In this article, a switching prescribed-time adaptive second-order sliding mode (ASOSM) control framework is proposed for a category of nonlinear systems with unknown time-varying parameters. The design procedure is systematically conducted in three steps. First, by appropriately constructing the sliding variables, the original uncertain system is transformed into a new sliding mode dynamics that alleviates the restrictive relative-degree requirement and reduces input-channel uncertainties. Second, leveraging a time-scaling transformation and a modified adding a power integrator (API) technique, a switching prescribed-time ASOSM controller integrated with parameter adaptation mechanisms is constructed. Third, a rigorous Lyapunov-based stability analysis is provided, showing that the sliding variables are driven into an arbitrarily small neighborhood of the origin within a user-assigned prescribed time, independently of the initial conditions, and subsequently stabilized to the equilibrium point in a finite time. The distinctive merit of the proposed switching control scheme is its capability to handle both matched and mismatched uncertainties, without requiring prior knowledge of their state-dependent bounds. Finally, two representative examples are provided to illustrate the effectiveness of the developed switching control strategy.

In this article, a high-order sliding mode control (SMC) method is proposed for a class of nonlinear systems with nonvanishing uncertainties. Unlike most methods, which treat the upper bound of disturbances and their time derivatives as known or unknown, the proposed approach does not require an upper bound for nonvanishing uncertainties. Moreover, these uncertainties and their time derivatives are usually time-invariant, such as the exogenous time-varying disturbances of unknown magnitude and the modeling uncertainties of unknown system parameters. First, a low-order virtual integral dynamics is introduced such that the system dynamics are reconstructed. Second, based on the introduced integral dynamics, an SMC law incorporating correction terms is designed using Lyapunov theory to handle the various disturbances with an unknown upper bound. Finally, the finite-time convergence of the closed-loop system is guaranteed, and the effectiveness of the method is verified by the application of the Buck converter system.

Autonomous berthing is a critical step in realizing the full autonomy of unmanned surface vehicles (USVs), which can essentially be regarded as a trajectory-tracking task. It can be further transformed into a problem of nonlinear systems with output constraints. This paper proposes a novel adaptive fixed-time backstepping control scheme based on the barrier Lyapunov function (BLF) for autonomous berthing of USVs. Firstly, a new barrier Lyapunov function is designed to solve the output asymmetric constraint requirement of the autonomous berthing system, and it is also adaptive to the unconstrained system without changing the control structure. Secondly, the convergence of adaptive fixed-time control and bounded tracking of BLF are combined to conquer the long convergence time and nonlinear system uncertainty. Finally, simulation and field tests are conducted to verify our proposed scheme’s superiority.

This paper introduces PaZO, a preconditioned accelerated zeroth-order optimization algorithm for fine-tuning large language models (LLMs). First, we theoretically demonstrate the necessity of preconditioning in zeroth-order optimization, proving that zeroth-order stochastic gradient descent (ZO-SGD) alone fails to achieve the ideal convergence rate. Building on this, we propose a Preconditioned Simultaneous Perturbation Stochastic Approximation (PSPSA) and theoretical version of PaZO, and demonstrate that setting the order of preconditioner as $-1/2$ in PSPSA yields the improved convergence rate for PaZO. Moreover, we design a practical version of PaZO that stabilizes training via diagonal Hessian estimate and moving average technique. Extensive experiments on diverse downstream tasks with models like RoBERTa-large and OPT show PaZO’s effectiveness. Compared to other zeroth-order baselines, PaZO achieves better performance across models and tasks.

An efficient formation-keeping strategy is essential for unmanned surface vehicles (USVs) to achieve complex cooperation missions in the Marine Internet of Things (MIoT) system. However, traditional methods make generating an efficient strategy to adapt to different formation patterns difficult in dynamic MIoT. To address this, we enhance the deep deterministic policy gradient (DDPG) algorithm and propose a novel formation control strategy generation approach. First, we design a generic reward mechanism based on the virtual leader–follower strategy to adapt to different formation patterns, simplify the design process, and optimize the formation control. Then, we adopt the intrinsic curiosity module (ICM) to alleviate the problem of sparse rewards and the prioritized experience replay (PER) mechanism to improve the utilization of experience and accelerate the learning rate. In addition, a Gaussian noise model is integrated into the DDPG approach to simulate various external disturbances, which can improve the robustness of the generated strategy. Finally, we built a virtual simulation environment based on Unity3D and conducted field tests to verify the feasibility and superiority of our approach.

This paper presents a novel event-triggered adaptive generalized super-twisting algorithm (ET-AGSTA) for uncertain nonlinear systems. The remarkable features of the developed method lie in that the control gains can be dynamically adjusted to avoid overestimation, and the transmission of unnecessary signals can be reduced to save computational costs and network resources. Under the proposed ET-AGSTA, it can be proved by the Lyapunov theory that the sliding variable finite-time converges to a desired domain around the origin. The size of the domain can be achieved by modifying the control parameters. Moreover, the lower bound of the triggering time intervals is verified to be always a positive constant, which guarantees Zeno-free behavior in the whole system. Finally, simulation results are given to demonstrate the effectiveness of the proposed scheme.Note to Practitioners— In this paper, the motivation is to handle the problem of the ET-AGSTA design for uncertain nonlinear systems. Although the super-twisting algorithm (STA) is an effective tool for studying uncertain nonlinear systems, there exist two problems in practical applications. On the one hand, the control gains will be overestimated because the upper bounds of the derivatives of the uncertainties are often unknown. This will lead to severe chattering due to the discontinuous term existing in the STA. On the other hand, in actual scenarios, the state signals are periodically sampled and then transmitted to the controllers through the limited network. As the sampling period is usually fixed, it will yield the transmission of redundant signals, resulting in a waste of resources. Therefore, based on the Lyapunov theory, a novel ET-AGSTA is designed to overcome the drawbacks caused by the discontinuous term in the STA. Future work will apply the proposed method to the robotic systems.

In this work, we devise an output feedback second-order sliding mode (SOSM) control protocol for a category of nonlinear systems with unmatched uncertainties and asymmetric output constraints. The procedure of the design and analysis for this control tactic primarily encompasses the following steps. To begin with, a nonlinear mapping is introduced to convert the output-constrained SOSM system into a new SOSM dynamics without output constraints. Next, through adopting a scaling transformation with properly scheduled gains, a SOSM controller via output feedback is explicitly constructed. Third, it is theoretically certified that the presented control strategy insures both the finite-time convergence of the whole system and the compliance with the preset asymmetric output constraint. Eventually, the simulation studies on a practical application example confirm the feasibility and benefits of the proposed algorithm. Distinct from the prevailing outcomes in the literature, our control frame reveals two compelling features. One is that the output constraint issue is tackled via the system conversion based control. The other is that the proposed output feedback control design is independent of the separation principle, i.e., the finite-time convergence for the total closed-loop SOSM system embracing a state feedback SOSM controller and a discontinuous observer is together analyzed. Note to Practitioners—The paper considers a class of asymmetric output-constrained nonlinear systems subject to unmatched uncertainties, whose models are pervasively adopted in the engineering fields, e.g., manufacturing sector, transportation, etc. For such systems, the output feedback SOSM control issue hitherto has not been tackled, since under the circumstance that merely the output information is obtainable, the unmatched uncertainties and the output constraints are simultaneously considered. To this end, we successfully establish a novel output feedback SOSM control scheme by introducing the nonlinear mapping, the scaling transformation and the backstepping-like technique. Moreover, the finite-time convergence of the entire system is analyzed and corroborated via the Lyapunov method, and the fulfillment of the pre-specified asymmetric output constraint is assured, which make the proposed strategy more engineering-oriented. In future work, the efforts will be directed towards the validation of the proposed approach on an experimental platform for electric vehicles.

Decoupling control of the air supply system is crucial for enhancing the performance and prolonging the service life of proton exchange membrane (PEM) fuel cells. However, the strong coupling and nonlinearity inherent in the system pose significant challenges. Current decoupling techniques typically rely on model knowledge and commonly overlook the avoidance of compressor surge, which motivates our work with a twofold contribution. We first design a data-driven feedforward (DDF) and propose a feasible domain constraint (FDC) to avoid surge. Subsequently, an adaptive generalized supertwisting algorithm (AGSTA) is presented that eliminates the residual tracking errors of the DDF. Furthermore, its gradient descent principle and stability are demonstrated. The proposed method has been validated on an air supply system test bench and a hardware-in-the-loop (HiL) platform carrying a fuel cell electric vehicle (FCEV) model. The results indicate that our approach is more advantageous in terms of tracking accuracy, response speed, overshoot suppression and computational cost.

This article is committed to the establishment of an integral-based high-order sliding mode (iHOSM) controller for one category of nonlinear systems when confronted with perturbations with unknown magnitudes. A striking characteristic is that an integral dynamics is deftly constructed and then incorporated into the original sliding mode system to dispose of the perturbations of unknown magnitudes. On account of the new sliding mode dynamics, we explicitly introduce a systematic design protocol to dexterously design a new iHOSM controller. This is fulfilled through amending the technique of adding a power integrator. The theoretical justification has been guaranteed by the rigorous Lyapunov analysis. The investigations of two elucidative examples are provided to validate the validity and feasibility of the designed methodology.

In this article, we propose an estimator-based second-order sliding mode (SOSM) controller tailored for uncertain nonlinear systems with unknown input delay. Distinct from existing SOSM control methods, this work tackles two principal challenges: 1) the difficulty of dealing with unknown input delay, especially given the discontinuity of sliding mode controllers; and 2) the uncertainties in the nonlinear systems bounded by functions rather than widely-used constants. We begin by establishing the SOSM dynamics with input delay and uncertainties, followed by the introduction of an auxiliary compensation system. Then, we design an input delay estimator suitable for discontinuous controllers by enhancing the convex optimization method. Leveraging this, a novel estimator-based SOSM controller is constructed by adding a power integrator technique to address the input delay issue. Rigorous Lyapunov analysis is conducted to confirm the finite-time stability of the closed-loop control system. Finally, comparative simulations validate the superiority of the proposed SOSM controller.

In this article, a novel adaptive second-order sliding mode (ASOSM) control law is constructed for a general category of sliding mode control (SMC) systems with mismatched uncertainties, including a nonvanishing external disturbance. This innovative control design proposal is accomplished through three key mechanisms. First, the new sliding mode dynamics subject to mismatched uncertainties is derived by selecting the appropriate sliding variables, which can significantly increase the uncertainties existing in the control input channel and relax the strict requirement on the relative degree assumption of the sliding variable. Second, a novel ASOSM controller, which contains some adaptive parameters generated via a three-layer nested adaptive mechanism, is constructed by utilizing the modified adding power integrator (API) approach and the adaptive control technique. Third, the practical finite-time stability of the closed-loop sliding mode system is confirmed by means of the systematic Lyapunov stability theory. The technical advancement of the developed adaptive control scheme lies in its ability to effectively deal with a more general sliding mode dynamics containing multiple uncertainties and guarantee that the practical second-order sliding mode (SOSM) is established in a finite time. Finally, simulation results, incorporating a practical application case, are provided to illustrate the effectiveness of the designed adaptive control scheme.

Focusing on the speed loop problem of permanent magnet synchronous motor (PMSM), a composite adaptive second-order sliding mode (ASOSM) controller with a fixed-time extended state observer (FTESO) is proposed, which both reduces the controller chattering and improves the interference rejection performance. Firstly, to cope with the chattering in first-order sliding mode, a novel SOSM control method is designed for the speed loop of the PMSM system. Secondly, an FTESO is constructed to ensure the anti-interference performance of the system during variable loads. In the meantime, this paper adopts a novel adaptive strategy to select the time-varying gain to avoid chattering due to the overestimation of the fixed controller gain. Finally, the validity of the proposed controller is demonstrated through a series of comparative simulations.

This paper considers the problem of global asymptotic stabilization (GAS) for second-order linearly uncontrol-lable/unobservable systems with long delays in state and input by designing a sampled-data homogeneous feedback controller. To transform a large delay nonlinear integrator chain into a small delay nonlinear system, the time rescaling and nonsingular transformations are presented. The homogeneous domination approach and Lyapunov-Krasovskii(L-K) stability theorem are employed in building a sampled-data homogeneous controller that achieves GAS of the time-delayed nonlinear systems. In order to verify the effectiveness of the algorithm, a simulation is conducted.

We study a typical optimization model where the optimization variable is composed of multiple probability distributions. Though the model appears frequently in practice, such as for policy problems, it lacks specific analysis in the general setting. For this optimization problem, we propose a new structural condition/landscape description named generalized quasar-convexity (GQC) beyond the realms of convexity. In contrast to original quasar-convexity \citep{hinder2020near}, GQC allows an individual quasar-convex parameter $\gamma_i$ for each variable block $i$ and the smaller of $\gamma_i$ implies less block-convexity. To minimize the objective function, we consider a generalized oracle termed as the internal function that includes the standard gradient oracle as a special case. We provide optimistic mirror descent (OMD) for multiple distributions and prove that the algorithm can achieve an adaptive $\tilde{\mathcal{O}}((\sum_{i=1}^d1/\gamma_i)\epsilon^{-1})$ iteration complexity to find an $\varepsilon$-suboptimal global solution without pre-known the exact values of $\gamma_i$ when the objective admits ``polynomial-like'' structural. Notably, it achieves iteration complexity that does not explicitly depend on the number of distributions and strictly faster $(\sum_{i=1}^d 1/\gamma_i \text{ v.s. } d\max_{i\in[1:d]} 1/\gamma_i)$ than mirror decent methods. We also extend GQC to the minimax optimization problem proposing the generalized quasar-convexity-concavity (GQCC) condition and a decentralized variant of OMD with regularization. Finally, we show the applications of our algorithmic framework on discounted Markov Decision Processes problem and Markov games, which bring new insights on the landscape analysis of reinforcement learning.

We consider the non-convex non-concave objective function in two-player zero-sum continuous games. The existence of pure Nash equilibrium requires stringent conditions, posing a major challenge for this problem. To circumvent this difficulty, we examine the problem of identifying a mixed Nash equilibrium, where strategies are randomized and characterized by probability distributions over continuous domains. To this end, we propose PArticle-based Primal-dual ALgorithm (PAPAL) tailored for a weakly entropy-regularized min-max optimization over probability distributions. This algorithm employs the stochastic movements of particles to represent the updates of random strategies for the $\epsilon$-mixed Nash equilibrium. We offer a comprehensive convergence analysis of the proposed algorithm, demonstrating its effectiveness. In contrast to prior research that attempted to update particle importance without movements, PAPAL is the first implementable particle-based algorithm accompanied by non-asymptotic quantitative convergence results, running time, and sample complexity guarantees. Our framework contributes novel insights into the particle-based algorithms for continuous min-max optimization in the general non-convex non-concave setting.

In this article, a new adaptive second-order sliding mode (SOSM) controller is designed for a type of nonlinear systems with parametric uncertainties and time-varying asymmetric output constraints. There are two notable features in the obtained results. One feature is that a two-layer adaptive mechanism is established to reconstruct the upper bound of the unknown uncertainty, where the uncertainty is bounded by an unknown state-dependent structure rather than an unknown constant. The other is that a universal tangent-type barrier Lyapunov function (Tan-BLF) is constructed to address the time-varying asymmetric output constraint requirements. By combining the designed Tan-BLF, adaptive control and revamped adding a power integrator techniques together, a novel design procedure is introduced to systematically construct an adaptive SOSM controller. A rigorous Lyapunov analysis indicates that under the developed control framework, the finite-time stability of the whole system and the realization of the prescribed constraints can be guaranteed. Finally, two simulation cases containing a practical one are provided to demonstrate the effectiveness of the proposed control scheme.Note to Practitioners—This article is motivated by the desire to deal with nonlinear systems in the presence of parameter uncertainties and time-varying output constraints. In practical applications, on the one hand, parameter uncertainties are an unavoidable problem for real-world systems, and on the other hand, output constraints are widely present in many engineering systems due to safety considerations and inherent physical constraints. Until now, these issues have not been solved effectively. Therefore, to resolve these issues, a new adaptive SOSM controller is constructed in this article by using the adaptive control technique, adding a power integrator method, time-varying asymmetric Tan-BLF and Lyapunov finite-time stability theory. The proposed control strategy not only ensures the finite-time stability of the resulting closed-loop system, but also guarantees that the system output satisfies the preset time-varying output constraints. In the future, we will attempt to apply the proposed method to more practical systems.

This article proposes a novel event-triggered second-order sliding mode (SOSM) control algorithm using the small-gain theorems. The developed algorithm has global event property in aspects of the triggering time intervals. First, an SOSM controller is designed related to the sampling error of states, and it is proved that the closed-loop system is finite-time input-to-state stable (FTISS) with the sampling error via utilizing the small-gain theorems. Second, combined with the constructed SOSM controller, a new triggering mechanism is proposed depending on the sampling error by designing the appropriate FTISS gain condition. Third, the practical finite-time stability of the closed-loop system is verified. It is shown that the minimum triggering time interval is always a positive value in the whole state space. Finally, the simulation results demonstrate the effectiveness of the developed control method.

The work is centered on developing a constructive method of synthesizing an output-feedback second-order sliding-mode (SOSM) controller. By leveraging a coordinate transformation and revamping the technique of adding a power integrator, a state-feedback SOSM controller is first constructed under the full-state measurement. In order to tackle the challenge posed by the unmeasurable first derivative of the sliding variable, a discontinuous observer with appropriately selected scaling gains is put forward to overcome the measurable lack. Through the interactive cooperation of the state-feedback SOSM controller and the discontinuous observer, an output-feedback SOSM controller is successfully designed without reliance upon the separation principle. The finite-time convergence of the whole system is rigorously validated by dint of the Lyapunov function-based analysis. The efficiency of the theoretical results is ultimately corroborated through a simulation study.

Intelligent control is a crucial technology for realizing Industry 5.0, which makes industrial engineering systems more efficient, robust, and resilient. It is noteworthy that uncertainties and disturbances will inevitably be detrimental to the control performances of Industry 5.0 engineering applications. To deal with these issues, we propose a novel super-twisting-like continuous extended state observer-based fixed-time composite learning fuzzy control scheme and apply it to a typical engineering system. Unlike conventional fixed-time adaptive fuzzy control methods that update parameters merely by closed-loop stability conditions, the proposed fixed-time control scheme utilizes both tracking errors and prediction errors to update parameters compositely, which achieves better-tracking performance and fuzzy approximation precision. First, fuzzy logic systems (FLSs) are developed to identify the unknown model functions in the Industry 5.0 engineering system. Second, to deal with the remaining approximation errors of the FLSs, parameter uncertainties, and external disturbances, the novel super-twisting-like continuous extended state observers are designed to estimate these lumped disturbances. Third, the prediction errors that indicate the fuzzy approximation precision are constructed by developing fixed-time parallel estimators. Moreover, rigorous Lyapunov stability analysis is carried out to illustrate the fixed-time convergence of the entire closed-loop control system. Finally, the proposed control scheme is applied to a practical buck converter engineering system toward Industry 5.0, and comparative hardware experiments verified the advantages of the control scheme.

To achieve rapid and high-precision servo control of an electronic throttle, an adaptive control scheme is proposed based on the extremum seeking (ES), which consists of a variable-gain adaptive proportional-integral (ES-API) controller and an adaptive compensator (ES-ACP). The two gains (${K_{p}}$,${K_{i}}$) of the ES-API controller are designed as maps with respect to the tracking error, and the parameters of these maps are learned by ES. Additionally, the ES-ACP is applied to compensate for the strong nonlinearity inherent in an electronic throttle control (ETC) system, whose parameters are also learned by ES. During parameter learning, an objective function is utilized to quantify the tracking error of the opening angle of the electronic throttle plate, and then the parameters are learned using a step reference signal and a ramp reference signal. ES optimizes the above parameters by reducing the objective function to achieve a more favorable tracking response. Five reference signals are used to evaluate the learned controller after the parameter learning process is completed. Experiments were performed on a test bench equipped with an electronic throttle, and the experimental results show that the control scheme is capable of tracking multiple reference trajectories quickly and accurately.

The work is dedicated to handling the issue of a new adaptive second-order sliding mode (ASOSM) controller design for a class of nonlinear systems subject to disturbances and nonlinear control gains with unknown magnitudes. Significantly, the proposed controller involves two adaptive parameters, which are generated from a dual-layer adaptive mechanism. The mechanism directs at the reestablishment of the upper bounds of the unknown disturbances and the handling of the nonlinear control gains. Through a combination of the mechanism and the finely renovated adding a power integrator technique, a novel design procedure is introduced to skillfully design an ASOSM controller. A rigorous Lyapunov analysis is afforded to evince the finite-time stability of the whole system. Finally, two illustrative examples are given to exhibit the effectiveness of the developed approach.

The work proposes a generalized supertwisting algorithm (GSTA) and its constructive design strategy. In contrast with the conventional STA, the most remarkable characteristic of the proposed method is that the discontinuous term in the conventional STA is replaced with a fractional power term, which can fundamentally improve the performance of the conventional STA. It is shown that if the fractional power in the nonsmooth term becomes -1/2, the GSTA will reduce to the conventional STA. Under the GSTA, it will be rigorously verified by taking advantage of strict Lyapunov analysis that the sliding variables can finite-time converge to an arbitrarily small region in a neighborhood of the origin by tuning the gains and the fractional power. Finally, simulation studies are provided to demonstrate the superiority of the theoretically obtained results.

For a class of nonstrict-feedback stochastic nonlinear systems with the injection and deception attacks, this article explores the problem of adaptive neural network (NN) fixed-time control ground on the self-triggered mechanism in a pioneering way. After developing the self-triggered mechanism and the delay-error-dependence function, a neural adaptive delay-constrained fault-tolerant controller is proposed by employing the backstepping technique. The self-triggered mechanism does not require an additional observer to determine the time of the data transmission, which reduces the consumption of the system resources more efficiently. In addition, the whole Lyapunov function with the delay-error-dependence term is developed to solve the deferred output constraint problem. Under the proposed controller, it can be proven that all the signals within the closed-loop system are semiglobally uniformly bounded in probability, while the convergence time is independent of the initial state and the deferred output constraint control performance is achieved. The feasibility and the superiority of the proposed control strategy are shown by some simulations.

This article is concerned with the control design of adaptive fuzzy fixed-time high-order sliding mode (HOSM) under asymmetric output constraints. The main objective of this article is to construct a control scheme to build the HOSM in a fixed time and fulfill the preset constraint condition. For this purpose, initially to conquer this obstacle regarding the output constraint, a barrier Lyapunov function is developed to keep the output variable within the predefined constraint during operation. Then, the unknown functional bounds of uncertainties in the considered system are modeled by invoking fuzzy logic systems. With the integrated use of adaptive fuzzy control and backstepping-like techniques, a novel protocol for the fixed-time HOSM control with asymmetric output constraints is developed. Through the strictly theoretical clarification, the HOSM is fixed time established under the suggested control strategy. The effectiveness of the derived results is eventually testified by some comparative simulation results.

This article proposes a novel event-triggered second-order sliding mode (SOSM) control method for uncertain nonlinear systems. First, three saturated-like functions are predesigned to construct a new switched triggering mechanism. Under the proposed triggering mechanism, an event-triggered SOSM controller is designed to ensure that the states of the SOSM system finite-time converge to a domain of the origin and never escape from the domain. Then, to avoid Zeno behavior, two positive minimum inter-execution intervals are obtained based on different triggering conditions. Finally, a simulation study is given to verify the effectiveness of the control strategy.

Active disturbance rejection control (ADRC) is promising for permanent magnet synchronous machine (PMSM) speed regulation system. However, the control performance of ADRC scheme is generally affected by the measurement noise introduced by position sensors. To solve this problem, a high-order nonlinear extended stated observer (NESO) is proposed in this paper to directly estimate the motor speed. The bode diagrams of the high-order NESO based measurement noise suppression system obtained by frequency-sweep approach are illustrated to show its frequency domain characteristics. Taking full advantage of nonlinear control and high-order observer techniques, the proposed strategy can maintain satisfactory noise suppression performance without sacrificing the robustness of PMSM system. Comprehensive experimental results are conducted to verify the superior properties of the proposed control strategy.

In this paper, a novel saturation-based control method is proposed for high-order sliding mode (HOSM) dynamics with upper-triangular nonlinearities. Firstly, a new HOSM dynamics with upper-triangular nonlinearities is constructed based on the traditional HOSM dynamics, so as to reduce the uncertainties in the control input channel. Then, a HOSM controller is established by means of the adding a power integrator method such that the new HOSM dynamics is locally stabilized. Finally, the saturation-based controller is constructed by a combination of the saturation technique and the local HOSM controller to guarantee that the sliding variables can converge into a domain of attraction in a finite time and retain inside it thereafter. The rigorous stability analysis is made by the Lyapunov theory. A simulation example is also given to demonstrate the effectiveness of the proposed method.

In this article, an adaptive fuzzy control design strategy is presented for p -norm nontriangular stochastic high-order nonlinear systems with asymmetric output constraints and unknown nonlinearities. To prevent the violation of the asymmetric output constraint, a novel barrier Lyapunov function (BLF) is constructed. Then, combining the constructed BLF with adding a power integrator approach, the adaptive fuzzy control algorithm is developed by the backstepping technique. Simultaneously, the rigorous proof displays that the designed controller can ensure that all variables of the closed-loop system are bounded in probability with the achievement of the output constraint. Eventually, the theoretical result is further demonstrated via the simulation results.

The output constraints are widespread in physical systems. Violation of output constraints may result in system damage and performance degradation. This article investigates the design issue of adaptive fuzzy second-order sliding-mode (SOSM) controller, which aims to handle a class of nonlinear systems with output constraints. The unknown bounds of uncertainties are approached dynamically by fuzzy logic systems. Through designing a new barrier Lyapunov function, the output constraint problem has been well solved. Then, by integrating adding a power integrator technology and adaptive fuzzy control, a novel adaptive fuzzy SOSM controller is proposed. It is proved that the proposed method makes the output variable not violate the specified constraint region. At the same time, it can be shown, based upon the Lyapunov approach, that the finite-time stability of the resulting closed-loop system under output constraint is ensured. Finally, a numerical example and a practical pendulum system are presented to demonstrate the validity of the proposed SOSM control strategy.

The work has devised a novel fixed-time control scheme for a class of nonlinear systems with output constraints. Two distinctive features are incorporated into the gained results. One is that the upper bound of settling time for the closed-loop system can be estimated without dependence on system initial states, and hence, can be acquired arbitrarily small through tuning control design parameters. The other is that the output constraint can be handled by means of a barrier Lyapunov function (BLF). Via the BLF and the backstepping-like technique, a fixed-time controller, which can cope with a type of nonlinear systems concurrently with and without output constraints, is systematically built. The rigorous analysis on the strength of the Lyapunov theory is given to show that the investigated system under the proposed controller is fixed-time stable, and the violation of a preset output constraint is averted. The case studies of a series elastic actuator system are offered to substantiate the derived theoretical results.

This paper is concerned with controller design for high-order sliding mode (HOSM) dynamics with upper-triangular uncertainties. First, we design an HOSM controller by means of the adding a power integrator method in order to locally stabilize the HOSM dynamics with upper-triangular uncertainties. On this basis, by combining the saturated technique and the local HOSM controller together, we devise a saturated-like controller in order to ensure the finite-time convergence of the sliding variables into a domain of attraction without an escape from the domain thenceforth. The stability results are established based on the Lyapunov theory. The efficiency of the designed saturated-like HOSM controller is validated by a numerical example.

This paper considers the control problem of p-norm stochastic nonlinear systems with output constraints, while the system nonlinearities are completely unknown and the system states are unavailable except the output. A nonlinear observer is constructed to estimate the unmeasurable states. Then, based on the constructed observer and a tan-type barrier Lyapunov function (BLF), an adaptive fuzzy output-feedback control strategy is developed by combining the technique of adding a power integrator with the fuzzy logic systems (FLSs). The proposed scheme enables that all the signals of the considered closed-loop systems are bounded in probability while the prespecified output constraint is not violated. Finally, a numerical example verifies the validation of the proposed scheme.

This article investigates the adaptive fuzzy control design for p-norm stochastic high-order lower triangular nonlinear systems with output constraints and unknown nonlinearities. First of all, a tan-type barrier Lyapunov function (BLF) is constructed to deal with the output constraint issue. Subsequently, an adaptive fuzzy control algorithm is developed by combining the constructed BLF with adding a power integrator technique. Simultaneously, the Lyapunov analysis shows that the designed controller can guarantee the boundness of all the variables in the closed-loop system in probability without violating the given output constraint. Finally, some comparative simulation results are provided to demonstrate the effectiveness of the proposed method.

This article addresses the problem of finite-time stabilization for a class of high-order nonlinear stochastic systems with asymmetric output constraints. A novel barrier Lyapunov function (BLF) is first presented to handle such asymmetric constraints. Further, based on the proposed BLF and the adding a power integrator technique, a controller design approach is developed by the backstepping method. It can be rigorously proved that the designed controller can not only make the system states finite-time converge to the origin in probability but also ensure that the constraint on system output is not violated. Another novelty of this approach is that it is a unified tool owing to its simultaneous application to the systems without output constraints. Finally, the validity of the proposed scheme can be verified by a simulation example.

The second-order sliding mode (SOSM) controller design problem for a class of sliding mode dynamics subject to an upper-triangular structure has been discussed in this paper. The proposed SOSM controller design involves two steps. First, a Lyapunov-based SOSM controller is developed by using the adding a power integrator technique to locally finite-time stabilize the sliding variables. Second, by combining the local SOSM controller with a saturation function, a novel SOSM controller with a saturation level is constructed. The feature of the new SOSM controller lies in that the saturation level can be tuned not only to guarantee the global convergence but also to improve the dynamic performance. Lyapunov analysis has been utilized to test the finite-time stability of the closed-loop sliding mode dynamics. The proposed method is eventually demonstrated by simulation results.

This paper mainly studies the control problem of permanent magnet synchronous motor (PMSM) speed control system. Firstly, by analyzing the error dynamics equation of PMSM, an appropriate integral fixed-time sliding mode surface is selected. Then, an integral fixed-time sliding mode control algorithm is designed through the selected integral sliding mode surface. Finally, comparison results of numerical simulations are provided to verify the effectiveness of the proposed control method.

This paper mainly investigates the attitude control problem for a spacecraft. Not only angular velocity constraint but also external disturbances are considered in the system model. Under the action of proposed controller, the posture can be converged to the desired value, and the angular velocity can be asymptotically converged to the origin.

A second-order sliding-mode (SOSM) control method is developed for the regulation problem of a dc-dc buck converter. By taking into account the model uncertainties and external disturbances in the mathematical model, a sliding variable with relative of degree 2 is first constructed. Then, a new SOSM controller is developed such that the output voltage will well track the desired reference voltage. Theoretical analysis shows that the resulting closed-loop system is globally finite-time stable, while similar SOSM control results only give the proof for finite-time convergence. The way on how to implement the proposed SOSM algorithm is also presented. The theoretical findings are verified by extensive simulations and experiments.

In this paper the problem of designing a second-order sliding mode controller for nonlinear systems with bounded uncertainties is addressed. The adding a power integrator technique is applied to develop a new second-order sliding mode control algorithm. It is shown that under the controller thus designed, the resulting closed-loop system can achieve the finite-time Lyapunov stability, which is superior to the similar results in the literature that can only give the finite-time convergence. The performance of the new second-order sliding mode control algorithm is demonstrated by an illustrative example.

In this paper a new design method is proposed for sliding mode control of a class of nonlinear second-order systems with input saturation. The main idea is to combine the conventional terminal sliding mode manifold with a saturation function for construction of a new nonsingular terminal sliding mode manifold. By virtue of the bound of the uncertainty, the constructed terminal sliding mode manifold is employed to design a saturated controller directly for the nonlinear system. It is shown that the designed saturated controller guarantees the finite-time convergence of the states of the resulting closed-loop system to zero.