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This paper investigates the unified tracking control problem for a class of high-order nonlinear systems with 7 kinds of irregular state constraints and input saturation based on the dynamic event-triggered mechanism. The irregular state constraints exist in practical systems, including time-varying constraints, alternation between positive and negative bounds, adding/removing constraints during system operation, and the state of the system being constrained only by the upper/lower boundaries. Auxiliary constraint boundaries are introduced to deal with these irregular state constraints. This unified method allows different auxiliary constrained boundaries in response to specific circumstances, without affecting the controller's structure. Nonlinear transformed functions (NTFs) are used to eliminate the feasibility condition of barrier Lyapunov functions (BLFs) methods. Subsequently, based on the dynamic event-triggered mechanism and adding a power integrator technique, an event-triggered controller is designed to effectively reduce communication burden and energy consumption between the controller and the actuator. Finally, a simulation example and a practical example are given to verify the effectiveness of the proposed unified control method. • This paper considers stronger nonlinearity and input saturation, which makes the system model more general. • Unlike previous works focusing on specific state constraints, we discuss seven irregular contrainted cases and provide a unified control strategy for various constrained cases. • A dynamic event-triggered controller is designed to maintain good tracking effectiveness while further reduce triggering times. [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 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]

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]

This paper presents a two-loop control framework for robotic manipulator systems subject to state constraints and input saturation, which effectively integrates planning and control strategies. Namely, a stability controller is designed in the inner loop to address uncertainties and nonlinearities; an optimization-based generator is constructed in the outer loop to ensure that state and input constraints are obeyed while concurrently minimizing the convergence time. Furthermore, to dramatically the computational burden, the optimization-based generator in the outer loop is switched to a direct model-based generator when the tracking errors are sufficiently small. In this way, both a high tracking accuracy and fast dynamic response are obtained for constrained robotic manipulator systems with considerably lower computational burden. The superiority and effectiveness of the proposed structure are illustrated through comparative simulations and experiments. • A general and systematic constrained control scheme for robotic manipulators. • Nonlinearities, uncertainties, state and input constraints are considered. • Adaptive robust controller is designed for high tracking accuracy. • Optimization-based generator is designed for fast dynamic response. • Experiments on Franka robotic manipulator reveal the effectiveness. [ABSTRACT FROM AUTHOR]

This paper addresses the fault-tolerant attitude tracking control problem for spacecraft with limited communication capability and input saturation. The design of a hysteresis quantizer aims to alleviate communication burden between the controller module and the actuator module. Then, the attitude tracking problem for spacecraft with input quantization, input saturation, actuator faults and external disturbances is transformed into an attitude control problem with uncertain input coefficients and bounded disturbances. Thereafter a dynamic loop gain function-based approach and a hyperbolic tangent function term with a time-varying boundary layer are introduced to address the uncertainties of input coefficients and the bounded disturbances, respectively. To facilitate the boundness analysis of the signals in the closed-loop system, a pertinent lemma about the dynamic loop gain function is proved. Finally, numerical simulations are employed to validate the effectiveness of the proposed scheme. • The spacecraft attitude tracking problem with disturbances and uncertainties. • The quantized control law alleviates communication burdens of spacecraft. • A dynamic loop gain function method is used to address the impact of uncertain. • A hyperbolic tangent term is devised to counteract bounded disturbances. [ABSTRACT FROM AUTHOR]

This paper considers an output feedback consensus control approach for the generic linear multi-agent systems (MASs) under input saturation over a directed graph. A region of stability-based approach has been established for dealing with the input saturation. A conventional Luenberger observer for estimating the states of followers by themselves and an advanced cooperative observer for estimating the state of leader by followers have been applied for an estimated state feedback control. The stability conditions have been derived by considering a three-term-based combined Lyapunov function. Moreover, computationally simple controller and estimator design conditions have been obtained by resorting to a decoupling approach A set of initial conditions has been investigated to achieve the leader-following consensus of MASs under the input saturation constraint. To the best of our knowledge, an output feedback consensus approach, providing a consensus region, for generic linear MASs under input saturation over directed graphs without requiring the exact state of the leader has been explored for the first time. In contrast to the existing methods, the proposed approach considers an output feedback approach (rather than the state feedback), accounts for both linear and nonlinear saturation regions, applies an estimate of the state of the leader through cooperative observer, and is based on a generalized sector condition for the saturation nonlinearity. In addition, it offers a computationally simple design solution owing to the proposed decoupling method. Simulation results are provided to validate the efficacy of the designed protocol for F-18 aircraft and unmanned ground vehicles. • Output feedback consensus approach with consensus region for linear MASs under input saturation. • A cooperative observer is designed for estimating the leader's state. • The approach allows linear and nonlinear saturation regions via a generalized sector condition. • A region of attraction for the consensus region has been provided. • A simple design condition through a decoupling approach has been revealed over directed graphs. [ABSTRACT FROM AUTHOR]

In this article, the attitude tracking problem for rigid spacecraft systems with the consideration of actuator fault, input saturation, inertia uncertainties. and external disturbances is investigated. By introducing a shifting function, the requirement for accurate values of the initial tracking errors has been removed. A novel adaptive prescribed performance function is developed to enable the relaxation and recovery of the performance bounds under the different conditions of the shifted tracking error. Then, an error transformation is employed to convert the problem of prescribed performance tracking into the stabilization problem of a new system. Subsequently, an adaptive controller is designed based on a nonsingular predefined-time sliding mode manifold and an auxiliary system. The proposed controller ensures a predefined-time convergence with prescribed static and transient performance for the tracking error. The stability analysis of the proposed attitude controller is rigorously established using Lyapunov methods. Finally, numerical simulations are conducted to exhibit the efficacy and superiority of the propounded scheme. • Transient and static behavioral bounds are specified for the attitude MRPs. • A shifting function is developed to achieve the initial condition-free purpose. • The system settling time is independent of the initial conditions. • An adaptive term is introduced to traditional performance function. [ABSTRACT FROM AUTHOR]

This paper studies the event-triggered H ∞ control based on the average dwell time (ADT) method for discrete-time switched system with input saturation and state saturation. Based on the convex hull method, the state feedback controller and the dynamic output feedback controller are designed respectively. The influence of input saturation and state saturation on the dynamic performance of the system is eliminated. The dynamic event-triggered mechanism is introduced, which saves the communication resources and computation resources of the system. Based on ADT, the H ∞ exponential stability of the closed-loop system is guaranteed.Finally, the effectiveness of the proposed method is verified by the numerical examples. • Based on the convex hull method, the state feedback controller and the dynamic output feedback controller are designed respectively. • The influence of input saturation and state saturation on the dynamic performance of the system is eliminated. • The dynamic event-triggered mechanism is introduced, which saves the communication resources and computation resources of the system. • Based on ADT, the exponential stability of the closed-loop system is guaranteed. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive fuzzy prescribed time tracking control problem for a class of strict-feedback systems simultaneously considering the user-defined asymmetric tracking performance, input saturation, and external disturbances. From the perspective of ensuring the reliability for control implementation, a saturation-based fixed-time funnel boundary is constructed by embedding the modification signals related to input saturation errors into a funnel function, which is capable of automatically enlarging or recovering itself when input saturation occurs or disappears, thereby reducing the risk of system singularity. Subsequently, by constructing a fixed-time tracking performance function, any known bounded tracking error is recast into a new variable with a zero initial value. With such a treatment, funnel boundaries are no longer redeveloped for different initial tracking errors, and meanwhile the behavior of the tracking error is pre-specified as needed over a finite time interval. Also, auxiliary systems are devised to generate the aforesaid modification signals, while compensating for the adverse impact resulting from input saturation. Remarkably, by feat of the backstepping design based on the fuzzy approximation, it is proven that the tracking error converges to a user-defined region within a prescribed time (known as the practically prescribed time tracking), which is achieved without the fractional power feedback of system states. Finally, two simulation examples are presented to confirm the feasibility and effectiveness of the developed approach. • A novel fixed-time tracking performance function is designed to relax the initial condition. • By a simple variable transformation, the asymmetric performance constraint is handled. • A new form of self-adjustable performance funnel is constructed to enhance the reliability of control designs. • A class of the practically prescribed time tracking problems is solved. [ABSTRACT FROM AUTHOR]

• A novel I&I adaptive scheme is presented. • Immersion and invariance based adaptive terminal sliding mode control is proposed. • Immersion and invariance based adaptive terminal sliding mode control with saturation compensation is presented. This work investigates attitude control of spacecraft with uncertainties and input saturation. An immersion and invariance based adaptive robust control (IIARC) is proposed to improve tracking performance of spacecraft. The proposed approach consists of an immersion and invariance (I&I) estimator, a robust adaptive law, and a terminal sliding mode control (TSMC). The continuous fast TSMC is designed to stabilize the system and obtain fast convergence rate. To estimate the disturbances and uncertainties, I&I methodology is introduced into the proposed approach. The robust adaptive law is applied such that the prior information of disturbances is not required. IIARC with saturation compensation (IIARCSC) is presented to reduce the effect of input saturation on the attitude tracking of spacecraft. It is proved that the developed approach could guarantee the finite-time convergence (FTC). Extensive comparative simulations demonstrate the effectiveness of the presented scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of guidance and control for underactuated unmanned surface vehicles (USVs) with state constraints and input saturation, in support of enabling an underactuated USV to follow a parameterized curved path in the case of unknown sideslip angle and cross-tracking error constraint. First, a cross-tracking error constraint line-of-sight (LOS) guidance law with sideslip angle compensation is originally designed to guide an underactuated USV to convergence to the desired path within a time-varying cross-tracking error constraint. Second, a novel nonlinear mapping (NM) function is first constructed to map the heading and surge control subsystems with state constraints to unconstrained nonlinear systems, transforming the constrained control problem into the unconstrained control problem. Subsequently, adaptive fuzzy control laws are designed to achieve the control objectives for the USV using the new unconstrained nonlinear systems with unknown disturbance and input saturation. Then, a series of theoretical analyses using input-to-state stability theories are presented to prove the boundness of the tracking errors for the underactuated USV during path following. Finally, numerical results obtained using a physics-based simulation model are shown to reveal the effectiveness of the guidance and control algorithms. • Design a cross-tracking error constraint LOS guidance algorithm with sideslip compensation. • Propose a novel nonlinear mapping function to deal with the constraint control for nonlinear systems. • Construct the unconstrained nonlinear system by the proposed nonlinear mapping function. • Propose adaptive fuzzy control laws with input saturation using the new unconstrained nonlinear system. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time attitude control problem for spacecraft under input saturation, actuator faults, and system uncertainties. Three novel saturated fixed-time nonsingular terminal sliding mode surfaces (NTSMSs) are designed, which can keep the system states fixed-time stable after the establishment of their sliding manifolds. Two of them are time-varying and firstly designed. Each of the two NTSMSs has an adjustment parameter that is adjusted dynamically and used to handle saturation and cancel the attitude dynamics. According to other related predesigned parameters, a conservative lower bound of this parameter is obtained. A saturated control scheme is then designed in conjunction with a newly proposed saturated reaching law. A modification strategy is carried out to facilitate the engineering applications of our methods. The fixed-time stability of the closed-loop systems is validated by Lyapunov stable theory. Simulation results validate the effectiveness and superiority of the proposed control scheme. • Three novel saturated terminal sliding surfaces are firstly designed which keep the states stable. • The lower bound of designed adjustment law can be calculated based on the predesigned parameters. • Our control scheme keeps the states fixed-time stable while rejecting uncertainties, actuator faults, and input saturation. • A modification strategy is developed to promote the application of our methods to engineering. [ABSTRACT FROM AUTHOR]

Spacecraft attitude control employs quaternion representation to avoid singularity issues and obtain global maneuver stability. However, it has redundancy associated, resulting in dual equilibrium points. The attitude control may confront the unwinding phenomenon due to the presence of the equilibria. In this paper, an anti-unwinding controller for spacecraft stabilization in the presence of external disturbances and inertial uncertainties, angular velocity limit, actuator saturation and faults is presented. Specifically, a modified extended state observer (ESO) is designed to obtain total disturbance estimates of the rigid-body spacecraft. Auxiliary parameters are added in the design to avoid initial high estimates in the proposed ESO design resulting in faster convergence. The proposed disturbance observer is to release the assumption that requires the estimated disturbance to be constant or varying at slow rates. Using the ESO estimates, a particular back-stepping-SMC (ESO-BTSMC) controller is devised to formulate anti-unwinding control law for spacecraft stabilization. Lyapunov stability theory is employed to prove closed-loop stability of system and estimation error convergence. Comparative simulations are performed to demonstrate the performance of the proposed control scheme. It is found that the proposed control scheme gives smooth and precise control performance along with faster transient response. Additionally, it also alleviates the chattering phenomenon. [ABSTRACT FROM AUTHOR]

This paper presents an optimal control design method for multi-satellite assembly in an elliptic orbit in close proximity operations considering input saturation constraints. Tschauner–Hempel (T–H) equations are utilized to model the relative motion dynamics of the satellites in the Local Vertical Local Horizontal (LVLH) frame of the target satellite, where every satellite in the assembly is modeled as a point mass. The communication topology between the satellites in the assembly is modeled using graph theory, where the graph has several nodes representing the satellites and several edges representing the data exchange direction. It is assumed that every satellite exchanges its states with a few neighbors in the team, where the neighbors of every satellite are prespecified and do not change during the mission. This graph is utilized to construct the global dynamic model of the assembly, in which every node is represented by the dynamic model of a single satellite. The local control law, which is applied to every satellite in the assembly, consists of a state feedback gain and a coupling gain. The state feedback gain is designed using the discrete-time periodic Riccati equation to guarantee the local stability of every satellite separately, while the coupling gain is selected to satisfy the Lyapunov condition to guarantee the global stability of the assembly. The invariant-set method is utilized to prove the stability of the global dynamic system that is subjected to symmetric input saturation. The precision and optimality of the proposed control law are successfully demonstrated by numerical nonlinear simulations in a MATLAB environment for a cubic formation satellite assembly. • Assembling multiple satellites into an elliptic orbit in a cubic configuration. • Controlling a discrete-time periodic multi-agent system. • Designing an optimal control system using the discrete-time periodic Riccati equation. • Analyzing the stability of a discrete-time periodic multi-agent system under input saturation. [ABSTRACT FROM AUTHOR]

Due to the harsh marine environment, the communication cost of multi-ship formation is expensive, but it is often ignored in the existing research. On this basis, this paper proposes a novel distributed anti-windup neural network (NN)-sliding mode formation controller of multi-ships with minimum cost. Firstly, distributed control is applied to devise the formation controller of multi-ships because it is a promising solution for the problem of single point failure. Secondly, the Dijkstra algorithm is introduced to optimize the communication topology, and then an optimized communication topology with minimum cost is used in the distributed formation controller design. Thirdly, to alleviate the influence of input saturation, an anti-windup mechanism is devised by combining an auxiliary design system with sliding mode control and radial basis function neural network method; and then a novel distributed anti-windup neural network-sliding mode formation controller of multi-ships is obtained, which can also handle the problem of nonlinearity, model uncertainty, and time-varying disturbances of ship motion. On the strength of Lyapunov theory, the closed-loop signals are proved to be stable. Multiple comparative simulations are carried out to validate the effectiveness and advantage of the proposed distributed formation controller. • The optimized communication topology can be obtained from Dijkstra algorithm. • Anti-windup mechanism mitigates the influence of input saturation. • Distributed formation controller of multi-ships is devised based on sliding mode and neural network. [ABSTRACT FROM AUTHOR]

Saturation is mainly characterized by its passivity and magnitude bound. But most of the saturation control methods only make use of either of these features. To enhance the performance of saturated systems, this paper develops a novel method capable of fully using both of these two features. This method is a two-stage design scheme which integrates the phase-shaping technique with the gain-scheduled control. The phase-shaping fully uses the passivity of saturation while the gain-scheduling actively utilizes the magnitude bound of saturation. In this way, the design conservatism associated with existing methods is reduced substantially. Specifically, a matrix-type phase-shaping method is developed through the placement of systems' frequency loci, and a meta-heuristic method is devised for the design of the phase-shaping function. Furthermore, the gain-scheduled control is transformed into the robust performance problem of a passive uncertain system, and designed by the passivity-based robust control method of the authors. Application to two practical control systems validates the effectiveness of the proposed method. The superiority is demonstrated via comparisons with typical saturation control methods. • Propose gain-scheduling with phase-shaping method for input-saturated linear systems. • Fully utilize the passivity in phase-shaping to maximize the system's phase margin. • Actively use the magnitude bound in gain-scheduling to reduce conservative design. • Extend the matrix phase-shaping by placing the nominal system's frequency locus. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive model-free optimal reinforcement learning (RL) neural network (NN) control scheme based on filter error is proposed for the trajectory tracking control problem of an autonomous underwater vehicle (AUV) with input saturation. Generally, the optimal control is realized by solving the Hamilton–Jacobi–Bellman (HJB) equation. However, due to its inherent nonlinearity and complexity, the HJB equation of AUV dynamics is challenging to solve. To deal with this problem, an RL strategy based on an actor–critic framework is proposed to approximate the solution of the HJB equation, where actor and critic NNs are used to perform control behavior and evaluate control performance, respectively. In addition, for the AUV system with the second-order strict-feedback dynamic model, the optimal controller design method based on filtering errors is proposed for the first time to simplify the controller design and accelerate the response speed of the system. Then, to solve the model-dependent problem, an extended state observer (ESO) is designed to estimate the unknown nonlinear dynamics, and an adaptive law is designed to estimate the unknown model parameters. To deal with the input saturation, an auxiliary variable system is utilized in the control law. The strict Lyapunov analysis guarantees that all signals of the system are semi-global uniformly ultimately bounded (SGUUB). Finally, the superiority of the proposed method is verified by comparative experiments. • An adaptive model-free optimal reinforcement learning control scheme is proposed for autonomous underwater vehicles (AUVs). • A simple control design based on filtering errors is proposed. • Reinforcement learning method is used to avoid solving a Hamilton–Jacobi–Bellman equation. • Input saturation and optimal characteristics of AUVs are considered in the controller design. • Simulation results show the validity and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

• This paper addresses the prescribed-time attitude cooperative control problem. • A quantized scheme is proposed to reduce inter-spacecraft communication burden. • A prescribed-time observer is proposed to estimate the reference attitude. • A distributed prescribed-time attitude cooperative controller is proposed. This paper investigates the problem of prescribed-time attitude consensus for multiple spacecraft under directed graph subject to limited communication bandwidth and input saturation. First, a quantized communication mechanism that transmits quantized states only when their values change is developed to deal with the limited communication bandwidth, which can markedly reduce communication burden. Under the quantized communication, a distributed prescribed-time observer is designed for each follower spacecraft to estimate the leader spacecraft's state. This observer can guarantee the observed values converge to the leader spacecraft's state in a user-defined time. Then, we design a prescribed-time sliding manifold by using the observed values. Next, a prescribed-time attitude control law is designed based on the proposed sliding manifold. The prescribed-time stability of multiple spacecraft system subject to input saturation is proved, and the simulation results highlight the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with the periodic event-triggered consensus of multi-agent systems subject to input saturation. Due to the nonlinearity caused by the input saturation constraint, the accuracy of the event-triggered mechanism to screen data will be reduced. To deal with this problem, a novel dual periodic event-triggered mechanism is first proposed, in which a saturation-assisted periodic event-trigger and a complemental periodic event-trigger work synergistically to screen data more efficiently under the input saturation constraint. In addition, considering the various disturbances in the environment, a more general mixed H ∞ and passive performance is introduced to describe the disturbance attenuation level. Based on the Lyapunov–Krasovskii functional, some less conservative consensus criteria are obtained for the multi-agent systems. In addition, under different input saturation constraints, the relationship between the disturbance attenuation level and the data transmission rate is explored. After that, a particle swarm optimization algorithm is a first attempt to estimate and enlarge the region of asymptotic consensus. Finally, an example is given to verify the effectiveness and superiority of our proposed method. • A novel dual PET mechanism is developed for MASs with input saturation. • A PSO is adopted for the first time to enlarge the region of asymptotic consensus. • A mixed performance is considered to reflect the disturbance attenuation level. [ABSTRACT FROM AUTHOR]

This paper investigates dynamic output feedback H ∞ control for singular Markovian jump systems with partly unknown transition rates and input saturation. Necessary and sufficient conditions that singular Markovian jump system satisfies stochastic admissibility and H ∞ performance index are successfully deduced in terms of linear matrix inequalities under the two different conditions of completely known transition rates and partly unknown transition rates. Mode-dependent dynamic output feedback controller is designed to ensure that the closed-loop singular Markovian jump system satisfies stochastic admissibility and H ∞ performance index. Novel set invariant condition is proposed, and it not only provides an estimate of the attractive domain of the closed-loop system but also allows the analysis of performance outside the stability region within this invariant set. Furthermore, the estimation of the attraction domain comes down to the determination of the largest contractively invariant ellipsoid satisfying the necessary and sufficient conditions and the novel set invariant condition, and it is solved as an optimization problem with linear matrix inequality constraints. Finally, the effectiveness and utility of the proposed method are verified by a numerical example and an oil catalytic cracking process. [ABSTRACT FROM AUTHOR]

The problem of fixed-time control is addressed for the autonomous proximity of non-cooperative targets with full-state constraints, input saturation, parameter uncertainties, and matched and unmatched disturbances. A six degrees of freedom (6-DOF) relative motion model for non-cooperative targets is constructed. Combining with a radial basis function neural network (RBF-NN), a fixed-time disturbance observer is proposed to estimate system disturbances. Model items and assumptions for the boundedness of the derivatives of the disturbances are not required in the proposed disturbance observer. The back-stepping technique provides an adaptive fixed-time controller to stabilize the full-state constrained relative error system and a unified framework for dealing with constrained and unconstrained cases is proposed by designing a coordinate transformation method. The fixed-time stability of the relative error system is guaranteed by the proposed controller regardless of the constraints. Finally, two simulation scenarios validate the effectiveness and robustness of the developed controller design. • A fixed-time neural network disturbance observer is presented to estimate disturbances with high frequency noise. • A unified coordinate transformation theory is proposed for the full-state constrained system. • An anti-saturation fixed time controller is designed to achieve spacecraft autonomous rendezvous and docking task. [ABSTRACT FROM AUTHOR]

In this article, the problem of decentralized fuzzy adaptive control is addressed for a class of stochastic interconnected nonlinear large-scale systems including saturation and unknown disturbance. Fuzzy logic systems (FLSs) are used to estimate packaged nonlinear uncertainties. The command filter technique is presented to eliminate the "explosion of complexity" obstacle associated with the backstepping procedures and the corresponding error compensation mechanism is constructed to alleviate the effect of the errors generated by command filters. The influence of input saturation is compensated by introducing an auxiliary system. Meanwhile, an improved adaptive fuzzy decentralized controller is developed and it is able to minimize calculation time since there is no need for repeated differentiation for the virtual control laws. The presented control scheme not only assures the semi-global boundedness of all the signals in the closed-loop system, but also makes the output tracking errors reach a small neighborhood around the origin. Finally, both numerical and practical examples are provided to illustrate the efficiency and effectiveness of our theoretic result. • A novel adaptive fuzzy decentralized controller is proposed for a class of stochastic interconnected nonlinear large-scale systems. • An auxiliary system is constructed to resolve the difficulty caused by input saturation. • The difficulty due to the interconnection of subsystems is eliminated by introducing two smooth functions. • The proposed adaptive fuzzy command filtered control scheme can solve the explosion of complexity problem inherent in the conventional backstepping control design. [ABSTRACT FROM AUTHOR]

• The actuator saturation, liquid sloshing and vibration of flexible solar panels are considered. • A novel predefined-time control developed base on sliding mode control. • The upper-bounded stabilization time is explicitly contained in the controller. • An adaptive law without the upper bound of the disturbance is proposed. • An auxiliary system is designed to deal with the problem of input saturation. A predefined-time attitude stabilization for complex structure spacecraft with liquid sloshing and flexible vibration is investigated under input saturation during orbital maneuver. First, the attitude dynamics model of liquid-filled flexible spacecraft is constructed. Meanwhile, the influence of solar panel vibration and liquid sloshing is treated as a disturbance in the controller design. Next, an adaptive predefined-time control scheme is proposed by applying sliding mode control theory. A predefined-time convergent sliding surface and reaching law are designed to ensure the predefined-time fast convergence rate. Furthermore, a novel adaptive algorithm is developed to handle the disturbances from liquid sloshing and flexible vibration, ensuring that the system converges to a small neighborhood of the equilibrium. Additionally, a new auxiliary system is constructed to deal with the effects of input saturation. At last, one simulation case is performed to verify the feasibility and advantages of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the prescribed-time leader–follower formation control problem is solved for surface vehicles (SVs) suffering from input saturation and unknowns including uncertain dynamics and external disturbances. Based on the information of neighboring vehicles, a distributed prescribed-time observer for estimating states of the leader is proposed. By virtue of input saturation, the saturation errors and system unknowns are observed by a reduced-order prescribed-time estimator. Moreover, to realize the satisfactory formation error constraints, a time scale transformation function based prescribed-time prescribed performance function is proposed, together with error transformations, the transient performance of formation errors is improved. Lyapunov stability theorem and backstepping method prove that the closed-loop system is prescribed-time stable. Simulations are given to illustrate the effectiveness of proposed theoretical results. • A distributed prescribed-time observer for estimating leader states is designed. • A prescribed-time prescribed performance function is developed with limited range. • A prescribed-time reduced-order observer is proposed for estimating unknowns. [ABSTRACT FROM AUTHOR]

To improve the control performance of the fractional order uncertain systems with multiple mismatched disturbances, an enhanced fractional order sliding mode control (FOSMC) method is developed in this paper. The multiple disturbances and uncertainties are estimated by the finite-time disturbance observers (FTDO) and a fractional order extended state observer (FOESO), respectively. A fractional order switching law is designed to provide a fast convergence mode for the system states. Then a novel FOSMC law is developed by incorporating the feedforward compensation, the fractional order switching law, and the auxiliary state for input saturation. The proposed method is applied to numerical examples and to a motor speed control problem. The effectiveness of the proposed method is demonstrated by the performance comparisons with some existing control methods. • A novel FOSMC scheme is developed for fractional order uncertain systems. • The control system is insensitive to multiple mismatched disturbances and uncertainties. • The convergence of the system states is accelerated without enlarging the chattering. [ABSTRACT FROM AUTHOR]

This paper investigates secure bipartite consensus (SBC) control problems of leader–follower multi-agent systems (MASs) subjected to denial-of-service (DoS) attacks via observer-based dynamic event-triggered control (DETC). An observer-based DETC protocol with two combining measurements (follower–follower and follower–leader) is first proposed corresponding to valid DoS attack intervals and valid safe intervals. It is concluded that the SBC of MASs without input saturation can be achieved via the observer-based DETC protocol under a signed directed graph if some sufficient inequality conditions hold. And the Zeno behavior can be excluded. Then, a resembling result corresponding to a signed undirected graph is obtained. Furthermore, by using low-gain feedback technic, the semi-global SBC issue under a saturated controller is also considered. Finally, a numerical simulation and two application simulations are displayed to illustrate the effectiveness of the proposed control protocol. [ABSTRACT FROM AUTHOR]

This article proposes a control strategy using a prescribed-time tracking control technique to address the challenges of achieving high-precision trajectory tracking control for USVs. The scheme considers marine environmental disturbances, model uncertainties, and unmodeled dynamics while imposing prescribed performance restrictions. Initially, a prescribed-time extended state observer is established to rapidly and precisely reconstruct unmeasured velocity and the lumped disturbances, including marine disturbances, model uncertainties, and unmodeled dynamics. Furthermore, a novel prescribed-time prescribed performance function is created to improve transient and steady-state performance. Then, a prescribed-time tracking control scheme utilizes the extended state observer technique, prescribed performance constraint, prescribed-time stability theory, and dynamic surface control algorithm to ensure that the tracking errors converge rapidly and precisely within the prescribed time while remaining within the predefined performance constraints. Additionally, the Lyapunov stability theory demonstrates the system's prescribed-time stability. In conclusion, simulation experiments are performed to validate the efficacy and superiority of the suggested control strategy. • A PTESO observer is designed to estimate the lumped uncertainties and unmeasured velocity. • A PTPPF function is implemented to achieve guaranteed transient and steady-state performance within a predefined time. • A prescribed-time prescribed performance tracking control scheme is proposed. [ABSTRACT FROM AUTHOR]

This paper addresses the semi-global stabilization problem of parabolic PDE–ODE systems with input saturation. Two low-gain controllers are proposed for two types of systems. It is shown that the proposed controllers can solve the semi-global stabilization problem of the concerned parabolic PDE–ODE systems with input saturation. Distributed-diffusion, counter-convection and Robin boundary condition are simultaneously considered. Moreover, the controllability of PDE–ODE systems with input saturation is discussed. It is shown that semi-global stabilization is impossible if the open-loop ODE system is exponentially unstable, which is another distinctive contribution of this work. Two illustrative examples are given to show the effectiveness of our proposed low-gain controllers. [ABSTRACT FROM AUTHOR]

In this paper, the domain of attraction (DOA) of the continuous-time positive polynomial fuzzy systems subject to input saturation is estimated by using the level set of the linear copositive Lyapunov function. To relax the estimation of DOA, the restriction on the level set is removed by embedding the expression of the level set into the stability conditions and positivity conditions. Referring to the nonconvex terms caused by above novel analysis strategy, some polynomial inequality lemmas are proposed to handle them; the nonconvex terms caused by imperfect premise matching (IPM) nonlinear membership functions are dealt with by sector nonlinear methods and advanced Chebyshev membership-function-dependent (MFD) methods. In this advanced MFD method, the state space segmentation and polynomial order selection of the Chebyshev approximation method are improved based on breakpoints of the first derivative and curvature, respectively, which is helpful to reduce the conservatism and computational burden of the result. Thus, this advanced Chebyshev MFD method not only optimizes the convexification strategy, but also can further be extended to estimate the DOA when it is used to introduce the membership functions information for convex stability and positivity conditions. Finally, a numerical example and the lipoprotein metabolism and potassium ion transfer nonlinear model are presented to validate the effectiveness and feasibility of the aforementioned analysis and convexification strategies in the expansion of DOA estimation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of dual-channel event-triggered prescribed performance adaptive fuzzy time-varying formation tracking control for multi-agent systems subject to actuator saturation, in which state variables are unmeasurable and nonlinear functions are totally unknown. A fuzzy state observer is constructed to estimate unmeasurable states. Meanwhile, fuzzy logic systems are used to approximate unknown nonlinear functions. To effectively save the usage of communication resources, this paper designs both sensor output signal and control signal triggering mechanisms, respectively. Unfortunately, the output triggering can lead to a problem that virtual control laws are non-differentiable. To solve this problem, we first utilize observer output signals to construct virtual control laws to ensure the first-order differentiation of virtual control laws. Then, a dynamic filtering technology is introduced to avoid the repeated differentiation of virtual control laws. Furthermore, an improved first-order auxiliary system is designed to compensate for the impact of actuator saturation. It is shown that the designed controller can guarantee tracking errors steer to a preset accuracy within a prescribed settling time, and all signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results verify the effectiveness of the developed control scheme. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive sliding mode control (SMC) strategy for dynamic positioning (DP) vessels with the model uncertainty, environmental disturbances, and input saturation. The adaptive updating laws for the parameter estimation are derived using Lyapunov theory. The low-level thrust allocation and the actuator limitations are considered. It is theoretically proved that all signals in the closed-loop system are uniformly ultimately bounded (UUB). The importance of the auxiliary system within the adaptive controller is highlighted, and potential instability issues when combined with thrust allocation are explored. Two methods to mitigate this instability are proposed and verified by numerical simulations. These methods achieve harmonious cooperation between high-level motion control and low-level thrust allocation by actively adjusting the target thrust values and auxiliary system parameters. Simulation results demonstrate that the proposed adaptive SMC are capable of maintaining DP vessel stability under the given uncertainties and disturbances. • Adaptive estimated values of mass parameters are used in the auxiliary system. • The instability caused by the auxiliary system and thrust allocation is analyzed. • Two methods are proposed to mitigate the instability caused by auxiliary system. [ABSTRACT FROM AUTHOR]

A finite-time adaptive sliding mode ship trajectory tracking control strategy is designed to address the problems of unknown external disturbances, model uncertainties and input saturation of underactuated ship during navigation. By using neural networks to approximate the model uncertainties and using adaptive laws to estimate upper bound on the sum of the unknown disturbances and the neural network approximation errors. The "differential explosion" problem is solved by using dynamic surface technique, and design the controller with the finite-time convergence theory. Finally, the theoretical analysis is carried out by Lyapunov method, which proves that all signals of the closed-loop system are bounded. The simulation results show that the proposed control scheme is able to achieve trajectory tracking for underactuated ship regardless of whether input constraints are considered or not, and has satisfactory robustness in the face of unknown external time-varying disturbances and model uncertainties. The research done can provide effective reference for ship trajectory tracking control and has certain theoretical guidance significance. • For the problems of unknown external disturbances, the existence of model uncertainties in the ship, and the "differential explosion" problem, the RBF neural networks are used to estimate the uncertainties, and then the adaptive laws are used to estimate the upper bound of the sum of the external disturbances and the neural network approximation errors, and finally the dynamic surface technique is used to solve the "differential explosion" problem. • To address the problem of slow convergence, the design of the controller will be done in conjunction with the theory of finite-time convergence. Firstly, desired surge velocity u d as well as sway velocity v d are designed by combining the hyperbolic tangent function so that z x and z y achieve finite-time convergence. Then, a finite-time term is similarly added during the design of the subsequent control inputs to further accelerate the convergence rate of velocity tracking errors. • The linear anti-windup compensator is able to subtly offset the nonlinear term caused by input saturation, therefore, the input saturation problem will be solved using the linear anti- windup compensator. The results of the simulation experiments show that this controller can still enable the ship to achieve trajectory tracking in the case of input constraints. [ABSTRACT FROM AUTHOR]

This paper proposes a protocol-based secure guaranteed cost sampled-data controller design problem of Takagi-Sugeno (T-S) fuzzy system under denial-of-service (DoS) attack and input saturation. First, in the absence of an effective description for the characteristics of received signals on controller, a novel scheduling protocol is proposed according to the characteristics of the round-robin protocol and DoS attack, which can guarantee the specific sequence characteristic for control updates. Then, via introducing input delay approach and switched system modeling method, a time-delay switched system with fixed switching sequence is introduced to describe the considered system with DoS phenomenon. Moreover, some novel control criteria are presented to ensure the resulting closed-loop system reaches a required cost level under the obtained control law. And an optimization problem is proposed to compute the optimal upper of the specified cost level. Finally, a simulation example is presented to demonstrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this article, we study the time-varying formation-containment (TVFC) tracking problem for linear multi-agent systems (MASs) and take the input saturation problem of the systems into account. An observer-based TVFC tracking protocol is proposed. It has been proven that the real leaders can realize the expected formation and track the virtual leader's trajectory, and followers can get into the convex envelope spanned by the leaders. In addition, to avoid unexpected large chattering caused by nonzero input, we propose a continuous protocol. Under this protocol, each error is uniformly ultimately bounded and is able to converge to any small zero neighborhood. At the end, the feasibility of the TVFC theory is demonstrated by simulation examples. [ABSTRACT FROM AUTHOR]

This study proposes two schemes for ship autopilot: the first is a follow-up mode, applying manual dynamics to the state-space-based underactuated large merchant ship (ULMS) model, using a steering wheel and joystick to emulate manual operation; the second is a Nav mode developed by path-following control. In this mode, a novel path-following control strategy is developed for ULMS with input saturation and delay, two novel auxiliary systems are employed to stabilize the plant with input constraints. The input delay auxiliary system (IDAS) effectively tackles the design challenges posed by input delay, while the input saturation auxiliary system (ISAS) is dedicated to generating actual control inputs under the constraint of saturation. Furthermore, the dynamic surface control (DSC) technique and the roust neural damping technique are introduced to mitigate the computational burden and simplify the controller structure, thereby enhancing the efficiency and performance of the entire control system. Lyapunov stability analysis proves the ship motion system is semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of these two schemes is verified through turning experiment, comparative simulations and a semi-physical simulation platform that integrates physical models with computer simulation technology. • The manual dynamic model is introduced into the state-space mathematical model of ULMS, realistically emulating the control mechanism of the telegraph joystick and steering wheel, and can be embedded into the ship autopilot as the follow-up mode. • Unlike the previous work, two auxiliary systems are introduced. IDAS eliminates the effect of input delay on the system performance by predicting and compensating the delayed signals to ensure that the control commands are delivered to the actuators in time. ISAS processes the input saturation using a smooth non-affine approximation function, which enables the control signals to transition smoothly at the saturation point, thus enhancing the performance and stability of the system and effectively avoiding the challenges when designing an adaptive back-stepping control technique to design adaptive controllers. • An innovative semi-physical simulation platform is developed, integrating physical models with computer simulation technology to provide an economical and efficient testing environment, closely resembling actual operational conditions. Using this platform provides reliable experimental evidence for the algorithm practical application, reduces costs, and enables realistic validation and assessment of the two ship autopilot algorithms performance and effectiveness. [ABSTRACT FROM AUTHOR]

Control of underactuated autonomous underwater vehicles (AUVs) not only needs to consider fault-tolerance, but also pursues optimal performance. To this end, a fuzzy adaptive optimal fault-tolerant trajectory tracking control scheme is proposed, which realizes three-dimensional optimal trajectory tracking control of underactuated AUVs with actuator faults and constraints, dynamic uncertainties, and environmental disturbances. The features of the scheme are: (1) System outputs are redefined by a coordinate transformation to handle the underactuation problem, and an asymmetric smooth saturation model is designed to constrain control inputs. (2) An adaptive disturbance observer is constructed to estimate compound disturbances consisting of actuator faults, uncertain dynamics, disturbances, and saturation compensation values. (3) A backstepping controller is designed to transform the original system into an equivalent tracking error dynamic system with an affine nonlinear form while compensating for compound disturbances. (4) A generalized fuzzy hyperbolic model and adaptive dynamic programming are utilized to establish an optimal controller to optimize control energy and tracking errors. Through analysis, all signals of the closed-loop system are uniformly ultimately bounded, and tracking errors can converge to arbitrarily small intervals. Pure software simulation and hardware-in-the-loop test results demonstrate the advantages and feasibility of the proposed scheme. • A novel fuzzy adaptive optimal fault-tolerant control scheme is proposed for three-dimensional trajectory tracking control of underactuated AUVs. • An adaptive disturbance observer and an asymmetric smooth saturation model are designed for handling actuator faults, uncertain dynamics, disturbances and input saturation. • An adaptive dynamic programming-based optimal controller is established by a generalized fuzzy hyperbolic model and an improved parameter updating law is designed for reducing conservativeness of system stability and requirements for initial parameter adjustments, respectively. [ABSTRACT FROM AUTHOR]

In this paper, the problem of fixed-time active fault-tolerant control is studied for systems with sector-bounded nonlinearities, intermittent faults, and input saturation. Since intermittent faults appear and disappear randomly, a fixed-time scheme is considered in the active fault-tolerant control algorithm, composed of detection, isolation, estimation, and the control unit. Utilizing homogeneity-based observers, the fixed-time state estimation is available in the presence of unknown but bounded disturbances, and a fault diagnosis unit is proposed. An input saturation compensator is introduced to analyze the effect of input saturation, and its auxiliary variables are used in the reconfigurable control law. The fault-tolerant controller, which is constructed via the information provided by the fault diagnosis unit and saturation compensator, has two switching modes. As a consequence, intermittent faults are compensated via the designed active fault-tolerant control method and the system reaches practical stability with the entire convergence time bounded in a fixed time. Finally, the example of a heat control system is exploited to demonstrate the effectiveness of the developed active fault-tolerant control scheme. [ABSTRACT FROM AUTHOR]

Cooperative control is both a crucial and hot research topic for multi-agent systems (MASs). However, most existing cooperative control strategies guarantee tracking stability under various non-ideal conditions, while the path decision capability is often ignored. In this paper, the integrated decision-execution (IDE) framework is newly presented for cooperative control of multi-agent systems (MASs) to accomplish the integrated task of path decision and cooperative execution. This framework includes a decision layer and a control layer. The decision layer generates a continuous trajectory for the virtual leader to reach the target from its initial position in an unknown environment. To achieve the goal of this layer, (1) the Step-based Adaptive Search Q-learning (SASQ-learning) algorithm is proposed based on reinforcement learning to efficiently find the discrete path, (2) an Axis-based Trajectory Fitting (ATF) method is developed to convert the discrete path into a continuous trajectory for mobile agents. In the control layer, this trajectory is used to regulate the following MASs to achieve cooperative tracking control with the presence of input saturation. Simulation experiments are presented to demonstrate the effectiveness of this framework. [ABSTRACT FROM AUTHOR]

This paper provides a novel safe reinforcement learning (RL) control algorithm to solve safe optimal problems for discrete-time affine nonlinear systems, while the safety and convergence of the control algorithm are proven. The algorithm is proposed based on an adjusted policy iteration (PI) framework using only the measured data along the system trajectories in the environment. The adjusted PI algorithm combines with the system predictive information. Unlike most PI algorithms, an effective method of obtaining an initial safe and stable control policy is given here. In addition, control barrier functions (CBFs) and an input constraint function are introduced to augment reward functions. And the monotonically nonincreasing property of the iterative value function maintains the safe set forward invariant in the PI framework. Moreover, the safety and convergence of the proposed algorithm are proven in theory. Then, the design and implementation of the proposed algorithm are presented based on the identifier-actor-critic structure, where neural networks are employed to approximate the system dynamics, the iterative control policy, and the iterative value function, respectively. Finally, the simulation results illustrate the effectiveness and safety of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this study, two nonsingular three-dimensional (3D) guidance strategies to intercept a stationary target with desired impact angles, subject to nonlinear coupled dynamics, field-of-view (FOV) limit and lateral acceleration bounds, are investigated. As a stepping stone, two novel sliding mode surfaces are designed, the convergence and boundedness of the two sliding mode surfaces can guarantee the impact-angle-constrained interception while maintaining the seeker's lock-on condition during the guidance. A novel auxiliary system is also presented to compensate for the effects caused by input saturation. In addition, the analytical achievable impact angles set is presented in terms of the initial engagement condition. Numerical simulations with various constraints, a realistic missile model and comparison study have been considered to show the feasibility and effectiveness of the proposed strategies. • Three-dimensional impact angle guidance strategy with physical constraints is proposed based on nonlinear coupled engagement kinematics, without decoupling into two subsystems. • Two novel sliding mode surfaces are presented, the finite-time convergence and boundedness of the two sliding mode surfaces guarantee the interception of the stationary target with desired impact angles while maintaining FOV constraints and robustness to uncertainties. • The proposed impact angle guidance strategy is nonsingular and lateral accelerations decrease to zero at terminal interception. • The analytical solution of the achievable impact angles set is presented to avoid unsuitable selection of desired impact constraints. [ABSTRACT FROM AUTHOR]