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In this paper, fuzzy linear singular differential equations under so-called granular differentiability are investigated in which the coefficients and initial conditions are as fuzzy numbers. Some new notions such as fuzzy nilpotent matrix, fuzzy linearly independent vectors, fuzzy eigenvectors, rank, index and fuzzy Jordan canonical form of a fuzzy matrix are introduced. Moreover, we compare the proposed method with other ones based on other derivatives, using some examples.

This article investigates an enhanced optimal robust time-delay stabilizer for an autonomous underwater vehicle in the descriptor model. Time-delay, model uncertainty, and actuator saturation constraint are some practical challenges in autonomous underwater vehicle controller design. In this regard, an appropriate autonomous underwater vehicle descriptor model is obtained, and sufficient stabilization conditions are determined in the terms of linear matrix inequality. The obtained criterion guarantees the system to be regular, impulse-free, and stable. Meanwhile, the delay-dependent and rate-dependent conditions are taken into account. Furthermore, uncertainty and time-delay are time-variant. This method includes a tuning factor for practical design aspects and tradeoff among desired requirements. Also, as an essential general requirement in non-linear systems, the maximal estimate of the attraction domain is proposed as an optimization problem. Numerical examples and simulations illustrate that the proposed methods are effective and useful in less conservative results. The technique can be generalized and applied to the most conventional autonomous underwater vehicles.

In this article, an observer-based adaptive hybrid attitude controller is presented that overcomes the topological obstructions associated with the global attitude stabilization. This hybrid controller consists of two major parts: an adaptive trimodal hybrid controller to eliminate $unwinding$ phenomenon, and a centrally synergistic potential function. In the adaptive trimodal hybrid controller, the first logic variable selects, which quaternion representation of the desired attitude should be tracked. Furthermore, an adaptive technique is introduced to collaborate with the second logic variable to adapt the hysteresis width. The third logic variable controls the mismatch between the auxiliary dynamical system and the actual attitude. Moreover, an auxiliary dynamical system and a nonlinear angular velocity observer are presented whose outputs are utilized in the proposed feedback control law to attain the necessary damping. Furthermore, a new centrally synergistic potential function is presented to cooperate with the trimodal hybrid controller to overcome the topological obstruction associated with the vector bundle structure. The robust global asymptotic stability of the consequent closed-loop system is guaranteed through a Lyapunov analysis. A comparative analysis in simulations illustrates the effectiveness and superiority of the proposed control scheme.

This paper peruses the Doppler-bearing passive target tracking (DBT), a task that is subject to the nonlinear measurement equations. These measurement equations form the target tracking a nontrivia...

The main purpose of this paper is to introduce a hybrid controller for global attitude tracking of a quadrotor. This controller globally exponentially stabilizes the desired attitude, a task that is impossible to accomplish with memoryless discontinuous or continuous state feedback owing to topological obstruction. Thereafter, this paper presents a new centrally synergistic potential function to construct hybrid feedback that defeats the topological obstruction. This function induces a gradient vector field to globally asymptotically stabilize the reference attitude and produces the synergy gap to generate a switching control law. The proposed control structure is consisting of two major parts. In the first part, a synergetic controller is designed to cooperate with the hybrid controller, whereas it exponentially stabilizes the origin of the error dynamics. In the second part, a hybrid controller is introduced to globally stabilize the attitude of the quadrotor, where an average dwell constraint is considered with the switching control law to guarantee the exponential stability of the switched system. Finally, the effectiveness and superiority of the proposed control technique are validated by a comparative analysis in simulations.

In this paper, a new fault-tolerant control strategy is suggested to control the induction motors (IMs). The mathematical model of IMs is supposed to be unknown and also the main disturbances such as perturbation in the rotor resistance, and suddenly changes in the load torque are considered. A general type-2 fuzzy system using a new non-singleton fuzzification is proposed to cope with the uncertainties. The robustness and the stability of the proposed control scheme is studied on basis of the Lyapunov theorem. The simulation results show that the suggested control method has good performance in the versus of unknown dynamics of IM, time-varying disturbances, abrupt faults and measurement errors. The proposed scheme is compared with other popular control systems and other kind of fuzzy systems and singleton fizzification.

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...

Chaotic secure communication via synchronization of chaotic systems has attracted increasing attention in recent years. This note aims to introduce the function projective synchronization (FPS) of ...

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.

This study investigates a novel fractional-order nonsingular terminal sliding mode controller via a finite-time disturbance observer for a class of mismatched uncertain nonlinear systems. For this purpose, a finite-time disturbance observer–based fractional-order nonsingular terminal sliding surface is proposed, and the corresponding control law is designed using the Lyapunov stability theory to satisfy the sliding condition in finite time. The proposed fractional-order nonsingular terminal sliding mode control based on a finite-time disturbance observer exhibits better control performance; guarantees finite-time convergence, robust stability of the closed-loop system, and mismatched disturbance rejection; and alleviates the chattering problem. Finally, the effectiveness of the proposed fractional-order robust controller is illustrated via simulation results of both the numerical and application examples which are compared with the fractional-order nonsingular terminal sliding mode controller, sliding mode controller based on a disturbance observer, and integral sliding mode controller methods.

This paper deals with the fuzzy control design for nonlinear impulsive switched systems modeled by a novel nonlinear Takagi-Sugeno (T-S) fuzzy structure. To model, this structure only uses some of the nonlinearities as premise variables. So, the derived model has fewer rules compared with the traditional T-S fuzzy models that utilize standard local sector nonlinearity; and accordingly, the number of stability/stabilization conditions is sharply reduced. In our structure, considering only a part of nonlinearities as premise variables causes that some of the local models in the consequent part of the fuzzy rules be nonlinear but with less complexity than the original nonlinear system. As a result, the feasibility of our model’s stability criteria is more than those that one can directly establish for the original nonlinear system. Besides, unlike the existing methods in the literature of impulsive switched systems that aim to permanently reduce the value of Lyapunov function candidates, this paper takes into account this process until trajectories reach a sufficient small region containing the origin. Then, within this region, the size of Lyapunov functions is just controlled at impulse instants. This strategy is useful when there are non-vanishing impulses and/or uncertainties, and it is more relaxed when the goal is ultimate bound stability. Finally, to achieve the stabilizing control signal that ensures practical control issues along with smallest ultimate bound and widest region of attraction, this paper also proposes an optimization problem with linear and bilinear constraints. The simulation results represent the performance of the proposed method.

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.

This paper peruses the attitude control problem of a rigid body, a task that is subjected to topological obstructions. These topological obstructions express that there is no globally asymptotically stable equilibrium point for a system evolving on a compact manifold. Therefore, there exist no continuous or discontinuous feedback control laws to globally stabilize the desired rigid body attitude. Thereafter, this paper presents quaternion-based hybrid feedback to defeat these topological obstacles. The proposed control law is derived from a new kind of centrally synergistic potential functions which is introduced in this paper. This function induces a gradient vector field that globally asymptotically stabilizes the desired attitude. Finally, a simulation study depicts the superior performance of the proposed quaternion-based hybrid feedback control technique.

This paper presents a novel adaptive control for a class of nonlinear switched systems by introducing a sufficient condition for stabilization. Based on the possible instability of all sub-systems, a variable structure (VS) switching rule with an adaptive approach and sliding sector was offered. Moreover, the stability condition of the system can be determined by solving linear matrix inequalities (LMIs) to ensure asymptotic stability. The application of H∞ analysis of nonlinear switched systems was also investigated through the design of the mentioned adaptive control system and defining a VS switching rule. Finally, simulation results were presented to validate the novelty of the proposed method.

This paper peruses the voltage control of a boost DC-DC converter. The hybrid model of the converter is utilized to introduce a new switching control law, which regulates the output voltage of the converter. In this switching control law an average dwell time constraint is considered. This suggestion guarantees the exponential stability of a desired output voltage value. Furthermore, in the proposed switching control law, there exist no Zeno solutions, since the existence of the average dwell time constraint. Moreover, in power converters, two significant concerns are switching loss and electromagnetic interference resulting from numerous rates of variations of voltage and current. Therefore, the salient features of the proposed controller are the mitigation of the switching rate as well as the regulation of the output voltage. Finally, simulation experiments are followed through on a boost converter to validate the effectiveness and superiority of the proposed control strategy.

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.

This paper investigates stabilization for a class of uncertain nonlinear impulsive periodic switched systems under a norm-bounded control input. The proposed approach studies stabilization criteria locally where the nonlinear dynamics satisfy the Lipschitz condition only on a subspace containing the origin, not on $$\mathbb {R}^{n}$$ . This makes the proposed approach applicable in most practical cases where the region of validity is limited due to physical issues. In presence of different resources of non-vanishing uncertainties, the main objective is to find a stabilizing control signal such that not only trajectories exponentially converge to a sufficient small ultimate bound, but also have the largest region of attraction. To this, for a more general model, we first propose several sufficient conditions using the common Lyapunov function approach. The proposed strategy allows the Lyapunov function to increase in some intervals, which is suitable when some of the subsystems are unstable and uncontrollable. We then apply these conditions to the targeted system, and the sufficient criteria are extracted in the forms of linear and bilinear matrix inequalities. To achieve the main goal, an optimization problem is also formulated which is solvable using augmented Lagrangian methods. Finally, some illustrative examples are presented to demonstrate the proposed approach.

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.

This paper aims to investigate an efficient numerical scheme for the optimal control of fractional-order dynamic systems. By using the Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations, the fractional optimal control problem under consideration is converted into a linear programming problem. Then, the internal model principle is employed in order to extend the new scheme for the fractional dynamic systems affected by the external persistent disturbances. Numerical examples and comparative results verify the validity and applicability of the new technique.

In this paper, the state estimation problem for fractional-order nonlinear discrete-time stochastic systems is considered. A new method for the state estimation of fractional nonlinear systems using the statistically linearized method and cubature transform is presented. The fractional extended Kalman filter suffers from two problems. Firstly, the dynamic and measurement models must be differentiable and, secondly, nonlinearity is approximated by neglecting the higher order terms in the Taylor series expansion; by the proposed method in this paper, these problems can be solved using a statistically linearized algorithm for the linearization of fractional nonlinear dynamics and cubature transform for calculating the expected values of the nonlinear functions. The effectiveness of this proposed method is demonstrated through simulation results and its superiority is shown by comparing our method with some other present methods, such as the fractional extended Kalman filter.

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.

This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems.

Among other methods, state estimation using filters is currently used to increase the accuracy of systems. These filters are categorized into the following three branches: linear, nonlinear with Gaussian noise, and nonlinear with non-Gaussian. In this paper, the performance of particle filters is investigated via nonlinear, non-Gaussian methods. The main aim of this paper was to improve the performance of particle filters by eliminating particle impoverishment. A resampling step was proposed to overcome this limitation. However, resampling usually leads to a dearth of samples. Therefore, to virtually increase the number of samples, the available samples were broken into smaller parts based on their respective weights via a clustering approach. The experimental results indicate that the proposed procedure improves the accuracy of state estimations without increasing computational burden.

This paper presents optimal control of uncertain switched systems in presence of the external disturbance and parametric uncertainty and generally every uncertainty due to modeling error. In this paper, the switching signal is selected a priori and control input is designed to minimize a given cost function. Discrete Linear Quadratic (DLQ) control has been efficiently applied to certain systems as an optimal control. There would seem to be some difficulties to apply discrete linear quadratic control to uncertain switched system. To overcome the problems, this paper presents an appropriate model. Then uncertainties of the uncertain switched system are compensated by robust time-delay controller. Then control input is designed by discrete linear quadratic control. The stability analysis and simulation verify effectiveness of the proposed control approach.