Design of LMI‐based global sliding mode controller for uncertain nonlinear systems with application to Genesio's chaotic system

Design of a novel global sliding mode control law for the stabilization of uncertain nonlinear systems is presented in this article. A sufficient condition is derived using the Lyapunov theorem and linear matrix inequality to guarantee the asymptotical stability of the states and to improve the stability of the system. Under the uncertainty and nonlinearity effects, the reaching phase is eliminated and the chattering is reduced effectively and then, the robustness and performance of the system are improved. Lastly, the proposed method is applied on Genesio's chaotic system and the simulation results demonstrate the effectiveness of this technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 94–98, 2015     

Terminal sliding mode control without singular for a class of uncertain system

An improved nonsingular terminal sliding mode method is proposed for a class of nonlinear systems with unmodeled dynamics. The proposed method can effectively avoid the singularity problem. The stability of the proposed procedure which could guarantee the robustness against uncertain unmodeled dynamic and external disturbances is proven by using the Lyapunov theory in finite time. An example is given to show the proposed improved terminal sliding mode control law without singular effectively. © 2016 Wiley Periodicals, Inc. Complexity 21: 566–572, 2016     

Design of sliding mode controller for a class of fractional-order chaotic systems

In this paper, a sliding mode control law is designed to control chaos in a class of fractional-order chaotic systems. A class of unknown fractional-order systems is introduced. Based on the sliding mode control method, the states of the fractional-order system have been stabled, even if the system with uncertainty is in the presence of external disturbance. In addition, chaos control is implemented in the fractional-order Chen system, the fractional-order Lorenz system, and the same to the fractional-order financial system by utilizing this method. Effectiveness of the proposed control scheme is illustrated through numerical simulations.     

Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems

In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlinear feedback (CNF) method is proposed. The aim of the controller is to improve the transient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feedback control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller.     

An adaptive-dynamic sliding mode controller for non-minimum phase systems

This paper presents a new algorithm for designing dynamic sliding-mode controllers. The proposed controller is based on dynamic sliding manifolds to circumvent the difficulties associated with the conventional sliding mode controllers in the face of non-minimum phase systems. Unlike previous works, a proper and easy to implement algorithm is presented for designing the dynamic sliding manifold which facilitates the design of the controller. The output tracking problem in nonlinear non-minimum phase systems with matched and unmatched disturbances and matched nonlinearities is addressed. Then, the performance of the dynamic sliding mode controller is significantly improved by combining the given dynamic sliding manifold with online parameter adaptation. Simulations results are presented to demonstrate the effectiveness of the proposed sliding mode controller in terms of performance, robustness and stability.     

Fast terminal sliding mode controller design for nonlinear second‐order systems with time‐varying uncertainties

This article investigates a novel fast terminal sliding mode control approach combined with global sliding surface structure for the robust tracking control of nonlinear second‐order systems with time‐varying uncertainties. The suggested control technique is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Using the new form of switching surface, the reaching phase elimination and the robustness improvement of the whole system are satisfied. Simulation results demonstrate the efficiency of the proposed technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 239–244, 2015     

High-order sliding mode controller with backstepping design for aeroelastic systems

A nonlinear system for controlling flutter in an aeroelastic system is proposed. The dynamic model describes the plunge and pitch motion of a wing. Interacting nonlinear forces such as structural and aerodynamic forces cause destabilizing phenomena such as flutter and limit cycle oscillation on the wing. Aeroelastic models have a wing section with only a single trailing-edge control surface for suppressing limit cycle oscillation. When modeling a single control surface, the controller design can achieve trajectory control of either plunge displacement or pitch angle, but not both, and internal dynamics describe the residual motion in closed-loop systems. Internal dynamics of aeroelasticity depend on model parameters such as freestream velocity and spring constant. Since single control surfaces have limited effectiveness, this study used leading- and trailing-edge control surfaces to improve control of limit-cycle oscillation. Moreover, two control surfaces were used to provide sufficient flexibility to shape both the plunge and the pitch responses. In this study, high order sliding mode control (HOSMC) with backstepping design achieved system stability and eliminated limit cycle phenomenon. Compared to the conventional sliding mode control design, the proposed control law not only preserves system robustness, but also avoids chatter phenomenon. Simulation results show that the proposed controller effectively regulate the response to origin in state space even under saturated controller input.     

Event-triggered sliding mode control for singular systems with disturbance

This paper investigates the event-triggered sliding mode control (SMC) problem for singular systems with disturbance. Firstly, an event-triggered sliding mode control law is designed to guarantee the reachability of sliding surface. Different from the related methods, in order to deal with the difficulty caused by event-triggered SMC strategy, a novel Lemma is proposed in this paper. Secondly, the admissibility of sliding motion is presented, which is used to solve the controller gain. Then, a positive lower bound of the inter execution time can be guaranteed and the Zeno behavior is avoided. Finally, two simulation examples are presented to show the effectiveness of derived theoretical results.     

Robust output feedback sliding mode control for uncertain discrete time systems

This paper proposes a robust output feedback controller for a class of uncertain discrete-time, multi-input multi-output, linear, systems. This method, which is based on the combination of discrete-time sliding mode control (DTSMC) and Kalman estimator, ensures the stability, robustness and an output tracking against the modeling uncertainties at large sampling periods. For this purpose, an appropriate structure is considered for sliding surface and the Lyapunov theory for the mismatched uncertain system is then used to design its parameter. This problem leads to solve a set of linear matrix inequalities. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show the effectiveness of the proposed method in the presence of parameter uncertainties and external disturbances at large sampling periods.     

Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty

A novel type of control strategy combining the fractional calculus with terminal sliding mode control called fractional terminal sliding mode control is introduced for a class of dynamical systems subject to uncertainties. A fractional-order switching manifold is proposed and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. The proposed fractional-order terminal sliding mode controller ensures the finite time stability of the closed-loop system. Finally, numerical simulation results are presented and compared to illustrate the effectiveness of the proposed method.     

RBF‐based discrete sliding mode control for robust tracking of uncertain time‐delay systems with input nonlinearity

In this article, a control scheme combining radial basis function neural network and discrete sliding mode control method is proposed for robust tracking and model following of uncertain time‐delay systems with input nonlinearity. The proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties, and external disturbances. The salient features of the proposed controller include no requirement of a priori knowledge of the upper bound of uncertainties and the elimination of chattering phenomenon and reaching phase. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 194–201, 2016     

Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

This article investigates the sliding mode control method for a class of chaotic systems with matched and unmatched uncertain parameters. The proposed reaching law is established to guarantee the existence of the sliding mode around the sliding surface in a finite‐time. Based on the Lyapunov stability theory, the conditions on the state error bound are expressed in the form of linear matrix inequalities. Simulation results for the well‐known Genesio's chaotic system are provided to illustrate the effectiveness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 14–19, 2016     

A new result on robust H∞ control for uncertain time‐delay singular systems via sliding mode control

This article is devoted to designing linear sliding surface and adaptive sliding mode controller for a class of singular time‐delay systems with parametric uncertainties and external disturbance. In terms of linear matrix inequalities (LMIs), a sufficient criteria of H_∞ performance, and admissibility for considered sliding motion restricted to linear sliding surface is achieved, and the controller which guarantees the finite‐time reachability of the predesigned sliding surface is then developed, respectively. Finally, three examples show the effectiveness of the proposed result. © 2016 Wiley Periodicals, Inc. Complexity 21: 165–177, 2016     

线性滞后广义系统的二阶滑模控制方法

讨论了时滞广义系统在不同条件下的变结构控制,根据终端滑模控制的特点,提出了一种由线性滑模与终端滑模构成的二阶终端滑模及相应控制策略.研究结果表明,该方法能够有效地清除系统的高频抖振,同时保证闭环系统的渐近稳定,实现滑模运动.举例说明了设计的合理性和有效性.     

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

The problem of H_∞ robust control based on event‐triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event‐triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H_∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean‐square admissible and has a prescribed H_∞ performance γ. Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method.     

Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach

In this paper, an adaptive sliding mode controller for a novel class of fractional-order chaotic systems with uncertainty and external disturbance is proposed to realize chaos control. The bounds of the uncertainty and external disturbance are assumed to be unknown. Appropriate adaptive laws are designed to tackle the uncertainty and external disturbance. In the adaptive sliding mode control (ASMC) strategy, fractional-order derivative is introduced to obtain a novel sliding surface. The adaptive sliding mode controller is shown to guarantee asymptotical stability of the considered fractional-order chaotic systems in the presence of uncertainty and external disturbance. Some numerical simulations demonstrate the effectiveness of the proposed ASMC scheme.     

Optimal LMI‐based state feedback stabilizer for uncertain nonlinear systems with time‐Varying uncertainties and disturbances

This article presents a nonlinear state feedback stabilizer using linear matrix inequalities for a class of uncertain nonlinear systems with Lipschitz nonlinearities. The proposed controller improves the transient performance and steady state accuracy simultaneously. To improve the stabilization performance, a nonlinear function is included in the control law and is optimally tuned using a modified random search algorithm. Simulation results are presented to show the effectiveness of the offered method. © 2015 Wiley Periodicals, Inc. Complexity 21: 356–362, 2016     

Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties

This paper is concerned with the stabilization problem for a class of nonlinear systems. Using second-order sliding mode control approach, a robust control scheme is established to make the states of system to zero or into predictable bounds for matched and unmatched uncertainties, respectively. Meanwhile, the chattering phenomenon is eliminated. A comparative example is given to emphasize the effectiveness and robustness of the proposed method.     

A sliding mode approach to robust stabilisation of Markovian jump linear time-delay systems with generally incomplete transition rates

This paper is devoted to investigating the problem of robust sliding mode control for a class of uncertain Markovian jump linear time-delay systems with generally uncertain transition rates (GUTRs). In this GUTR model, each transition rate can be completely unknown or only its estimate value is known. By making use of linear matrix inequalities technique, sufficient conditions are presented to derive the linear switching surface and guarantee the stochastic stability of sliding mode dynamics. A sliding mode control law is developed to drive the state trajectory of the closed-loop system to the specified linear switching surface in a finite-time interval in spite of the existing uncertainties, time delays and unknown transition rates. Finally, an example is presented to verify the validity of the proposed method.     

Synchronization of fractional‐order chaotic systems with disturbances via novel fractional‐integer integral sliding mode control and application to neuron models

In this paper, a novel fractional‐integer integral type sliding mode technique for control and generalized function projective synchronization of different fractional‐order chaotic systems with different dimensions in the presence of disturbances is presented. When the upper bounds of the disturbances are known, a sliding mode control rule is proposed to insure the existence of the sliding motion in finite time. Furthermore, an adaptive sliding mode control is designed when the upper bounds of the disturbances are unknown. The stability analysis of sliding mode surface is given using the Lyapunov stability theory. Finally, the results performed for synchronization of three‐dimensional fractional‐order chaotic Hindmarsh‐Rose (HR) neuron model and two‐dimensional fractional‐order chaotic FitzHugh‐Nagumo (FHN) neuron model.