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Backstepping is a popular control method for uncertain pure-feedback nonlinear systems (PFNSs). However, it usually suffers from the "complexity explosion problem" caused by repeatedly differentiating virtual control inputs and the complex recursive design process. This article focuses on a novel direct control method for uncertain PFNSs with input saturation and unmeasured states without relying on the backstepping framework. The uncertain PFNS is transformed into a canonical system through a coordinate transformation. The tanh function is employed to handle the input saturation, and an observer is established to estimate unmeasurable states. Specially, a fuzzy echo state network, combining fuzzy logic system with echo state network, is created to estimate the ideal controller, and a composite adaptation law that utilizes both tracking error and the approximation of learning error is developed. Without any additional control term, all variables involved are bounded and the tracking error convergence can be guaranteed. The simulation results of two experiments validate the efficacy of the theoretical results. [ABSTRACT FROM AUTHOR]

This article studies the cluster consensus problem for the nonlinear multi‐agent systems subject to input saturation under the context of event triggered control. Taking ordinary consensus object as a special case, this article considers the problem of cluster consensus. The event triggered mechanism is designed and the Zeno phenomenon is ruled out. The sufficient conditions of control protocol and range estimation of domain of attraction are formulated by the linear matrix inequalities for the constraints of input saturation and nonlinear terms existed in the system dynamics. Finally, the proposed results are validated by one example in the background of spring damping system. [ABSTRACT FROM AUTHOR]

This paper deals with the discrete-time antiwindup compensator (AWC) synthesis for nonlinear discrete-time systems under input saturation. The proposed method considers the objective of an optimal AWC design for fast convergence and for improved performance against the saturation nonlinearity. A discrete-time full-order AWC architecture is presented for nonlinear discrete-time systems to achieve an improved performance against the saturation nonlinearity. Additionally, an equivalent decoupled AWC architecture for nonlinear discrete-time system is derived through algebraic analysis and transformation of saturation to dead-zone function. To achieve fast convergence, a more generic Lyapunov function has been applied for the AWC design by incorporating an exponential term in the Lyapunov function. Then, new conditions for the AWC synthesis are revealed by application of the resultant decoupled discrete-time architecture, nonlinearity condition, a modified quadratic-exponential Lyapunov function, optimally exponential L 2 approach, and input saturation properties. The design conditions are provided for both global and local design scenarios, which can be applied to both stable and unstable plants. Compared with the conventional methods, the proposed approach deals with nonlinear systems, can be more practical due to discrete-time scenario, provides an optimal design for both fast convergence and performance, and applicable to both stable and unstable plants. A simulation example has been provided to demonstrate the efficacy of the proposed nonlinear AWC design. [ABSTRACT FROM AUTHOR]

This paper investigates the finite‐time preview saturated control problem for linear parameter‐varying systems with input saturation. The external disturbances and input saturation, previewable reference signals, and parameter variations are considered simultaneously. First, using the error system method, we construct an augmented error system with previewed information. This transforms the finite‐time preview saturated control problem into a finite‐time stabilization problem. Next, static output‐feedback controllers are used to guarantee the finite‐time boundedness of the closed‐loop system. Sufficient conditions guarantee the existence of the desired controllers are obtained using linear matrix inequalities. At last, we use a numerical simulation to show the proposed design method's effectiveness. [ABSTRACT FROM AUTHOR]

This paper presents an innovative approach that integrates a fixed-time control (FTC) algorithm with an improved sparrow search algorithm (ISSA) to enhance the trajectory tracking accuracy of a two-degree-of-freedom (two-DOF) robotic arm. The FTC algorithm, which incorporates barrier Lyapunov function (BLF) and adaptive neural network strategies, ensures rapid convergence, effective vibration suppression, and the robust handling of system uncertainties and input saturation. The ISSA, inspired by the foraging behavior of sparrows, improves search efficiency through dynamic weight adjustments and chaotic mapping, balancing global and local search capabilities. By optimizing control parameters, ISSA minimizes tracking errors. Simulation results demonstrate that the combined FTC and ISSA approach significantly reduces tracking errors and improves response speed compared to the use of FTC alone, underscoring its potential for achieving high-precision control in robotic arms and offering a promising direction for precise robotic control applications. [ABSTRACT FROM AUTHOR]

One‐dimensional thrust vectoring turbojet vertical takeoff and landing (VTOL) aircraft have attracted research attention due to their high thrust‐to‐weight ratios and their solution for the slow speed response of turbojet engines. However, there are some uncertainties and physical limitations in their systems, such as external disturbances, unknown parameters and input saturation. To improve the accuracy and convergence speed of trajectory tracking, a fixed‐time control method that is robust to saturation is proposed. The system dynamics are established, and an auxiliary system is built within a fixed time control framework to address the influence of input saturation and increase the error convergence rate. Nonsingular fast terminal sliding mode technology is combined with a few adaptive laws to ensure the robustness of the closed‐loop system against dynamic uncertainties and improve the precision of steady‐state control. The stability of the control system is proven based on Lyapunov, and the controller parameters are optimized based on particle swarm optimization (PSO). The proposed method based on fixed‐time stability guarantees that the states of the closed‐loop system can reach the residual set around zero within the designed time, and an expression for the upper bound on the convergence time is given. Finally, numerical simulations demonstrate the superiority of the proposed method based on the error integral criterion. [ABSTRACT FROM AUTHOR]

ABSTRACT In order to improve the penetration ability of missiles in the end guidance stage, and considering the delay problem when designing the guidance control loop separately, this article mainly studies the design problem of an integrated guidance control law under input saturation and attitude angle constraints. For the lower triangular structure model of the integrated guidance and control system, this article mainly uses an improved backstepping method to design the controller, and introduces an error compensation term in the design of the virtual controller to improve system stability. Introducing auxiliary variables and barrier Lyapunov functions to handle saturation and state constraint problems; in the face of the main problems of atmospheric disturbances, unmodeled dynamic errors of the system, and unknown acceleration of the target, this article mainly adopts a finite time observer for processing. The final simulation results demonstrate the effectiveness and superiority of the controller designed in this article. [ABSTRACT FROM AUTHOR]

A fixed-time distributed formation control strategy is investigated for multiple underactuated unmanned surface vehicles (USVs) with unmeasured velocities and input saturation. Initially, a necessary coordinate transformation is applied to the mathematical model of USVs to address the underactuated issue. Subsequently, a fixed-time extended state observer (FESO) is constructed to estimate unmeasured velocities and lumped disturbances of USVs based on input and output data in the control loop. Meanwhile, the leader–follower approach is applied to achieve a preset formation. A fixed-time differentiator is utilized to compute real-time differential signals for virtual control laws, which simplifies the complexity of controller design. Furthermore, a fixed-time distributed formation controller is designed based on an asymmetric differentiable saturation model. The effects of input saturation are eliminated by a designed auxiliary system. Finally, the fixed-time stability of the closed-loop system is analyzed through the Lyapunov stability theory. The comparison simulation results verify the effectiveness and superiority of the proposed formation control scheme. • A distributed fixed-time control strategy is proposed for USV formation. • The designed controller with asymmetric and smooth saturated curves. • The proposed control method scaled flexibly without communication burden. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust coordination control based on interval observers for multi‐agent systems in the presence of input saturation and disturbances. Firstly, in the scenario where the system state is not directly measurable, two types of interval observers are, respectively, constructed by resorting to the upper and lower bounds on external perturbances as well as the output information. Secondly, a parametric Lyapunov equation‐based low‐gain feedback control method is proposed to guarantee semiglobal bounded consensus. In contrast to the conventional approach based on parametric algebraic Riccati equations, the proposed method offers the advantage of allowing the parameters to be determined in advance. Finally, a simulation example and a practical electrical circuit model are conducted to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of adaptive containment fault‐tolerant control for nonlinear multiagent systems with periodic disturbances. Different from most existing fault‐tolerant control schemes, the form of multiple faults is explicitly considered in this paper, including actuator faults and sensor faults. By combining the Fourier series expansion with neural networks, the unknown nonlinear dynamics subject to time‐dependent periodic disturbances are approximated. Then, the "complexity of explosion" issue that exists in traditional backstepping‐based results is avoided by introducing a first‐order sliding‐mode differentiator. It is proved that the developed containment control policies can ensure that all signals of the close‐loop systems are uniformly ultimately bounded, and all followers can converge to a convex area formed by multiple leaders. Simulation results verify the validity of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper investigates a challenging heading control problem for a flexible paraglider recovery system with input saturation. A fixed‐time observer‐based control approach is presented. In this approach, a fixed‐time disturbance observer is preliminarily designed to estimate the aerodynamic uncertainties and the complex coupling of the subsystems. A fixed‐time auxiliary system is then proposed to compensate for input saturation impact. With the application of the estimated and compensation values, a novel heading tracking controller is synthesized with compensated disturbance. The key feature of the scheme is that it is not only fixed time stable regardless of any initial state, but also it prevents control performance degradation due to input saturation and various disturbances. Simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper explores the control strategy for toolface tracking in the stabilized platform of a rotary steerable system, considering both input saturation and output constraint. To mitigate the impact of unknown friction torque and modeling error on the stabilized platform, we propose an adaptive fuzzy backstepping control approach. A fuzzy state observer is specifically devised to handle the uncertain state arising from unknown friction torque and modeling errors. Introducing an auxiliary system effectively compensates for input saturation, and the resolution of the output error constraint is achieved through the construction of a barrier Lyapunov function. Furthermore, employing the Lyapunov method establishes that all signals in the entire closed-loop control system are semi-globally uniformly ultimately bounded. Simulation results confirm the efficacy of the proposed control methodology. [ABSTRACT FROM AUTHOR]

In this paper, the attitude control problem of uncertain multi-rotor unmanned aerial vehicles (UAVs) subject to input saturation and external disturbance is considered. First, by introducing a set of low-pass filters, filter-based estimators are utilized for compensating parametric uncertainties to achieve good estimation. Second, a full-order auxiliary system is constructed, which integrates the functions of removing the command filtered error between virtual control and filtered virtual control as well as the deviation between the unsaturated input and the saturated input. In order to deal with the external disturbance more effectively, a filter-based disturbance observer and an adaptive bounding law are developed to suppress it. Simulation results applied to an octorotor system and experimental results applied to a quadrotor system verify the control performance of the proposed method under different conditions. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive super-twisting control design method to solve tracking problems for a class of perturbed MIMO nonlinear systems under the condition of input constraints. A partial state's observer is firstly designed to estimate the unmeasurable states. Then, one designs a sliding surface function and crafts an adaptive super-twisting sliding mode controller under the constraints of input saturation for solving the tracking problems. The signs of the upper and lower bounds of the input saturation functions are not restricted to positive and negative respectively. Under certain conditions, the tracking errors and state estimation errors are all tend to zero within a finite time. Furthermore, there is no need to know the upper bounds of perturbations beforehand due to the usage of adaptive mechanisms embedded control both in the scheme and the state's observer. An application example is given to demonstrate feasibility and effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This work proposes a resource efficient robust control scheme for missile-target engagement scenarios subjected to external disturbances. The robustness is achieved by using an annular event-triggered artificial time-delayed control (ET-TDC) methodology with input saturation. The ET-TDC philosophy uses the TDC strategy through a dynamic predefined triggering mechanism which overcomes the requirement to update the control periodically for every sampling instant, unlike conventional TDC and other robust control schemes. Thus the proposed methodology can tackle uncertainties with minimal a-priori knowledge while significantly reducing the over-utilisation of system resources. In addition, the adopted event-triggered mechanism facilitates further conservation of energy which might be crucial for mid-to-long range engagement scenarios. The closed-loop stability is derived analytically and the simulation results illustrate the efficacy of the proposed guidance framework in comparison with other state-of-art robust control methodologies. [ABSTRACT FROM AUTHOR]

In this paper, a class of linear discrete-time systems with input saturation is studied in a data-driven framework. Firstly, the input-state data are collected to represent the open-loop and closed-loop systems. While the open-loop data-based representation is a result that is parallel to system identification, the closed-loop representation bypasses the system identification and can be used for direct data-driven control law synthesis. Then, by a novel Lyapunov technique, sufficient conditions for system stability are derived, such conditions are independent of system matrices. Moreover, the attraction domain is estimated using two classes of shape reference sets. Finally, two examples are used to test the correctness of the data-driven control laws. [ABSTRACT FROM AUTHOR]

This paper presents a data-driven model-free adaptive containment control (MFACC) scheme for uncertain rehabilitation exoskeleton robots, where the robotic exoskeleton dynamics are uncertain with saturation constraints. To handle uncertainties of the robotic dynamics, a model-free adaptive control (MFAC) strategy is established by linearizing the robotic exoskeleton dynamics into an equivalent data model. Considering the integral additive effect of the traditional MFAC method, an improved MFAC controller is designed in this paper. Since actuators with saturation constraints constantly affect the safety of patients during rehabilitation training, we construct a new criterion function with active constraints for the critical function of the MFAC algorithm and adopt the Hildreth quadratic programming algorithm to find the constrained optimal solution to overcome this limitation. The proposed MFACC scheme is rigorously proven by the compression mapping method to demonstrate model-free stability. Finally, the proposed control scheme is verified to be effective by simulation studies of the robotic SimMechanics model. [ABSTRACT FROM AUTHOR]

This paper solves a fixed-time trajectory tracking control problem for a marine surface vessel in the presence of model uncertainties, external disturbances, input saturation and prescribed performance constraints. Firstly, a fixed-time disturbance observer (FXDO) is designed, which not only realizes fixed-time stability, but also solves the design method problem in the existing disturbance observer. Secondly, a fixed-time nonsingular terminal sliding mode manifold (FXNTSMM) with simple structures is designed, whereby the designed FXNTSMM reduces the calculation burden of the system. Thirdly, a fixed-time trajectory tracking control scheme in the presence of model uncertainties, external disturbances, input saturation and prescribed performance constraints is proposed based on the FXDO, the FXNTSMM and a prescribed performance function, and the entire constrained closed-loop control system is with fixed-time stability, simplicity and nonsingularity. Finally, several numerical simulation results are presented to demonstrate the effectiveness of the proposed trajectory tracking control scheme. [ABSTRACT FROM AUTHOR]

Abstract This study focuses on the highway platoon driving mode and proposes a distributed adaptive control algorithm based on an observer. Firstly, the adaptive observer is designed to compensate for the effect of unknown driving resistance and thus enhance the adaptation ability of the system to uncertainty. Secondly, an auxiliary system is introduced to specifically address actuator saturation constraints, ensuring the stability of the platoon driving in extreme conditions. Lastly, combining an event‐triggered mechanism, a control strategy is designed to achieve the stability of the entire platoon while maximizing the conservation of communication resources. The algorithm's viability and efficiency are confirmed through simulation outcomes.

Hybrid optical systems with integrated control mechanisms enable a dynamic adjustment of optical components, ensuring real-time optimization, adaptability to changing conditions, and precise functionality. This control requirement enhances their performance in applications demanding responsiveness, such as autonomous systems, adaptive optics, and advanced imaging technologies. This research introduces a novel approach, employing a dynamic-free Takagi-Sugeno fuzzy sliding mode control (TS-fuzzy SMC) technique, to regulate and stabilize a specific category of chaotic fractional-order modified hybrid optical systems. The method addresses uncertainties and input-saturation challenges within the system. Leveraging a novel fractional calculus definition along with the non-integer type of the Lyapunov stability theorem and linear matrix inequality principle, the TS-fuzzy SMC approach was applied to effectively mitigate and regulate the undesired behavior of the fractional-order chaotic-modified hybrid optical system. Notably, this scheme achieved control without experiencing undesirable chattering phenomena. The paper concludes by offering concrete examples and comparisons, demonstrating how the theoretical findings are applied in real-world scenarios. This provides practical insights into the effectiveness of the proposed approach in diverse applications.

This study focuses on the highway platoon driving mode and proposes a distributed adaptive control algorithm based on an observer. Firstly, the adaptive observer is designed to compensate for the effect of unknown driving resistance and thus enhance the adaptation ability of the system to uncertainty. Secondly, an auxiliary system is introduced to specifically address actuator saturation constraints, ensuring the stability of the platoon driving in extreme conditions. Lastly, combining an event‐triggered mechanism, a control strategy is designed to achieve the stability of the entire platoon while maximizing the conservation of communication resources. The algorithm's viability and efficiency are confirmed through simulation outcomes. [ABSTRACT FROM AUTHOR]

In this article, anti‐unwinding sliding mode attitude maneuver control with predefined time is investigated for rigid spacecraft with input saturation. First, a nonsingular sliding function containing two equilibrium points is designed to ensure the predefined‐time convergence of system states and unwinding‐free performance of the closed‐loop system on the sliding phase. Then, an auxiliary system with a dynamic parameter is presented to compensate the impact of input saturation. With this parameter, the auxiliary system can handle input saturation that occurs. Based on the sliding function and the auxiliary system, an attitude maneuver controller is developed to guarantee the robustness of the closed‐loop system to bounded external disturbance. Under the designed controller, the states of the closed‐loop system are driven into a neighborhood of the sliding surface within a predefined time. Moreover, the unwinding phenomenon is also avoided on the reaching phase. Numerical simulation results illustrate the unwinding‐free performance and predefined‐time convergence of the closed‐loop system under the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper studies the prescribed-time relative motion control problem of spacecraft formation flying under input saturation. Using prescribed-time theory, a prescribed-time sliding mode is designed such that the states on the sliding mode converge to the equilibrium in the prescribed time. Based on the prescribed-time sliding mode, a prescribed-time relative motion tracking controller is developed, which guarantees fast formation maneuvers with feasible fuel consumption and strong robustness under input saturation. Furthermore, a simulation example is carried out to verify the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper proposes a novel multi-unmanned aerial vehicle (UAV) connectivity preservation controller, suitable for scenarios with bounded actuation and limited communication range. According to the hierarchical control strategy, controllers are designed separately for the position and attitude subsystems. A distributed position controller is developed, integrating an indirect coupling control mechanism. The innovative mechanism associates each UAV with a virtual proxy, facilitating connections among adjacent UAVs through these proxies. This structuring assists in managing the actuator saturation constraints effectively. The artificial potential function is utilized to preserve network connectivity and fulfill coordination among all virtual proxies. Additionally, an attitude controller designed for finite-time convergence guarantees that the attitude subsystem adheres precisely to the attitude specified by the distributed position controller. Simulation results validate the efficacy of this distributed formation controller with connectivity preservation under bounded actuation conditions. The simulation results confirm the effectiveness of the distributed connectivity preservation controller with bounded actuation. • A connectivity preservation controller is designed by bounded potential functions. • An indirect coupling framework is employed to tackle input saturation. • The stability analysis of the connectivity preservation controller is given. [ABSTRACT FROM AUTHOR]

In this article, an adaptive fixed‐time sliding mode control method is proposed for the quadrotor unmanned aerial vehicles (UAVs) with external disturbances and input saturation. Firstly, the fixed‐time sliding mode surface with a piecewise function enhances convergence speed and avoids singularity problems. The radial basis function neural networks (RBFNNs) are selected to estimate disturbances, and auxiliary systems are designed to address input saturation. Subsequently, an adaptive controller is created to ensure that the error system can converge into the neighborhood of origin within a fixed time. Furthermore, based on the proposed control approach, the stability of the closed‐loop system is analyzed with rigorous theoretical proof. Finally, comparative simulations are provided to illustrate the effectiveness and superiority of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper investigates the group consensus of hybrid‐order heterogeneous multi‐agent systems (MASs) consisting of first‐order linear agents and second‐order nonlinear agents with and without input saturation. First, group consensus algorithms are introduced. Then, by using various mathematical methods, including the graph theory, LaSalle invariant set principle, and Lyapunov stability theory, it is shown that hybrid‐order heterogeneous MASs can reach group consensus if sufficient conditions are satisfied. Further, the simulations are conducted to verify the theoretical results. Finally, the simulation results demonstrate that hybrid‐order heterogeneous MASs with and without input saturation can achieve the group consensus. [ABSTRACT FROM AUTHOR]

In this study, we propose an adaptive neural network (NN) control approach for a 2-DOF helicopter system characterized by finite-time prescribed performance and input saturation. Initially, the NN is utilized to estimate the system’s uncertainty. Subsequently, a novel performance function with finite-time attributes is formulated to ensure that the system’s tracking error converges to a narrow margin within a predefined time span. Furthermore, adaptive parameters are integrated to address the inherent input saturation within the system. The boundedness of the system is then demonstrated through stability analysis employing the Lyapunov function. Finally, the effectiveness of the control strategy delineated in this investigation is validated through simulations and experiments. [ABSTRACT FROM AUTHOR]

Hybrid optical systems with integrated control mechanisms enable a dynamic adjustment of optical components, ensuring real-time optimization, adaptability to changing conditions, and precise functionality. This control requirement enhances their performance in applications demanding responsiveness, such as autonomous systems, adaptive optics, and advanced imaging technologies. This research introduces a novel approach, employing a dynamic-free Takagi-Sugeno fuzzy sliding mode control (TS-fuzzy SMC) technique, to regulate and stabilize a specific category of chaotic fractional-order modified hybrid optical systems. The method addresses uncertainties and inputsaturation challenges within the system. Leveraging a novel fractional calculus definition along with the non-integer type of the Lyapunov stability theorem and linear matrix inequality principle, the TSfuzzy SMC approach was applied to effectively mitigate and regulate the undesired behavior of the fractional-order chaotic-modified hybrid optical system. Notably, this scheme achieved control without experiencing undesirable chattering phenomena. The paper concludes by offering concrete examples and comparisons, demonstrating how the theoretical findings are applied in real-world scenarios. This provides practical insights into the effectiveness of the proposed approach in diverse applications. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time tracking control problem for agile missiles with multiple heterogeneous actuators in the presence of saturation constraints and external disturbances. To reduce the turning radius and promote maneuvering envelope, a novel combination scheme for blended actuators is introduced in this paper, consisting of a flexible mechanism control system (FCS), reaction-jet control system (RCS), and aerodynamic control. Based on the proposed nonsingular terminal sliding mode surface, a fixed-time anti-saturation controller with an auxiliary system is presented first to ensure global fixed-time stability and to compensate for the adverse effects of input saturation. Subsequently, a fixed-time disturbance observer is constructed to estimate uncertainties and lumped disturbances, and to address the chattering problem. To assign the total virtual control command to different actuators, a control allocation based on dynamic programming considering actuator dynamics is established. Finally, detailed numerical simulations and comparisons are provided to verify the effectiveness and superiority of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the consensus problem of heterogeneous multi-agent systems (HMASs) consisting of second-order linear and second-order nonlinear agents under input saturation. First, the consensus control protocols for HMASs in the leaderless case and the leader-following case are designed under undirected connected topology respectively, where there is a static leader under the leader-following network. Then, based on the knowledge of graph theory and Lyapunov stability theory, it is proved that HMASs can finally reach consensus if sufficient conditions are satisfied. Eventually, the effectiveness of the above theory is further illustrated by simulation examples. [ABSTRACT FROM AUTHOR]

Summary This article considers the output regulation problem of continuous‐time linear systems subject to input saturation in the scenario that the system dynamics are unknown. Based on the low‐gain technique and the output feedback technique, we construct an output feedback control law to solve the output regulation problem with input saturation. Since the system dynamics are unknown, we estimate the feedback and feedforward terms in the control law with a two‐step data‐driven method. An output feedback adaptive dynamic programming algorithm is proposed to estimate the feedback term. An online updating algorithm based on output tracking error is proposed to estimate the feedforward term directly without solving the output regulation equations. Both algorithms don't rely on the measurement of the internal states of the exosystem and the original system. We show that the input saturation caused by the iterative feedforward gain matrix in the online updating algorithm doesn't affect the convergence of the algorithm. With these two data‐driven algorithms, the control law doesn't rely on the dynamics anymore. The low‐gain control law obtained by the model‐free method prevents input saturation from occurring and hence solves the output regulation problem. Finally, a numerical example is provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a finite-time disturbance observer-based adaptive control strategy is proposed for the ship course control system subject to input saturation and external disturbances. Based on the Gaussian error function, a smooth saturation model is designed to avoid the input saturation of the system and reduce steering engine vibrations, and an auxiliary dynamic system is introduced to compensate for the effect of the rudder angle input inconsistency on the system. By constructing an auxiliary dynamic, a finite-time disturbance observer is designed to approximate the external disturbance of the system; an adaptive updating law is also constructed to estimate the upper bound of the derivative of the external disturbance. Combining the finite-time disturbance observer with the auxiliary dynamic system, a novel adaptive ship course control law is proposed by using the hyperbolic tangent function. Moreover, according to LaSalle's Invariance Principle, a system stability analysis method with loose stability conditions and easy realizations is designed, while the stability of the closed-loop system and the ultimately uniformly boundedness of all its signals are proven. Finally, the course control simulation analysis of a surface ship is carried out. The results show that the proposed control law has a strong resistance to external disturbances and a strong non-fragility to system parameter perturbations, which ensure that the course control system has great control performance. [ABSTRACT FROM AUTHOR]

This article investigates the issue of robust control based on interval observers for continuous-time linear time-invariant (LTI) systems with input saturation and disturbances. Firstly, an interval observer is derived by resorting to the system's output information and the interval bounds on the disturbances. Then, a parametric Lyapunov equation (PLE)-based low-gain feedback control method is introduced to guarantee semi-global boundedness. In contrast to the current parametric algebraic Riccati equation (PARE)-based method that requires an iterative approach to solve the PARE online, all relevant parameters in the adopted low-gain design approach are offline determined a priori. Moreover, considering the characteristics of the interval observer, a new stability analysis architecture is given by using a Lyapunov function with a mixture of quadratic and copositive types. Finally, two numerical examples are employed as a means of substantiating the theoretical results. [ABSTRACT FROM AUTHOR]

Addressing input saturation, external disturbances, and uncertain system parameters, this paper investigates the position tracking control problem for bilateral teleoperation systems with a time delay communication channel. Based on a composite energy function, we propose an adaptive iterative learning control (AILC) method to achieve the objective of position tracking under the alignment condition. This extends the existing research on the control of nonlinear teleoperation systems with time delay. The saturation constraint property of the Softsign function ensures that no state of the system exceeds its constraints. The controller learns to simultaneously deal with the uncertainty of system parameters online, reject external disturbances, and eliminate positional errors along the time and iteration axes. All signals in the system for any constant time delay are proved to be bounded. Ultimately, the performance of the proposed controller is further verified through numerical simulations. [ABSTRACT FROM AUTHOR]

A novel full state‐constrained integrated guidance and control (IGC) schema for aerial interceptors under input saturation with tunnel‐prescribed performance is proposed. To achieve an appointed‐time engagement with less overshoot phenomenon, the tunnel‐prescribed performance control (TPPC) technique is applied to generate virtual guidance laws, where the tracking of desired line of sight (LOS) angles possesses predefined‐time convergent property. For the sake of the flight safety of interceptors in a practical flight environment, the physical limitations on the flight angles and the angular rates of attitude systems are taken into consideration. The integral barrier Lyapunov function (iBLF) technique is adopted to ensure all the attitude states within a user‐defined domain. The nominal virtual commands are generated adaptively by the backstepping method combined with some novel dynamic surfaces. To further eliminate the possible input saturation, a novel one‐order auxiliary system is constructed to compensate for the discrepancy of the virtual input commands. All the signals in the closed‐loop system are strictly proven to be bounded by Lyapunov theory. The simulation results show the effectiveness of the proposed IGC schema by comparison with other IGC laws. [ABSTRACT FROM AUTHOR]

This paper investigates a distributed adaptive finite‐time containment control scheme for multiple unmanned aerial vehicles subject to external disturbances and input saturation. Combined with a novel indicator of the saturation degree designed by the hyperbolic tangent function, an adaptive method is proposed to deal with the input saturation issue, which considers both symmetry and asymmetry saturation. Moreover, to address the problem of the "explosion of terms" inherent in the traditional backstepping controller design, a fixed‐time sliding mode differentiator is utilized to approximate the derivative of the virtual signal in the command‐filtered backstepping method. Finally, the convergence of the errors and the practicability of the control law are verified by Lyapunov stability analysis and numerical simulations. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time adaptive practical tracking control for a class of high-order nonlinear systems with full-state constraints and input saturation. The state constraints are handled by applying nonlinear transformed functions (NTFs) and the input saturation is estimated by an auxiliary hyperbolic tangent function. On the basis of adding a power integrator technique and adaptive control method, an adaptive state feedback controller is designed for the closed-loop system. With the aid of finite-time stability theory, the tracking error converges to a bounded neighbourhood of the origin in a finite time, and all the signals in the closed-loop system are bounded. At last, a simulation example and a practical example are presented to show the effectiveness of the proposed control procedure. [ABSTRACT FROM AUTHOR]

In this paper, the global stabilization problem of control systems with input saturation and multiple input delays is studied, and a new method is proposed to design nonlinear stabilization control laws. First, based on Luenberger's canonical decomposition, the multiple-input delay system is transformed into a series of linear time-delay systems with single inputs and input saturation. However, for the converted system, each subsystem is coupled to the others. Therefore, the idea of recursion is adopted to construct a special state transformation with time delay for each subsystem and convert it into a linear system with time delay for both state variables and input variables. For the conversion system, a nonlinear controller with cascade saturation control is designed, and the controller includes some free parameters. The control performance of the controller is improved by adjusting the free parameters online. At the same time, a less conservative stability condition is established to ensure the dynamic performance of the closed-loop system. Finally, the effectiveness and superiority of the proposed method are verified by numerical simulation and practical applications in a spacecraft rendezvous system. [ABSTRACT FROM AUTHOR]

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For the tracking control problem of a class of nonlinear systems with input saturation constraint and time-varying delay, an adaptive tracking control scheme based on multi-dimensional Taylor network (MTN) is designed, and the proposed control scheme has the advantages of simple structure and small computation. A Gaussian error function is introduced to transform the input saturation into a linear model with bounded error. The Lyapunov-Krasovskii function is constructed, and the nonlinearity of the system is approximated using MTN, and an adaptive control strategy is constructed based on the backstepping method. The results show that the proposed control method can both ensure that all signals in the closed-loop system are bounded and achieve convergence of the tracking error to a small neighborhood near the origin. Numerical simulations verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In uncertain environments with robot input saturation, both model-based reinforcement learning (MBRL) and traditional controllers struggle to perform control tasks optimally. In this study, an algorithmic framework of Curiosity Model Policy Optimization (CMPO) is proposed by combining curiosity and model-based approach, where tracking errors are reduced via training agents on control gains for traditional model-free controllers. To begin with, a metric for judging positive and negative curiosity is proposed. Constrained optimization is employed to update the curiosity ratio, which improves the efficiency of agent training. Next, the novelty distance buer ratio is defined to reduce bias between the environment and the model. Finally, CMPO is simulated with traditional controllers and baseline MBRL algorithms in the robotic environment designed with non-linear rewards. The experimental results illustrate that the algorithm achieves superior tracking performance and generalization capabilities. [ABSTRACT FROM AUTHOR]

The present study focuses on controller design for high-order fully actuated systems that experience input saturation and are affected by bounded disturbances, such as nonlinear uncertainties and time-varying unknown parameters. A saturated adaptive controller is developed via the fully actuated system approach and the Lyapunov stability theory to achieve output control and reject disturbances. The disturbances are treated as an extended state and then estimated by introducing an extended state observer. An adaptive variable is used to handle the estimation error between the actual and estimated values of the disturbances. An auxiliary system is designed to mitigate the saturation effect. Lyapunov's direct method verifies that the estimation error, the tracking error, the adaptive state, and the auxiliary system state will eventually stabilise within a bounded ellipsoid. An illustration of spacecraft attitude control demonstrates the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this article, a fuzzy adaptive finite time (FT) output feedback tracking fault-tolerant control (FTC) scheme is designed for stochastic non-strict feedback nonlinear systems (NSFNSs) with actuator failure, input saturation, and unknown control direction. The system studied in this article is more complex than previous results and more in line with the actual situation. The advantages of this study are as follows: (i) A fuzzy state observer of high gain is established to deal with the states unmeasured problem of the system. (ii) The Nussbaum function is employed to address unknown control direction and actuator failure problems, and the Smooth non-affine function is utilized to dispose of the input saturation. (iii) The dynamic surface technique introduces errors that are eliminated by using the error compensation technology, and fuzzy logic systems (FLSs) are applied to appropriate unknown nonlinear functions in the system. The controller developed in this study guarantees that tracking errors can converge to a small neighborhood around the origin within FT and overall signals in the stochastic system are semi-global finite-time stable in probability (SGFSP). Finally, three simulation examples are introduced to verify the effectiveness of the suggested control strategy. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to address the issue of vibration control for a class of Euler–Bernoulli beam systems that are subject to external disturbances and input saturation. The proposed controller differs from other backstepping methods in that it employs a radial basis function (RBF) neural network to accurately estimate boundary disturbances and incorporates the hyperbolic tangent function to ensure input constraints. The nonlinear partial differential equation (PDE) model is initially derived based on Hamilton's principle to capture the dominant dynamic characteristics of the flexible beam. In the framework of the Lyapunov direct approach, an adaptive RBF neural network-based law is subsequently designed to estimate the state-related boundary disturbances. The backstepping approach is then developed to propose sufficient conditions for ensuring the stability and convergence of closed-loop systems subject to input saturation. Finally, the effectiveness and superiority of the proposed methodology are further demonstrated by comparing the simulation results of constrained backstepping controllers. [Display omitted] • The paper addresses the issue of vibration control for Euler–Bernoulli beam models. • This system is susceptible to unknown external disturbances and input saturation. • A constrained boundary controller is developed based on backstepping technology. • An RBF neural network observer is proposed to estimate the boundary disturbances. • The closed-loop stability is established by considering the above constraints. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy of trajectory tracking control of wheeled mobile robot (WMR), a backstepping optimized double sliding mode control strategy was proposed. Initially, based on the kinematics and dynamics model of WMR, the kinematic backstepping sliding mode controller and dynamic backstepping integral sliding mode controller are designed. The stability of the designed controllers is proved by Lyapunov theory. Then particle swarm optimization (PSO) algorithm is used to optimize the controller parameters. Finally, considering the external disturbance and system input saturation, Matlab/Simulink is used to verify the control strategy. The results show that the proposed control strategy not only ensures the robustness and real-time performance of the system, but also improves the control accuracy of the system. [ABSTRACT FROM AUTHOR]

This research studies the stabilization of the linear KdV equation with time-delay on boundary feedback in the presence of a saturated source term. Under certain hypotheses, the proof of well-posedness is established. The result of exponential stability is demonstrated using an appropriate Lyapunov functional. [ABSTRACT FROM AUTHOR]

This article addresses the containment control issue for multi-AUV systems with the intervention of both external disturbance and input saturation. Firstly, a distributed estimator is established for the sake of acquiring precise estimation information of the desired position and its derivative for each follower AUV in the system. Next, on the basis of the proposed distributed estimator, a virtual control law is designed for each follower AUV. Then, due to the difficulty in obtaining accurate information about the derivative of the virtual control law, a linear tracking differentiator is introduced. Additionally, a disturbance observer is employed to tackle the composite disturbance, which mainly contains the internal model uncertainties and external bounded disturbances. Meanwhile, the issue of input saturation is handled by constructing the auxiliary system. Furthermore, a containment control law is designed with the assistance of the introduced linear tracking differentiator, the established disturbance observer, and the constructed auxiliary system. Additionally, the Lyapunov stability theory is applied to analyze the stability of the multi-AUV system. Finally, simulation results are given to confirm the feasibility of the proposed containment control scheme. [ABSTRACT FROM AUTHOR]

This paper studies the problem of prescribed performance tracking control for the lower limb exoskeleton under time-varying state constraints and input saturation. A prescribed performance control method is proposed to achieve the specified tracking accuracy within a preset time. Under the framework of system transformation, the control problem with specified performance and state constraints is transformed into the boundedness problem of auxiliary variables. Meanwhile, the hyperbolic tangent function is employed to deal with the input saturation. Through rigorous theoretical analysis, it can conclude that the tracking error converges to a prescribed region near the origin within a given time and all signals of the closed-loop system are bounded. The superiority of this control scheme is verified through a practical simulation example. [ABSTRACT FROM AUTHOR]