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The present paper proves chaos phenomenon for a range of parameters in attitude dynamic of a satellite and designs an appropriate nonlinear controller, while ensuring optimal system performance, the controller guarantees control of a chaotic state. As the dynamic equations of a three-axis satellite are defined as a nonlinear non-autonomous system, a technique is offered for calculating the Lyapunov exponents of such systems that may express the system’s chaotic state. Using the technique, the chaotic behavior of a system is proved within a range of parameters. Then a back-stepping sliding mode controller is proposed based on the desired performance and the closed-loop system stability is proved based on the Lyapunov’s theorem. Moreover, converting the system into a compatible form with the conditions of the Melnikov theorem using this analytical method ensures removing chaos phenomenon in the controlled system. Calculating Lyapunov exponents of the closed system confirms this issue. Finally, the simulation results obtained from the proposed controlling actions for different work fields are presented.

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This paper describes load torque estimation (LTE) issue in induction motors with uncertainty, using dynamic sliding mode control (DSMC). In DSMC the chattering is removed due to the integrator which is placed before the input control of the plant. However, in DSMC the augmented system is one dimension bigger than the actual system and then, the plant model should be completely known. To solve this problem, a new nonlinear observer called integral-chain observer (ICO) has been used. The advantage of the proposed approach is to have the system controlled as well as its main task i.e. LTE. Moreover, we assume that only output of system is accessible which is important in practical implementation. Simulation results are presented to demonstrate the approach.

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In this paper, the guidance law designing problem in the presence of the control loop dynamics using sliding mode control has been studied. For this purpose in the design process, stable control loop dynamic considered that usually not considered by the designers. In practice there is a lag for control loop that may lead to instability in the guidance loop. In this paper the control loop dynamic that is stabilized with an autopilot, approximated as first order lag and then is considered with kinematic equation of motion in designing procedure. To solve the problem because of the nonlinearity in equations and target maneuvers as uncertainty, the sliding mode control scheme is used. So just having the bounds of the uncertainty we can design guidance law and the measure or estimate of uncertainty is not required. The sliding variable is defined with respect to parallel navigation idea using relative lateral velocity between the interceptor and the target. Then a controller is designed for reaching the sliding variable to sliding surface. Therefore the line of sight rate will be zero and collision is inevitable. Also for removing chattering, the continues approximation method is used.

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In this paper, a new combination of fractional order calculus and finite time sliding mode control, used to design an aircraft autopilot. This combination aims to reduce the chattering phenomena and have a smoother control signal than conventional sliding mode. Fractional order control uses fractional integrator and derivative to improved integer order control methods. The sliding surface and sliding mode control law is proposed to reduce the chattering phenomena and also, closed-loop stability is guaranteed too. Using this algorithm, a robust autopilot against aerodynamic coefficients uncertainty is designed for an aircraft and proposed control law is utilized to stabilize the close loop system by Lyapunov stability theorem. The proposed autopilot is applied to the aircraft model and simulation results illustrate the reduction of chattering phenomena.

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In this paper, a finite-time stabilized guidance law is addressed in presence of some measurement noises. The measurement noise would effect on the guidance system stability and or performances. Hence, in presence of measurement noise, the guidance law must be modified such a way that the noise effect on the guidance system response would be reduced. By using the stochastic stability theory, a modified guidance law, depended on the measurement noises variance, will be proposed such that the line of sight angle rate is stabilized in a finite time. After such a finite-time, no force would be applied to the vehicle actuators. Then the line of sight angle would be a constant one. The proposed method would be used in a two-dimensional numerical example. The effectiveness of the suggested method is shown in the simulation results.

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In this paper, by combining fractional calculus and sliding mode control theory, a new fractional order adaptive terminal sliding mode controller is proposed for the maximum power point tracking in a solar cell. To find the maximum power point, the incremental conductance method has been used. First, a fractional order terminal sliding mode controller is designed in which the control law depends on knowing the upper bound of uncertainty in the system, but in practical application it is difficult or in some cases impossible to calculate this upper limit. In this paper, an adaptive law is given for online calculating of this parameter. The stability proof of the sliding surface, as well as the proof of finite time convergence of closed-loop system, are investigated using the Lyapunov theory. Finally, the performance of the proposed controller is evaluated both in normal and partial shading conditions. For a better comparison of the proposed controller, the performance of this controller is compared in the presence of load variations and the variations of system parameters with the conventional (integer order) terminal sliding mode control.

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In this paper, a fractional-order robust adaptive intelligent controller (FRAIC) is designed for a class of chaotic fractional order systems with uncertainty, external disturbances and unknown time-varying input time delay. The time delay is considered both constant and time varying. Due to changes in the equilibrium point, adaptive control is used to update the system's momentary information and the intelligent controller is used to estimate the uncertainties and disturbances and non-linearities of the system according to the momentary information obtained. The sliding mode control, which provides closed loop asymptotic stability in the system despite the uncertainties and disturbances, is used as a robust controller. Using the Lyapunov theorem and Barbalat's Lemma, the asymptotic stability of a chaotic fractional order system with input delay and uncertainty as well as external disturbance is proved by designed controller. Finally, using the simulation results of financial as well as supply and demand systems, the performance of designed controller would be examined.

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This paper considers the design of observer-based distributed adaptive controllers to achieve a leader-follower consensus for high-order nonlinear multi-agent systems in the presence of non-symmetric input saturation constraint and system uncertainties. Solving the consensus problem for nonlinear multi agent systems in the presence of unknown terms in the dynamics equations of follower that are due to model simplification, parameters uncertainty or external disturbances are investigated. In order to reduce the conservatism, the upper bound of uncertain term is considered to be unknown, which is obtained by adaptive laws. In addition, it is assumed that all states variables of agents are not directly measurable; therefore firstly, by designing the nonlinear distributed observers, the states variables of agents are estimated. Then, by using the sliding mode technique, the observer-based distributed adaptive control laws are designed to ensure the consensus between the agents, and the output of the followers can track the output of the leader, in the presence of non-symmetric input saturation and uncertain terms. Finally, the results of the simulations have completely confirmed the achievements of the proposed laws.

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Owing to an increasing need of control community for providing a precise and integrated model of natural and practical structures switching systems have attracted much attention. On the other hand, the multi-model inherent in many practical systems has increased the importance of reviewing these types of systems. In this paper, the problem of adaptive fault tolerant finite-time control of a class of nonlinear switching systems in the presence of actuator fault, external disturbances and dead-zone input nonlinearity is investigated. The boundary of the uncertain terms of the system is assumed to be unknown and adaptive rules are used to eliminate the destructive effects of these terms on the system response. The subsystems of switching system are considered as nonlinear systems with a canonical structure. This paper sets no restrictive assumption on the switching logic of the system. Therefore, the purpose is to propose a controller that works under any desired switch signal and can overcome the actuator fault, disturbances and dead-zone input nonlinearity. To achieve this purpose, after providing a smooth sliding manifold, an adaptive control input is developed such that the system trajectories approach the prescribed sliding mode dynamics in finite-time sense. Finally, by using the Lyapunov stability theory, it is proved that the origin is the finite-time stable equilibrium point of the overall closed-loop system. The simulation results provided by MATLAB software show the performance of the proposed controller.

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In this paper, a control input based on terminal sliding mode control is provided for a mobile robot with four Mecanum wheels to move in a predetermined path and convergence into the path in a fixed-time. First, according to the robot structure, a dynamic model of the robot is presented. The dynamic model follows a nonlinear second-order equation. Based on terminal sliding mode control, a nonlinear sliding surface which is a function of position error vector is defined and then the control input is designed based on this sliding surface. Using the Lyapunov theorem, it has been proven that, using this control input, the robot converges to the predetermined path at a fixed time. The convergence time is a function of the constants defined in the control input. Finally, the simulation is presented based on the control input and the results are shown.

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In this paper, the problem of stabilization and synchronization of Lorenz and Chua chaotic in the presence of uncertainty using fractional order sliding mode control strategy based on nonlinear adaptation law has been investigated. Lorenz and Chua systems denote third order dynamics models which are chaotic for certain parameters. The proposed control law is composed of two prats sliding mode control and adaptive control law. Firstly, by supposing that instantaneous information of nonlinear part of chaotic system is not available, a linear regressor equation including an unknown section has been used. Using Lyapunov stability theorem and based on fractional calculus, adaptation law is developed to instantaneous estimation of unknown part. Moreover, by defining based on error signals and realizing exponential reaching law for insuring closed-loop stability, the sliding mode control law including equivalent and switching control has been derived. Eventually, the final control law has been derived by synthesizing sliding mode control and adaptive laws. The important aspect of the proposed approach is ability to encounter unstructured uncertainties and nonlinear effects of chaotic systems dynamic and guiding the state variables into sliding surface for arbitrary initial conditions. The performance of the proposed algorithm has been evaluated by realizing the stabilization problem of chaotic Lorenz system and synchronization of chaotic Lorenz and Chua systems.
 

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Electromagnetic suspension technology has been developed in recent years due to advantages such as no contact and reduced friction. Of course, ensuring efficiency in these systems requires precise control of the position of the suspended object. Therefore, electromagnetic suspension is considered as a process by control engineers. The dynamics of electromagnetic suspension systems is nonlinear and also include model and parametric uncertainties such as the weight of the suspended object. In this paper, a finite time nonlinear hybrid method is used to stabilize the electromagnetic suspension system. Proof of finite time stability of the proposed method is performed using Lyapunov theory and a relation for calculating the convergence time depends on the controller gains is presented. To ensure the finite time convergence of the system state and output variables, the backstepping algorithm is used and in each step, the finite-time convergence theory is used. The controller designed in this paper is compared with the backsteping method and the superiority of the proposed method in various simulations is shown.

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In this paper, a new adaptive controller based on the barrier function is designed for high-order nonlinear systems with uncertainties in mind. Accordingly, this paper uses a sliding mode controller that can simultaneously create asymptotic convergence and deal with perturbations. The main problems controlling the slip mode can be considered asymptotic convergence, umbrella phenomenon, stimulus saturation, control gain estimation and failure to deal with time-varying uncertainties. In this paper, the terminal slip mode controller is used to deal with the phenomenon of asymptotic convergence and umbrella and the barrier function is used to overcome the uncertainties of time variable. The advantages of the proposed method include the elimination of the Chattering phenomenon, convergence in finite time, compatibility with time-varying uncertainties, no use of estimates and no need for information on the high limit of perturbations. Stability analysis shows that in the proposed controller, the tracking errors approach the convergence region in the zero range and provide faster convergence. Finally, to prove the efficiency of the controller, based on the chaos synchronization theory, we apply the proposed controller to a new 5D hyperchaotic system. The results show that the proposed controller, despite the disturbances applied to the system, provides rapid convergence and eliminates the umbrella phenomenon.

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The control of unmanned aerial vehicles is a challenging problem due to their lightweight and intense coupling between longitudinal and lateral motion. Considering this issue, in this article, an automatic landing system for a fixed-wing unmanned aircraft exposed to wind disturbances and parametric uncertainties is designed using the backstepping algorithm and the disturbance observer-based sliding mode control. Two controllers are designed based on the backstepping algorithm and sliding mode control to stabilize the attitude angles. The longitudinal speed controller uses the sliding mode technique to maintain the total speed relative to the ground at a constant desired value in all landing phases. A nonlinear disturbance-observer is considered in the sliding mode controller structure to estimate wind disturbance and parametric uncertainty. The new robust automatic landing system is software implemented, and its performance is investigated by several numerical simulations; Lateral deviation relative to the runway is eliminated while the unmanned aerial vehicle maintains its desired trajectory slope angle in all phases of the landing at the desired value. Therefore, the results of numerical simulations prove that the new control structure is stable and robust against different initial conditions, different types of wind disturbances (wind shear and discrete gust), and parametric uncertainty.

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Disturbance and uncertaities exist in industrial systems and greatly affect the performance and stability of these systems. The robotic manipulator is one the most widely used devices in the industry that is highly affected by various disturbances. Hence establishing a proper control algorithm to estimate and eliminate disturbances seems crucial. Since the robotic manipulator is a highly nonlinear system, we need to design a nonlinear disturbance observer. In this thesis a nonlinear disturbance observer is proposed to estimate the constant and oscillatory disturbances in the studied system. On the other hand, since proportional-derivative controllers (PD) are widely used in industrial systems, so in this thesis, a suitable proportional derivative controller will be designed. This controller is not capable of dealing with disturbances and uncertainties, so a new supervisory controller structure has been proposed to estimate disturbances and stabilize the system. The core of proposed controller uses a new sliding model controller. Finally, some comparisions with PD and super twisting sliding mode controllers have been performed in several cases and the numerical results show the advantages of the proposed controller.

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In this paper, formation control based on the virtual structure for the non-holonomic mobile robot system with two models of certain and uncertain kinematic equations is discussed. First, the formation equations of a certain model are calculated and then it is proved that it is possible to create a geometric shape and maintain that state by using the sliding model control theory for any two moving mobile robots. Then, after deriving the formation equations of the uncertain model, a sliding model controller is designed that is able to control the uncertain model provided that the uncertainty range of the kinematic equation is present. For each design, the stability of the system is guaranteed using the Lyapunov stability theorem. Finally, in order to compare the performance of the designed controllers, a pre-designed back-stepping controller is introduced and the results will be presented in the form of simulations. The simulation results show the effective performance of the designed controllers.

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Usually, constrained lateral acceleration would have undesirable effects on the stability and performance of a guidance system. The composite nonlinear feedback (CNF) can be effectively used to improve the transient response of the closed-loop system in the presence of the constrained input. In this way, guidance law consists of an extra nonlinear term besides the conventional linear one. As a result, such a term adjusts the qualitative characteristics of the transient response. Meanwhile, the nonlinear term is a function of the rate of line-of-sight (LOS) angle which is not activated at origin and infinity. Thus it would be effective only in a specified region. In this paper, proportional navigation is employed for the linear term of the CNF-based guidance law. Therefore, a guidance algorithm is developed for tracking problems using the CNF idea. Applying the proposed guidance method, the closed-loop stability is analytically proved via the well-known Lyapunov stability theory. The suggested approach is simulated in a numerical example. Then the results are compared with an existing technique. As expected, guaranteeing closed-loop stability, in contrast to a similar method, the addressing scheme considerably improves the performance and transient response of the guidance system in the presence of lateral acceleration limitations.
 

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This paper presents a new method of the adaptive non-singular Second-order Terminal Sliding Mode (SOTSM) control for the fast and finite time stabilization of Cyber-Physical Systems (CPSs) in the simultaneous presence of parametric uncertainties, unwanted disturbances and actuator cyber-attacks. By utilizing the presented non-linear manifold and sliding surface, the reaching mode is deleted and the entire system’s robust performance is improved. The proposed online adaptive laws deal with parametric uncertainties, unwanted disturbances and cyber-attacks, so that there is no need to identify their upper bounds. The designed adaptive non-singular SOTSM control method guarantees the robust performance of the system in the mentioned conditions along with fast and smooth response, high accuracy and flexibility, without transient fluctuations and chattering, as well as proper convergence in finite time. The numerical simulation results show the effectiveness and success of the adaptive non-singular second-order terminal sliding mode control method in comparison with the results of adaptive integral sliding mode control, traditional sliding mode control and state feedback control.
 

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Thrust vector control is a special method to change the attitude and position of flying objects, which can only be applied in some missions. These systems require feedback control and lead to better maneuverability. In this paper, a finite time adaptive sliding model controller is presented for controlling the thrust vector of a flying object. The first-order sliding model method requires information about the upper bound of system uncertainties and also this method causes chattering in the control signal. The standard adaptive sliding model method has solved the problem of the need for the uncertainty bound and also reduces the chattering range. But this method does not guarantee finite time stability. In this article, the finite time type of adaptive sliding model is used to control the thrust vector. This method guarantees finite time stability without the need for upper bound information of system uncertainties, and in it, the convergence time of the tracking error and estimation depending on the initial conditions can be calculated. The performance of the proposed thrust vector control system has been investigated by computer simulation and its efficiency is shown in comparison with other methods.