Sliding Mode Control Law Research Articles

Adaptive event-triggered finite-time sliding mode control for singular T–S fuzzy Markov jump systems with asynchronous modes

This paper investigates the finite-time asynchronous control issue for singular fuzzy Markov jump systems (SFMJSs) with mode-dependent derivative-term coefficient through the sliding mode control (SMC) approach. Firstly, a new adaptive event-triggered scheme (ETS), which satisfies the system conditions by changing the threshold, is adopted to further reduce the communication consumption. Meanwhile, a mode-dependent fuzzy sliding surface (SS) function on account of hidden Markov model is designed. Based on a state observer, an asynchronous SMC law is proposed in accordance with the adaptive ETS to ensure that SFMJSs are finite-time boundedness (FTB). Finally, two examples are provided to certify the availability and practicability of the presented results.

Sliding mode control for the discrete cyber‐physical systems under aperiodic denial‐of‐service attacks

AbstractIn this work, the problems of stability analysis and sliding mode control (SMC) for discrete‐time cyber‐physical systems (CPSs) under denial‐of‐service (DoS) attacks are investigated. Firstly, the model of aperiodic DoS attacks is established by introducing the constraints on the upper bound of the attack interval and the lower bound of the non‐attack interval. Next, by utilizing the SMC and switching strategies, the input‐to‐state stability (ISS) of the CPSs can be guaranteed in terms of the upper and lower bounds restrictions. Then, the sliding mode control law is designed for the considered CPSs. Finally, one example is given to illustrate the applicability of our proposed theoretical result.

Discrete control of nonlinear stochastic systems driven by Lévy process

In this paper, the stabilization is studied for a complex dynamic model which involves nonlinearities, uncertainty, and Lévy noises. This paper also discusses the controller discretization and presents a new algorithm to obtain the upper bound for the sample interval through which the exponential stability of the discrete system can still be guaranteed. Firstly, an integral sliding surface is designed to obtain the sliding mode dynamics for the considered stochastic Lévy process. By using Lyapunov theory, generalized Itô formula and some inequality techniques, the exponential stability is proved in the sense of mean square for sliding mode dynamics. The reachability of the sliding mode surface is also ensured by designing a sliding mode control law. Secondly, the continuous-time controller is discretized from the point of control cost, and the squared difference is analyzed for the states before and after the discretization. Different from those classical stochastic differential equations driven by Brownian motions, the noise is supposed to be Lévy type and the squared difference is analyzed in different cases. Furthermore, we obtain the largest sampling interval through which the discretized controller can still stabilize the Lévy process driven stochastic system. Finally, a simulation for a drill bit system is given to demonstrate the results under the algorithms.

Asynchronous observer‐based sliding mode control for 2‐D Markov jump Roesser systems

AbstractThis article deals with the state reconstruction and sliding mode control problem for continuous‐time two‐dimensional Roesser systems. Aiming at the phenomena of mode mismatch between the controlled system and the controller, the asynchronous control strategy is employed by constructing the conditional probability matrix and utilizing the hidden Markov model. Considering not full state information is unavailable in some practical applications, the observer‐based sliding mode control scheme is developed. Two types of sliding mode surfaces are synthesized based on system state and observer state, respectively. Accordingly, different sliding mode control laws are synthesized for these two scenarios to ensure the resulting system trajectories to reach onto the prescribed sliding mode surfaces. Sufficient conditions are provided to guarantee the stochastic stability for corresponding overall closed‐loop systems. Finally, the feasibility and effectiveness of the proposed method are verified by numerical simulations.

Integration of sEMG-Based Learning and Adaptive Fuzzy Sliding Mode Control for an Exoskeleton Assist-as-Needed Support System

This paper presents an adaptive Fuzzy Sliding Mode Control approach for an Assist-as-Needed (AAN) strategy to achieve effective human–exoskeleton synergy. The proposed strategy employs an adaptive instance-based learning algorithm to estimate muscle effort, based on surface Electromyography (sEMG) signals. To determine and control the inverse dynamics of a highly nonlinear 4-degrees-of-freedom exoskeleton designed for upper-limb therapeutic exercises, a modified Recursive Newton-Euler Algorithm (RNEA) with Sliding Mode Control (SMC) was used. The exoskeleton position error and raw sEMG signal from the bicep’s brachii muscle were used as inputs for a fuzzy inference system to produce an output to adjust the sliding mode control law parameters. The proposed robust control law was simulated using MATLAB-Simulink, and the results showed that it could instantly adjust the necessary support, based on the combined motion of the human–exoskeleton system’s muscle engagement, while keeping the state trajectory errors and input torque bounded within ±5×10−2 rads and ±5 N.m, respectively.

H∞ observer-based sliding mode control for uncertain discrete-time singularly perturbed systems

This paper studies the sliding mode control (SMC) problem of discrete-time singularly perturbed systems (DTSPSs) with external perturbations and nonlinear inputs. First, to estimate the state of the original system, a novel state observer is constructed. Under this condition, the observer error system is ensured to be input-to-state stable (ISS) and satisfies the given H∞ performance index. Then, an appropriate sliding mode control law is proposed to satisfy the reachability condition. On this basis, the ISS criterion for the sliding mode dynamics (SMDs) is given, and the controller gain matrix is also obtained. In addition, a feasible algorithm is given to compute the upper bound for the small parameter. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

Adaptive sliding mode control for uncertain nonlinear switched system under probabilistic replay attacks: The output feedback approach

SummaryThis article investigates the output‐feedback‐based adaptive sliding mode control problem for a class of switched systems with probabilistic nonlinearities and replay attacks. The adversary might attack the system during the communication transmissions. The objective of the problem addressed is to design a new output‐feedback‐based adaptive sliding mode control law by utilizing the actual measured output information such that the impacts of immeasurable states and probabilistic replay attacks are compensated. In addition, the input‐to‐state stability in probability of closed‐loop switched system and the reachability analysis of the specified sliding surface are discussed, where the sufficient conditions are established accordingly. Finally, two simulations are provided to illustrate the effectiveness of the proposed sliding mode control method.

Event-Triggered Sliding-Mode Control for Polynomial Fuzzy Singular Systems

This article focuses on the problem of the observer-based sliding-mode control (SMC) for polynomial fuzzy singular systems via a novel dynamic event-triggered (DET) mechanism. First, the DET mechanism is introduced to reduce the transmission burden in the communication network. Second, the DET-based observer is constructed to estimate the unavailable state variables. On this basis, the integral sliding variable is provided, and the observer dynamics can be obtained. A sufficient condition is then proposed to make sure that the whole closed-loop system composed of the observer dynamics and the estimation error system is admissible and passive by utilizing the sum-of-squares approach. Meanwhile, the sliding surface parameter matrix, the observer gain, and the trigger weighting matrix are co-designed. It should be emphasized that the common equality constraints, nonstrict and nonlinear inequality constraints are removed through equivalent sets and several inequality techniques in this design process. Moreover, the DET observer-based SMC law is derived to assure the reachability of the specified sliding surface. Finally, the theoretical results are verified by simulation results.

Fractional-order robust fixed-time sliding mode control for deployment of tethered satellite

Tether deployment of the space tether system is the first step of related on-orbit experiments, which requires an advanced and reliable control scheme to realize rapid deployment without overshoot. In this paper, we propose a fractional-order fixed-time controller based on hierarchical sliding mode control to be applied to the deployment process of the tether system. The application of fractional calculus improves the local effect of the controller. Through strict mathematical derivation, we prove that the proposed control law satisfies the global fixed-time stability. So the closed-loop system has the performance of fixed-time convergence. Part of the simulation uses a fractional sliding mode control law for comparison, which further illustrates the superiority of the control law proposed in this paper. In view of the uniqueness of tether system dynamics, the research ideas in this paper are also of reference value to similar under-actuated systems.

Sliding-mode anti-disturbance speed control of permanent magnet synchronous motor based on an advanced reaching law

In order to improve the performance of a permanent magnet synchronous motor (PMSM) speed controller, an advanced reaching law sliding mode control (ASMC) strategy is proposed in this study. The advanced sliding mode reaching law (ASMRL) introduces a power term of the system state and a checkmark function term about the sliding mode function based on the traditional constant-proportional rate reaching law(TSMRL) , and replaces the sign function with a hyperbolic tangent function. A detailed theoretical analysis of the characteristics of the ASMRL is then presented. The theoretical analysis shows that the ASMRL converges to the sliding mode surface more quickly and with less chattering than the TSMRL. In addition, a sliding mode disturbance observer (SMDO) is designed to estimate the total disturbance of the system, and the estimated disturbance is compensated to ASMC. Then the stability of the system with ASMC and the stability of the system with ASMC+SMDO is proved by Lyapunov’s theorem. Finally, the proposed control strategy is validated on an experimental platform of PMSM. The experimental results show that the ASMC has a faster convergence speed, smaller chattering, better disturbance rejection performance than the traditional constant-proportional rate reaching law sliding mode control(TSMC), and better performance with the addition of SMDO.

Performance-based model-free adaptive finite-time control for shape memory alloy actuated swing platform

Shape memory alloy (SMA), a kind of smart material, can be used as an actuator in many fields; however, its strong nonlinearity and parameter uncertainty hinders its application in high-tracking accuracy tasks. This paper addresses the tracking control problem of the SMA actuated swing platform suffering from completely unknown nonlinear model information and prescribed finite-time error constraints. First, the equivalent dynamic linearization model of the swing platform is established, and the unknown disturbance is estimated and compensated by the extended state observer. Meanwhile, a novel discrete-time performance function is proposed, and the prescribed finite-time tracking error constraints are transformed into a new equivalent unconstrained task. Second, the model-free adaptive sliding mode controller is designed using the unconstrained error, and the complete control law, including sliding mode control law and equivalent control law, is derived. Third, the stability of the closed-up swing platform is guaranteed by employing the Lyapunov method. Finally, experiments reveal that the proposed method is preferable.

Trajectory tracking of Stanford robot manipulator by fractional-order sliding mode control

In this work, a fractional integral sliding-mode control scheme based on the Caputo–Fabrizio derivative and the Atangana–Baleanu integral of the Stanford robot for trajectory tracking tasks is developed and presented. The coupled system is composed of the robot manipulator and the induction motors that drive its joints. The mathematical model of the system is obtained by the Euler–Lagrange method and generalized to an arbitrary order via the Caputo–Fabrizio derivative. The actuators are controlled by fractional PI controllers based on the Atangana–Baleanu integral, while a fractional integral sliding mode control law is also developed for trajectory tracking control. In this context, a fractional version of the sliding surface via the Caputo–Fabrizio derivative is introduced to improve the performance of the control system. In addition, to attenuate the chattering effects, a fractional integral term, based on the Atangana–Baleanu integral, is introduced on the sliding surface further improving system performance with less power consumption. The conventional integral sliding mode control and an optimal super-twisting sliding mode control are also introduced for comparison with the proposed control strategy. The control schemes were tuned using the Cuckoo method. External disturbances are also considered in the system dynamics, as well as different end-effector reference trajectories, which were designed to carry out manufacturing tasks. Simulation results confirm the superiority of our control scheme for trajectory-tracking applications over its conventional version and the optimal super-twisting sliding mode control, even with external disturbances and trajectory changes. To show the robustness of the proposed control scheme under different operating conditions, all the numerical simulations were performed considering the same orders and gains. Finally, our control law introduces the fractional derivative and integral of Caputo–Fabrizio and Atangana–Baleanu respectively, which have not been used enough in the modeling and control of robotic systems. Therefore, it is interesting to analyze the contributions and advantages that arise when using them.

A Tube Model Predictive Control Method for Autonomous Lateral Vehicle Control Based on Sliding Mode Control.

This paper aims to enhance the lateral path tracking control of autonomous vehicles (AV) in the presence of external disturbances. While AV technology has made significant strides, real-world driving scenarios often pose challenges such as slippery or uneven roads, which can adversely affect the lateral path tracking control and reduce driving safety and efficiency. Conventional control algorithms struggle to address this issue due to their inability to account for unmodeled uncertainties and external disturbances. To tackle this problem, this paper proposes a novel algorithm that combines robust sliding mode control (SMC) and tube model predictive control (MPC). The proposed algorithm leverages the strengths of both MPC and SMC. Specifically, MPC is used to derive the control law for the nominal system to track the desired trajectory. The error system is then employed to minimize the difference between the actual state and the nominal state. Finally, the sliding surface and reaching law of SMC are utilized to derive an auxiliary tube SMC control law, which helps the actual system keep up with the nominal system and achieve robustness. Experimental results demonstrate that the proposed method outperforms conventional tube MPC, linear quadratic regulator (LQR) algorithms, and MPC in terms of robustness and tracking accuracy, especially in the presence of unmodeled uncertainties and external disturbances.

Robust [formula omitted]-dissipative event-triggered sliding mode control of discrete T-S fuzzy descriptor systems with partial unmeasurable premise variables

In this paper, the admissibility analysis and dissipative sliding mode control (SMC) based on event-triggered mechanism (ETM) are studied for discrete T-S fuzzy descriptor systems (D-TSFDS). The problem of partial unmeasurable premise variables in D-TSFDS is dealt with by nonlinear dynamic programming. Based on ETM, a sliding mode surface based on measurable premise variables is proposed for the first time. Since the delay between the sensor and the controller in ETM, a Lyapunov-Krasovskii function is used to acquire the sufficient conditions for the closed-loop system to be admissible with dissipative performance. A new SMC law is given to ensure the reachability conation. The simulation results demonstrate the effectiveness of the proposed method.

Design of Continuous Finite-Time Controller Based on Adaptive Tuning Approach for Disturbed Boost Converters

This research study proposes a continuous finite-time controller based on the adaptive tuning approach for the boost converters with unknown disturbances. A Lyapunov candidate function which contains an absolute function based on the fractional power of the sliding surface is employed to attain a smooth continuous control input. The recommended technique can eliminate the chattering phenomenon made by the sliding mode control signal and improve the control performance. Furthermore, the continuous adaptive-tuning control law is given to estimate the unknown bounds of exterior disturbances. The performance of the adaptive-tuned terminal sliding mode control law to the load variations and parametric uncertainties, and the input voltage, are studied in the MATLAB-Simulink environment. The obtained simulation results confirm the effectiveness of the suggested technique.

Backstepping Sliding Mode Method for Attitude Stabilization Control of Small Satellites

To address the problem that the attitude of a rigid satellite in orbit is susceptible to external disturbing moments, a control method based on the backstepping sliding mode method is proposed, which has strong robustness and anti-disturbance capability. Firstly, the coupling term in the mathematical model of satellite attitude is eliminated by using the backstepping method, secondly, the sliding mode control law is designed to reduce the sensitivity of the system to the external disturbance moment change and accelerate the response speed of the system, and the stability of the system is proved by using Lyapunov stability theory. Finally, the effectiveness and superiority of the rigid satellite attitude control based on the backstepping sliding mode method are verified by simulation.

Fixed time robust control for tower cranes with unmatched disturbances and input saturation

SummaryTo address the challenging problem of fixed‐time anti‐sway and positioning control for tower cranes with uncertain disturbances and input saturation, a novel fixed‐time anti‐saturation robust algorithm is proposed. First, on the basis of a newly designed fixed‐time convergence system, a fixed‐time disturbance observer (FTDO) is developed to estimate the matched and unmatched disturbances. Then, an anti‐saturation compensator is employed to deal with the input saturation and make the control input leave the saturated region rapidly. Upon which, a novel non‐singular fast terminal sliding mode surface is presented. Furthermore, in order to ensure the stability of each subsystem, a hierarchical sliding mode surface taking into account unmatched disturbances and input saturation is designed. Finally, the FTDO based hierarchical sliding mode control law is introduced to improve the transient control performance and robustness of tower cranes. The fixed‐time convergence of the closed‐loop system is proved by Lyapunov technique. Numerical simulations for four scenarios demonstrate the validity of the presented control scheme and fastest convergence speed in comparison to the recently proposed fixed‐time control methods.

Observer-based Finite-time Event-triggered Asynchronous Sliding Mode Control for Interval Type-II Fuzzy Semi-Markov Jump Systems with Quantization and Fading Channels

In this paper, we investigate the finite-time event-triggered sliding mode control(SMC) issue of a class of interval type-II fuzzy semi-Markov jump systems affected by quantization and fading channels. Firstly, the data needs to be quantized by logarithmic quantizers before being transmitted over the channel. To alleviate network pressure, a periodic event-triggered scheme is introduced to govern whether the data are sent to the sensor-tocontroller(S/C) channel or not. As the transmitted data passes through the S/C channel, it could undergo fading. Then, considering the asynchronous issue between the system mode and the controller mode, an asynchronous control scheme is applied; Thereafter, a feasible fuzzy observer-based SMC law is developed, which enables the state trajectories of the system to reach the specified sliding surface within finite-time; And with the aid of the time partition strategy, sufficient conditions for the system to be bounded in finite-time during the arrival and sliding stages are derived. Besides, by means of the linear matrix inequality(LMI) toolbox, the controller and the observer gains are computed. Finally, the advantages of the SMC strategy are validated by emulation products.

Dissipative control of switched nonlinear systems with sliding mode: an event-triggered control scheme

This paper introduces the event-triggered scheme to study the problems of dissipative control and dissipativity-based sliding mode control (SMC) for switched nonlinear systems. Firstly, based on a designed event-triggered scheme, a piecewise continuous state feedback controller is constructed; sufficient conditions for $$\left( Q,S,R\right) $$ - $$\alpha $$ -dissipativity of the resulting system are derived by the approaches of a switched Lyapunov function and an average dwell time. Secondly, these two methods are extended to the study of $$H_\infty $$ performance and passive performance; the corresponding sufficient conditions are provided. Thirdly, the dissipative control problem is solved by introducing an event-triggered scheme into SMC method. Sufficient conditions for dissipativity of the resulting system are derived, and an SMC law is designed to guarantee the reachability. At the end of this paper, the correctness of the proposed methods is proved by two numerical examples.

Security control for Markovian jump systems under fading channel: A finite‐time sliding‐mode method

AbstractThe finite‐time sliding mode control (SMC) design is developed in this work for Markovian jump systems with peak‐bounded external disturbances, where the system state may suffer from the channel fading and deception attacks over the sensor‐to‐controller channel. The multiplicative fading model is introduced to describe the fading phenomenon in the unpredictable communication network, and the channel coefficients are mutually independent random variables that take values in certain intervals. Besides, the deception attacks on the transmitted state signals may be stochastically launched. Under the effect of channel fading and deception attacks, a sliding surface involving fading parameter is devised, and a security finite‐time SMC law is designed to achieve the finite‐time reachability of the specified sliding surface. Furthermore, by adopting the partitioning strategy during the reaching phase and sliding phase of SMC design, the derived sufficient criteria can achieve the stochastic finite‐time boundedness. Finally, the numerical simulation results are provided to illustrate the developed finite‐time SMC approach under the fading communication and malicious attacks.