Super-twisting observer-based sliding mode control with fuzzy variable gains and its applications to fully-actuated hexarotors

In this paper, we consider the super-twisting observer-based sliding mode control algorithm with fuzzy variable gains (STOSMC) for the fully-actuated hexarotor. Our hexarotor has full actuation due to six titled propellers that allows to control position and orientation (attitude) simultaneously, and resolves the singularity problem of the rotational matrix by using the quaternion modeling framework. We show that the proposed STOSMC for the hexarotor guarantees finite-time convergence of the estimation error and asymptotic stability of the hexarotor. In simulations, we demonstrate the nonsingularity and fully-actuated control performance of the hexarotor by considering extreme position and attitude control scenarios. Moreover, the simulation results show that the hexarotor achieves the fast and precise tracking performance to the desired position and the desired attitude and the chattering phenomenon is reduced compared with the fixed-gains observer-based super-twisting sliding mode control due to the fuzzy mechanism.     

Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances

In this paper, a flatness-based adaptive sliding mode control strategy is presented to solve the trajectory tracking problem of a quadrotor. According to the differential flatness theory, the typical under-actuated quadrotor dynamics is transformed into a fully-actuated one. Based on this model, backstepping sliding mode controllers are designed to solve the trajectory tracking problem. To improve the robustness to disturbances, extended state observers are applied as a feedforward compensation of disturbances. Moreover, considering the high-order dynamics and possible instability caused by large observer gains, the adaptive method is applied to compensate for the estimation error. The effectiveness of the proposed control scheme is verified in simulations.     

Robust stabilization of uncertain 2-D discrete-time delayed systems using sliding mode control

This paper aims to solve the problem of sliding mode control for an uncertain two-dimensional (2-D) systems with states having time-varying delays. The uncertainties in the system dynamics are constituted of mismatched uncertain parameters and the unknown nonlinear bounded function. The proposed problem utilizes the model transformation approach. By segregating the proper Lyapunov–Krasovskii functional in concert with the improved version of Wirtinger-based summation inequality, sufficient solvability conditions for the existence of linear switching surfaces have been put forward, which ensure the asymptotical stability of the reduced-order equivalent sliding mode dynamics. Then, we solve the controller synthesis problem by extending the recently proposed reaching law to 2-D systems, whose proportional part is appropriately scaled by the factor that does not depend on some constant terms but rather on current switching surface’s value, which in turn ensures the faster convergence and better robustness against uncertainties. Finally, the proposed results have been validated through an implementation to a suitable physical system.     

Finite-time fractional-order adaptive intelligent backstepping sliding mode control of uncertain fractional-order chaotic systems

This paper precedes chaos control of fractional-order chaotic systems in presence of uncertainty and external disturbances. Based on some basic properties on fractional calculus and the stability theorems, we present a hybrid adaptive intelligent backstepping-sliding mode controller (FAIBSMC) for the finite-time control of such systems. The FAIBSMC is proposed based on the concept of active control technique. The asymptotic stability of the controller is shown based on Lyapunov theorem and the finite time reaching to the sliding surfaces is also proved. Illustrative and comparative examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.     

Robust sliding mode control of a DC/DC Boost converter with switching frequency regulation

This paper presents the design of a hysteresis band controller to regulate the switching frequency in a sliding mode controlled nonlinear Boost power converter. The proposed architecture relies on a piecewise linear modeling of the switching function behavior within the hysteresis band, and consists of a continuous-time integral-type controller that modifies the amplitude of the hysteresis band of the comparator in accordance with the error between the desired and the actually measured switching period. The study provides the dynamical models of the converter operating in sliding mode and the switching frequency control loop. Moreover, the design of the parameters of both the sliding mode control and the switching frequency controller guarantee the fulfilment of the desired output voltage regulation of the Boost converter and the steady state setting of the switching frequency with a known, taylored dynamics. A Boost power converter prototype has been built to validate the proposal. Experimental results confirm the predicted good performance of the controllers, as well as the robustness with respect to changes in the switching frequency reference and the system parameters.     

Robust adaptive visual tracking control for uncertain robotic systems with unknown dead-zone inputs

This paper is concerned with the image-based visual servoing (IBVS) control for uncalibrated camera-robot system with unknown dead-zone constraint, where the uncertain kinematics and dynamics are also considered. The control implementation is achieved by constructing a smooth inverse model for dead-zone-input to eliminate the nonlinear effect resulting from the actuator constraint. A novel adaptive algorithm, which does not require a priori knowledge of the parameter intervals of dead-zone model, is proposed to update the parameter values online, and the dead-zone slopes are not required the same. Furthermore, to accommodate the uncertainties of uncalibrated camera-robot system, adaptation laws are developed to estimate the uncertain parameters, simultaneously avoiding singularity of the image Jacobian matrix. With the full consideration of unknown dead-zone constraint and system uncertainties, an adaptive robust visual tracking control scheme together with dead-zone compensation is subsequently established such that the image tracking error converges to the origin. Based on a 3-DOF manipulator, simulations are conducted to verify the tracking performance of the proposed controller.     

Disturbance observer-based robust missile autopilot design with full-state constraints via adaptive dynamic programming

This paper aims to develop a robust optimal control method for longitudinal dynamics of missile systems with full-state constraints suffering from mismatched disturbances by using adaptive dynamic programming (ADP) technique. First, the constrained states are mapped by smooth functions, thus, the considered systems become nonlinear systems without state constraints subject to unknown approximation error. In order to estimate the unknown disturbances, a nonlinear disturbance observer (NDO) is designed. Based on the output of disturbance observer, an integral sliding mode controller (ISMC) is derived to counteract the effects of disturbances and unknown approximation error, thus ensuring the stability of nonlinear systems. Subsequently, the ADP technique is utilized to learn an adaptive optimal controller for the nominal systems, in which a critic network is constructed with a novel weight update law. By utilizing the Lyapunov's method, the stability of the closed-loop system and the convergence of the estimation weight for critic network are guaranteed. Finally, the feasibility and effectiveness of the proposed controller are demonstrated by using longitudinal dynamics of a missile.     

Containment control of multi-agent systems via a disturbance observer-based approach

This paper deals with the containment control problem for multi-agent systems with exogenous disturbances. A disturbance observer-based control approach is employed to estimate the disturbances generated by an exogenous system. Consequently, distributed disturbance observer-based containment control protocols are proposed by using the state feedback control and the output feedback control, respectively. Furthermore, with the help of algebraic graph theory and Lyapunov stability theory, sufficient conditions are established to ensure that multi-agent systems with exogenous disturbances can achieve containment control via the disturbance observer-based approach. Finally, the effectiveness of our theoretical results is verified by providing numerical simulation examples.     

Fuzzy observer-based sampled-data control for a class of pure-feedback nonlinear systems

This paper aims at the sampled-data control problem for a class of pure-feedback nonlinear systems. A fuzzy state observer is constructed to evaluate the unavailable states. In this process, fuzzy logic systems are applied to approximate the uncertain nonlinear functions. Based on the new designed state observer, a sampled-data control scheme for the pure-feedback nonlinear systems is proposed. The designed sampled-data controller ensures the boundedness of the nonlinear systems. Finally, two numerical examples are used to demonstrate that the proposed method is efficient.     

Security control for Markov jump system with adversarial attacks and unknown transition rates via adaptive sliding mode technique

This paper is concerned with the security control problem for a class of Markov jump systems subject to false data injection attack and incomplete transition rates. An on-line estimation strategy is provided for the time-variant and unknown cyber-attack modes. And then, an adaptive sliding mode controller is synthesized with different robust terms for different modes to guarantee the reachability of the specified sliding surface. Moreover, the sufficient conditions for the stability of the closed-loop systems are derived. Finally, it is shown from simulation results that the effect of both false data injection attack and incomplete TRs can be effectively attenuated by the present adaptive SMC method.     

Position control of Stewart manipulator using a new extended adaptive fuzzy sliding mode controller and observer (E-AFSMCO)

Previously proposed adaptive fuzzy sliding mode control (AFSMC) and adaptive fuzzy sliding mode observer (AFSMO) methods are mixed and extended for the case of affine systems in which the input gain matrix is state-dependent, non-diagonal and non-positive definite. The proposed Extended AFSMCO (E-AFSMCO) method is then applied for position control of a Stewart Manipulator (SM), whose parameters are strongly state-dependent and complex and not suitable for practical control purposes. A robust observer-based control method which can work with a simplified model of the plant, and at the same time can preserve the stability and performance of the overall complex system is of great need. In this study, the SM dynamic model is simplified by removing the dynamic effects of the legs and the neglected terms are considered as un-modeled dynamics, for which the upper bound of the uncertainty is progressively estimated using the proposed adaptation rules. The final controller is comprised of a fuzzy controller in parallel with a robust switching controller. The second Lyapunov theorem is used to prove the closed-loop asymptotic stability. The proposed E-AFSMCO method is verified numerically and experimentally, depicting the effectiveness of the method for real-time industrial applications.     

Robust least mean logarithmic square adaptive filtering algorithms

The conventional logarithm cost-based adaptive filters, e.g., the least mean logarithmic square (LMLS) algorithm, cannot combat impulsive noises at the filtering process. To address this issue, we present a novel robust least mean logarithmic square (RLMLS) algorithm by using a generalized logarithmic cost function. The proposed RLMLS algorithm can provide robustness against impulsive noises with the improvement of filtering accuracy. For theoretical analysis, the mean square analysis of RLMLS is provided in terms of the mean square deviation (MSD) and excess mean-square error (EMSE) with a white Gaussian reference. For further performance improvement in different noises, the variable step-size RLMLS (VSSRLMLS) based on the statistics of error is proposed to improve the convergence rate and steady-state mean square error, simultaneously. Analytical results and superiorities of RLMLS and VSSRLMLS in the context of system identification are supported by simulations from the aspects of filtering accuracy and robustness in Gaussian and impulse noises.     

Fault-tolerant sensorless control of wind turbines achieving efficiency maximization in the presence of electrical faults

This paper proposes a sensorless fault-tolerant control strategy solving the tracking problem of the maximum delivered power characteristic for a wind energy conversion system equipped with a permanent magnet synchronous generator. A previously published control scheme ensuring the maximum power efficiency of the wind turbine, not requiring feedback information about rotor speed and position, and about wind velocity, is here extended to make the control scheme fault-tolerant with respect to possible electrical faults affecting the equations of the permanent magnet synchronous generator (PMSG) in the original (α, β) frame. The control law is based on a number of interconnected nonlinear observers. Closed loop asymptotic vanishing of the observation errors is proved. The proposed control solution has been validated on the National Renewable Energy Laboratory (NREL) 5-MW three-blade wind turbine model.     

Sparsely distributed sliding mode control for interconnected systems

This paper proposes a framework for the design of sparsely distributed output feedback discrete-time sliding mode control (ODSMC) for interconnected systems. The major target here is to develop an observer based discrete-time sliding mode controller employing a sparsely distributed control network structure in which local controllers exploit some other sub-systems’ information as well as its own local information. As the local controllers/observers have access to some other sub-systems’ states, the control performance will be improved and the applicability region will be widened compared to the decentralised structure. As the first step, a stability condition is derived for the overall closed-loop system obtained from applying ODSMC to the underlying interconnected system, by assuming a priori known structure for the control/observer network. The developed LMI based controller design scheme provides the possibility to employ different information patterns such as fully distributed, sparsely distributed and decentralised patterns. In the second step, we propose a methodology to identify a sparse control/observer network structure with the least possible number of communication links that satisfies the stability condition given in the first step. The boundedness of the obtained overall closed-loop system is analysed and a bound is derived for the augmented system state which includes the closed-loop system state and the switching function.     

Robust packet-based nonlinear fuzzy networked control systems

A class of networked nonlinear control systems with norm-bounded uncertainties is presented in this paper. The class is represented by Takagi–Sugeno (T-S) fuzzy models with packet processing. The network loop delay is considered either as known delay or random delay. For the former case, we develop conditions that guarantee the robust asymptotic stability and state-feedback stabilization with strict dissipativity and cast the results in linear matrix inequality (LMI) framework. Next employing a probabilistic-based delay partitioning method to deal with random delay, we establish novel LMI criteria for strict dissipative stability analysis and feedback synthesis. The efficacy of the ensuing techniques is demonstrated by numerical solution of typical examples and Mont Carlo simulation.     

Novel integral sliding mode control for small-scale unmanned helicopters

Integral sliding mode (ISM) control which consists of a nominal control and a sliding-mode motion control, provides a nice framework for high tracking performance and good disturbance reduction. Our work develops ISM to attenuate the adverse effect of mismatched perturbations. By properly choosing sliding-manifold surface, the elimination of disturbances on control outputs enables to be achieved. Additionally, the chattering of sliding-mode control part is attenuated based on second-order sliding mode idea. Then, the proposed novel ISM control scheme is applied to address trajectory tracking problem for helicopters under perturbations. Approximated input-output linearization is implemented, such that the obtained linearized model is suitable for applying the proposed ism control. The stability of the closed-loop system for helicopter and its convergence to zeros of tracking errors are demonstrated by Lyapunov theory analysis. Several comparison simulations illustrate the effectiveness and superiority of the proposed methods.     

A novel direct torque control method for brushless DC motors based on duty ratio control

Conventional direct torque control (DTC) suffers from large torque ripple and nonconstant switching frequency, which are caused by the hysteresis band amplitude and the motor speed. Many methods have been proposed to tackle these problems. However, these methods are usually complicated and parameter dependent. A novel DTC method for brushless DC motors based on duty ratio control is proposed to reduce torque ripple and maintain a constant switching frequency. During each switching period, an active voltage vector and a zero voltage vector are applied. A simple and effective method implemented to calculate the duty ratio relies only on the torque error, reducing the parameter dependence. The proposed method has the advantages of conventional DTC and effectively reduces torque ripple, which improves the performance of conventional DTC. Simulation and experimental results are given to confirm the method’s validity.     

Robust predictive control based on the Meixner-like model

This paper is devoted to the issue of a robust predictive control for linear discrete-time systems by using Meixner-like model. The Meixner-like functions are an extension of Laguerre functions and convenient when the system has a slow start or delay. To ensure the reduction of the parameter number in the Meixner-like model, the optimization of parameters characterizing the Meixner-like functions is proposed. This proposed robust predictive control copes with physical constraints and geometrical constraints due to parameter uncertainties, which are estimated by using the Unknown But Bounded Error (UBBE) approach, and leads to the min-max optimization problem.     

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H_∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.     

Dissipative consensus problems for multi-agent networks via sliding mode control

In this paper, dissipative consensus problems are discussed for multi-agent networks. Firstly, sufficient conditions are proposed to ensure $(Q,S,R)?$dissipative consensus for multi-agent networks with external disturbances. Then, by designing an integral-type sliding surface function, a controller is obtained and the corresponding sufficient conditions are given to guarantee $(Q,S,R)?$dissipative consensus for multi-agent networks with external disturbances. Moreover, the sliding mode control law is formulated such that multi-agent networks drive onto the predefined surface in finite time. Finally, an example is given to illustrate the effectiveness of the obtained results.