables researchers to solve FDEs more conveniently than ever before. Moreover, we showed that this approach does not necessitate that the diameter of the fuzzy function be monotonic. It is also proved that the result of each of the four basic operations on fuzzy numbers introduced based on the proposed approach leads to a fuzzy number. Moreover, the condition for the existence of the granular derivative of a fuzzy function is provided by a theorem. Additionally, by two examples, it is shown that the existence of the granular derivative of a fuzzy function does not imply the existence of the generalized Hukuhara differentiability of the fuzzy function, and vice versa. The terms doubling property and unnatural behavior in modeling phenomenon are also introduced. Furthermore, using some examples, the paper proceeds to elaborate on the efficiency and effectiveness of the proposed approach. Moreover, as an application of the proposed approach, the response of Boeing 747 to impulsive elevator input is obtained in the presence of uncertain initial conditions and parameters.

In the Extended Kalman Filter EKF, only the first-order term of the Taylor series is employed. Hence, the nonlinearities in the system dynamics are not fully considered. In the proposed method, to overcome this drawback, the higher-order terms of the Taylor series are considered and a new filter, based on the Modal series, is designed. In this paper, based on the Modal series and careful approximations, a nonlinear filter is converted to a series of linear filters, and the extracted filter is named the Modal Kalman Filter MKF. The efficiency and advantage of MKF are analytically proven and its applicability examined with some simulations.

In this paper, the global asymptotic stabiliser design of rational systems is studied in detail. To develop the idea, the state equations of the system are transformed to a new coordinate via polynomial transformation and the state feedback control law. This in turn is followed by the satisfaction of the linear growth condition (i.e. Lipschitz at zero). Based on a linear matrix inequality solution, the system in the new coordinate is globally asymptotically stabilised and then, leading to the global asymptotic stabilisation of the primary system. The polynomial transformation coefficients are derived by solving the bilinear matrix inequality problem. To confirm the capability of this method, three examples are highlighted.

Motivated by the needs of multi-agent systems in the presence of sensing and communication which is delayed, intermittent, and asynchronous, we present a Kuramoto-type model as the delay inherent in such systems is taken into account. First, we have investigated a condition on maximum delay for the frequency entrainment of non-identical Kuramoto oscillators with heterogeneous delays and a constant coupling gain. Our next mission is to investigate the model of delayed coupled Kuramoto oscillators, which are characterized by non-identical natural frequencies and non-homogeneous coupling strength. We assume that the difference between the coupling gains is less than a certain limited value \(M\), and on the basis of Lyapunov stability theorem, we present a strictly positive lower bound for \(M\) to achieve a consensus on the derivatives of the phases. This consensus property is even more surprising because the phases themselves do not necessarily reach a consensus. We apply our results to these oscillators and show that synchronization is guaranteed for appropriate initial conditions.

This work presents an improved model of characteristic equations for gas metal arc welding process. In this paper, a dynamic electrical model is introduced as a rectifier power source instead of pervious common simple models. In addition, an electrical resistance model is proposed for bridge in short circuit period to consider the effect of melting temperature and variation of the conducting area. Furthermore, the arc length equation during the arc period is modified considering the size of the cross zone between the arc and drop. Finally, the introduced modifications are simulated and compared with the experimental results.

This paper presents a new off-line nonlinear model predictive control (NMPC) approach for continuous-time affine-input nonlinear systems. In this approach, the NMPC-related nonlinear two-point boundary value problem derived from the Pontryagin’s maximum principle is solved by the extended modal series method. The resulting suboptimal control law explicitly depends on the initial conditions and is updated by replacing the initial conditions with the new state measurements in future sampling instants. Therefore, there is no need to repeat the recursive online optimization process in each sampling instant. Since the applicability of NMPC is generally restricted by computational burden of the online optimization, we propose an NMPC scheme, which not only reduces the online computational burden significantly, but also can be applied to fast dynamic systems with short prediction horizons. An efficient algorithm is presented which approximates the order of the modal series such that feasibility of the optimization problem is guaranteed. Closed-loop stability of the proposed NMPC approach is shown using the off-line terminal region calculations suggested in quasi-infinite horizon NMPC scheme. The applicability and effectiveness of the proposed approach are illustrated by two numerical examples.

This paper proposes an adaptive fault tolerant attitude controller, based on variable structure control, to address tracking control problem of spacecraft in the presence of unknown actuator failure, control input saturation and external disturbances. In contrast to traditional robust fault tolerant attitude controllers, the proposed controller is capable of controlling the transient response of the closed loop system by means of a dedicated parameter. Also this method does not require exact knowledge of the actuator faults and is implemented with uncertain value of fault information. By adjusting a simple parameter dynamically and using Lyapunov direct method and the properties of quaternion representation, the ultimate boundedness of attitude and angular velocity errors in presence of external disturbances is proven. Numerical simulations used to prove the success of proposed controller in achieving high attitude performance in the presence of external disturbances, inexact knowledge of fault information, actuator failures and control input saturation.

In this paper, a continuous globally stable tracking control algorithm is proposed for a spacecraft in the presence of unknown actuator failure, control input saturation, uncertainty in inertial matrix and external disturbances. The design method is based on variable structure control and has the following properties: (1) fast and accurate response in the presence of bounded disturbances; (2) robust to the partial loss of actuator effectiveness; (3) explicit consideration of control input saturation; and (4) robust to uncertainty in inertial matrix. In contrast to traditional fault-tolerant control methods, the proposed controller does not require knowledge of the actuator faults and is implemented without explicit fault detection and isolation processes. In the proposed controller a single parameter is adjusted dynamically in such a way that it is possible to prove that both attitude and angular velocity errors will tend to zero asymptotically. The stability proof is based on a Lyapunov analysis and the properties of the singularity free quaternion representation of spacecraft dynamics. Results of numerical simulations state that the proposed controller is successful in achieving high attitude performance in the presence of external disturbances, actuator failures, and control input saturation.

In this paper, an immersion and invariance (I&I) adaptive fault tolerant satellite attitude tracking control scheme is proposed. The proposed controller is capable of track the desired trajectory in the presence of unknown actuator multiplicative faults and unknown inertial matrix. Also based on Lyapunov direct method, all closed loop signals are proven to be globally asymptotically stable. The main advantage of this controller is improving closed loop performance while maintaining stability in the presence of unknown actuator faults. This method does not rely on certainty equivalence principle so it can be used to control the transient response of overall closed loop system by means of controlling the parameter estimation behavior which is not possible in traditional adaptive control. Numerical simulations are performed to demonstrate the effectiveness of proposed control scheme.

SUMMARY This paper proposes a new approach for estimating the robust domain of attraction (RDA) and directional enlargement of the DA for dynamical systems. The proposed method analyzes stability of dynamical systems by Markov modeling and employs invariant measure as the stability indicator. Markov chains analysis focuses on asymptotic behaviors of systems and ignores the transient ones. The proposed method expresses the problem of estimating RDA and directional enlargement of DA as an infinite dimensional linear problem. The resulting linear problem is converted to a finite dimensional optimization problem using approximated Markov transition function. As a novel application, the directional enlargement of DA is used in order to increase the critical clearing time of power systems. The efficiency of proposed methods is shown via simulations. Copyright © 2012 John Wiley & Sons, Ltd.

This paper investigates the dynamical behavior of two oscillators with nonlinearity terms, which are coupled with finite delay parameters. Each oscillator is a general class of second-order nonlinear delay-differential equations. The system of delay differential equations is analyzed by reducing the delay equations to a system of ordinary differential equations on a finite-dimensional center manifold, the corresponding to an infinite-dimensional phase space. In addition, the characteristic equation for the linear stability of the trivial equilibrium is completely analyzed and the stability region is illustrated in the parameters space. Our analysis reveals necessary coefficients of the reduced vector field on the center manifold for studying the bifurcations of the trivial equilibrium such as transcritical, pitchfork, and Hopf bifurcation. Finally, we consider the delay-coupled van der Pol equations.

Anobserver-basedadaptivefuzzymodelfollowingcontrollerisproposed for a class of MIMO nonlinear uncertain systems to cope with time-delay, uncertainty in plant structure and disturbances. Based on universal approximation theorem the unknown nonlinear functions are approximated by fuzzy systems, where the premise and the consequent parts of the fuzzy rules are tuned with adaptive schemes. To have more robustness, and at the same time to alleviate chattering, an adaptive discontinuous structure is suggested. Moreover, the availability of the states measurement is not required and an adaptive observeris usedto estimatethestates. Asymptoicstabilityoftheoverallsystem is ensured using suitable a Lyapunov-Krasovskii functional candidate.

This paper presents a novel fuzzy model and a fuzzy logic controller for an isolated signalized intersection. The controller controls the traffic light timings and phase sequence to ensure smooth flow of traffic with minimal waiting time and length of queue. Usually fuzzy traffic controllers are optimized to maximize traffic flows/minimize traffic waiting time under typical traffic conditions. Consequentially, these are not the optimal traffic controllers under exceptional traffic cases such as roadblocks and road accidents. We apply state-space equations to formulate the average waiting time vehicles in traffic network at fixed time control. also, We propose a novel fuzzy model and new fuzzy traffic controller that can optimally control traffic flows under both normal and exceptional traffic conditions. Results show that the performance of the proposed traffic controller at novel fuzzy model is better that of conventional fuzzy traffic controllers under normal and abnormal traffic conditions.

In this paper, position control of servomotors is addressed. A radial basis function neural network is employed to identify the unknown nonlinear function of the plant model, and then a robust adaptive law is developed to train the parameters of the neural network, which does not require any preliminary off-line weight learning. Moreover, base on the identified model, we propose a new dynamic sliding mode control (DSMC) for a general class of nonaffine nonlinear systems by defining a new adaptive proportional-integral sliding surface and employing a linear state feedback. The main property of proposed controller is that it does not need an upper bound for the uncertainty and identified model; moreover, the switching gain increases and decreases according to the system circumstance by employing an adaptive procedure. Then, chattering is removed completely by using the DSMC with a small switching gain.