In this paper, a switched prescribed performance (SPP)-based tracking control problem is addressed for satellite attitude system with actuator faults, actuator saturation and external disturbance. To address the problems that actuator faults or saturation may cause the tracking error to violate the prescribed performance function (PPF), an SPP-based controller is designed. Unlike existing flexible or self-adjustable prescribed performance control (PPC) methods, which continuously adjust a single PPF, these methods may still suffer from singularity under actuator faults or saturation. The proposed control approach overcomes this limitation by employing a switching mechanism that switches to a more relaxed PPF when the tracking error is predicted to violate the original PPF. Furthermore, according to the output of the fuzzy logic system (FLS), a disturbance observer (DO) is designed. The stability of the closed-loop system is proven by applying the multiple Lyapunov function method. Finally, a numerical simulation is employed to demonstrate the effectiveness of the designed SPP-based control scheme.

This article addresses the adaptive neural network-based optimal resilient control problem for a class of air–ground cooperative systems subject to the false data injection (FDI) attacks and the composite disturbances. First, a novel funnel boundary is designed to constrain formation errors with prescribed transient and steady-state performance, ensuring collision avoidance. Second, a composite disturbance observer (CDO) is proposed to accurately estimate and compensate for both external and neighbor-induced coupled disturbances. Furthermore, an optimal resilient control strategy is formulated within a backstepping framework with an actor–critic neural network (NN) to mitigate FDI attacks, ensuring stable formation tracking and performance optimization. The theoretical analysis proves the boundedness of all closed-loop signals and the convergence of formation errors within the funnel. The numerical simulations validate the approach’s effectiveness and superiority.

Cyber-physical system (CPS) security has become a paramount concern as the integration of digital and physical systems continues to grow. This survey article provides an in-depth analysis of cyber-attacks targeting CPSs, along with existing methodologies for attack modeling, defense, and design. It begins by categorizing the major types of cyber-attacks affecting CPSs, followed by a detailed discussion of the mathematical models representing typical cyber-attacks within cyber-physical space. This article then examines defense mechanisms, covering both detection and response strategies, and emphasizes techniques for designing stealthy attacks. Finally, it identifies promising directions for future research, aiming to provide researchers with a broad perspective that supports the development of robust, real-time security solutions for the increasingly complex CPS landscape.

In this paper, to develop a backstepping-based finite-time control (BFTC) method for the three-dimensional integrated guidance and control (IGC) system with target maneuvers and disturbances, a novel decoupled finite-time approximation auxiliary system (DFTAAS) is proposed together with a finite-time disturbance observer (FTDO). To accurately estimate the target maneuvers and the disturbances, the FTDO is designed. To approximate the virtual control law derivative and avoid the explosion of complexity problem, the DFTAAS is proposed. To solve the singularity issue and guarantee the boundedness of the virtual control law derivative, the piecewise functions are designed to derive the DFTAAS and the virtual control. Besides, to make the controller parameters independent of the norms associated to the control matrices, the control matrices are introduced into the DFTAAS so that the conservatism of the controller parameters is restrained. Furthermore, the finite-time stability properties of the system state stabilization and the disturbance estimation are integrated into the Lyapunov stability to guarantee the finite-time stability of the whole closed-loop IGC system. Finally, the hardware-in-the-loop experiment is implemented to verify the effectiveness of the proposed method. Note to Practitioners—The aim of this paper is to design a BFTC scheme for the three-dimensional IGC system with target maneuvers and disturbances. In the practical IGC application, to solve the explosion of complexity problem, the finite-time dynamic surface control is designed to implement the BFTC. Nevertheless, the boundedness of the virtual control law derivative, which is essential for the system stability, can not be guaranteed due to the singularity. Besides, the parameter conservatism is inevitable due to the control matrices. In addition, the finite-time stability properties of the system state stabilization and the disturbance estimation, which interact and influence each other in the control process, is rarely integrated in practical. In view of the above actual issues, the piecewise function is designed to develop the DFTAAS and the guidance law to solve the explosion of complexity problem and ensure the boundedness of the virtual control law derivative. The control matrices are introduced into the DFTAAS to solve the problem of parameter conservatism. The finite-time stability properties of the system state stabilization and the disturbance estimation are integrated into the Lyapunov stability, which is more in line with the practical needs to sufficiently consider the coupling of them.

In this paper, a discrete-time embedded model control (EMC) scheme is proposed for a class of disturbed nonlinear systems under model uncertainty. First, by invoking the current state, a linear discrete-time embedded model (EM) is real-timely generated by linearizing and discretizing nominal model of nonlinear system. Then, as for the reference dynamics for our control scheme, a reference generator is designed to generate a group of reference control input and reference state. Meanwhile, as for control dynamics for proposed scheme, an auxiliary system and a predictor are combined to compensate for the error of control input. Based on above, a synthetic controller is derived to stabilize the controlled system by combining the reference dynamics and control dynamics. Thus, the discrete-time Lyapunov stability theory is utilized to analyze the overall closed-loop system, and a sufficient stability condition is proposed to guarantee that all the closed-loop states under the proposed EMC scheme are semi-globally ultimately uniformly bounded (UUB), ensuring the ultimate error bounds to be adjusted into tolerable regions. Finally, as for the nonlinear system of quadrotor UAV, some simulations are conducted to illustrate the effectiveness of the proposed control scheme. Note to Practitioners—The motivation of this paper aims to investigate the control stability issue of a disturbed nonlinear system. Currently, these relevant results proposed in existent paper mainly relied on the complicated continuous-time controllers, which are hard to be implemented in practice. Yet, this paper proposes a control scheme based on a discrete-time embedded model, which can ensure the desired control performance. First, a reference signal generator is designed by generating a linear discrete-time embedded model. Based on this, the control error is compensated by combining an auxiliary system and a predictor. Then, a synthetic controller is derived to stabilize the controlled system. The effectiveness of the overall control scheme is validated using a quadrotor UAV nonlinear system, demonstrating that all signals in the closed-loop system under our control scheme are semi-globally uniformly bounded, and the ultimate error bounds can be adjusted to a tolerable range. In future work, we will investigate the problem on input delay compensation based on the control scheme of this paper.

Deep reinforcement learning (DRL) has emerged as a promising solution for autonomous operations of autonomous aerial vehicles (AAVs) in unknown environments. However, learning to navigate and avoid obstacles under sparse reward settings remains challenging. In this article, we propose an end-to-end learning approach that synthesizes imitation learning with DRL for AAV navigation and obstacle avoidance. Specifically, we formulate this problem as a partially observable Markov decision process with sparse rewards and learn an end-to-end policy that maps imperfect sensor data to control signals. To efficiently optimize the policy under the sparse reward setting, we propose the selective behavior cloning enhanced actor-critic (SBCAC) algorithm. By integrating an experience filter and a Q-value based action selector to selectively mimic an artificial potential field based non-expert policy, our approach significantly improves the learning performance and sample efficiency. Extensive simulations with fixed-wing and multi-rotor AAVs in different scenarios demonstrate that SBCAC achieves an average improvement of up to 16.07% in success rate, a 72.46% reduction in crash rate, and a 94.62% reduction in stray rate compared to the state-of-the-art selective imitation baseline. Furthermore, hardware-in-the-loop and physical experiments validate the effectiveness of our approach, showing its potential for practical applications in complex environments.

The adaptive neural network (NN) control for the fixed-wing unmanned aerial vehicle (FUAV) under the unmodeled dynamics and the time-varying switching disturbance (TVSD) is investigated in this article. To better describe the TVSD induced by the change in the flight area of the FUAV, a switching augmented model (SAM) based on the known information about the TVSD is proposed first. The parameter adaptation technique is used to estimate the related TVSD. Thereafter, the time-varying disturbance that cannot be described by the SAM is estimated by the disturbance observer (DO). The radial basis function NN (RBFNN) is adopted to approximate the unknown unmodeled dynamics. The coupling terms derived from the co-design of DO and the parameter adaptation (PA) are separated by some inequality techniques. Then, the separated unknown terms are eliminated by designing the parameters of the controller and that of the adaptive law. The separated known terms are tackled by adding robust control terms to the controller. In addition, to improve the estimation performance for the TVSD and RBFNN, the auxiliary system in the DO form is designed. Sufficient stable conditions about the closed-loop switched system (CLSS) are obtained with and without the inequality about the switching times. Finally, an illustrative example is given to show the feasibility and advantage of the proposed control strategy by the attitude model of the FUAV.

In this article, a dual event-triggered (ET)-based fault-tolerant attitude flexible performance tracking control problem is studied for the satellite with input saturation, actuator fault and external disturbance. To make the prescribed performance function (PPF) be adjusted only when the attitude tracking error of the satellite violates the PPF, a predictive tracking error-based ET mechanism is designed. With the designed mechanism, the fault factor adaptive law and saturation difference are updated only when the tracking error violates the PPF. In addition, an ET command regulation scheme is designed, taking into account the performance of the system and the saving of communication resources. It is proved that the closed-loop system is stable by the Lyapunov method. Finally, the simulation results demonstrate the availability of the proposed tracking control scheme.

This article studies two robust adaptive dynamic programming (ADP) approaches for uncertain discrete-time (DT) nonlinear systems. Since the uncertainty is implicit in the traditional Hamilton-Jacobi–Bellman (HJB) equation, it is difficult to deal with the uncertainty. In this article, the Taylor series approximation technique is utilized to convert the traditional HJB equation into an explicit form of the uncertainty. In virtue of the first-order Taylor series approximation technique, a robust first-order approximate HJB equation is established. To further improve the approximation accuracy, a robust second-order approximate HJB equation is exploited by using the Hessian matrix of the value function. It is shown that the second-order approximate HJB equation could be extended to the uncertain DT linear systems. Aiming at obtaining the solutions of the two robust approximate HJB equations, we propose two corresponding policy iteration (PI) algorithms. More importantly, the convergence and optimality of the designed PI algorithms are clarified. Finally, a numerical case is conducted to test the validity of the designed robust DT PI ADP approaches.

This paper studies the disturbance-observer-based adaptive neural network cooperative event-triggered control problem for six-rotor unmanned aerial vehicles with finite-time prescribed performance. Six-rotor unmanned aerial vehicle systems are divided into the position subsystem and the attitude subsystem. The switching threshold event-triggered mechanism that considers the influence of event triggering on the consensus control performance is designed of each six-rotor unmanned aerial vehicle to save the transmission resources, which excludes the Zeno behavior. Neural networks are introduced for estimating the uncertainties and solving the algebraic loop problem. In addition, for the position subsystem, by combining the prescribed performance with the velocity function, a finite-time control scheme is proposed, which can guarantee that the consensus errors converge to a prespecified neighborhood of the origin, and all closed-loop signals are bounded. Based on the designed control input signal of position subsystem, an adaptive neural network event-triggered control mechanism is designed to stabilize the attitude subsystem. Finally, some verification results are given to test the rationality of the proposed control strategy. Note to Practitioners—The purpose of this paper is to design an event-triggered cooperative control scheme to save the transmission resources for six-rotor unmanned aerial vehicle systems with performance limitations and lumped disturbances. In practical applications, if the impact of the event-triggered mechanism on the system performance is not taken into account, the system performance may be significantly degraded while the information transmission resource is saved. Thus, this paper designs an event-triggered mechanism that considers the system performance, which can effectively weigh the relationship between system performance and transmission resource consumption and better meet the practical requirements. Moreover, a finite-time specified performance control strategy is introduced to avoid the problem of difficult determination of residual set and improve the transient-state and steady-state performances of unmanned aerial vehicle systems, which is more in line with the actual demand.

In this article, an adaptive neural tracking control based on saturation disturbance observer (SDO) and command filter is studied for multiple-input-multiple-output nonlinear systems with time-varying constraints and system uncertainties. By employing neural networks (NNs), the system uncertainties are approximated. The SDO is proposed to estimate the composited disturbances which consist of NN approximation errors and the external bounded disturbances. Compared with the traditional disturbance observer, the SDO can reduce the estimation error to some extent. The control requirements are achieved based on the multiconstraints which contain three layers: 1) prescribed performance functions (PPFs); 2) actual constraints; and 3) virtual constraints. The errors remain within the prescribed small neighborhood of zero by using the PPFs, the error constraints ensure that the time-varying constraints are never violated even if the PPFs are not available, and the virtual constraints are applied in a new time-varying barrier Lyapunov function (TVBLF) to design virtual controllers and controller to solve the singularity problem of the traditional TVBLF. In addition, the command filter is introduced to solve the problem of "explosion of complexity." Finally, a numerical simulation verifies the effectiveness of the proposed scheme for a flight control of unmanned aerial vehicle.

In this article, an improved event-triggering-learning (ETL)-based adaptive dynamic programming (ADP) method for the post-stall pitching maneuver of aircraft is proposed to achieve the robust optimal control and reduce the computational cost. First, a feedforward control with the nonlinear disturbance observer (NDO) technique is designed to attenuate the adverse effects caused by the unsteady aerodynamic disturbances. Subsequently, the ADP method with a critic neural network which is constructed to approximate the value function in the Hamilton-Jacobi-Bellman equation is employed to conduct the optimal control of aircraft. In addition, to reduce the computational cost of learning, the event-triggering (ET) mechanism with an improved ET condition is applied. The Lyapunov stability theory is utilized to prove that all signals in the closed-loop control system are uniformly ultimately bounded. Finally, simulation results are presented to illustrate the effectiveness of the proposed ETL-based ADP method.

This article studies the problem of memory event-triggered cooperative adaptive control of heterogeneous nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks based on the multiplayer mixed zero-sum (ZS) game strategy. First, a neural-network-based reinforcement learning scheme is structured to obtain the Nash equilibrium solution of the proposed multiplayer mixed ZS game scheme. Then, a memory-based event-triggered mechanism considering the historical data is proposed. This effectively avoids incorrect triggering information caused by unknown external factors. Moreover, thanks to the idea of switching topology, the mixed ZS game problem under the influence of node-based DoS attacks is solved efficiently. In accordance with the Lyapunov stability theory, it is proved that all signals of heterogeneous MASs are bounded, all heterogeneous followers can track the trajectory of the leader during the no-attack period, the attacked follower can achieve stabilization control during the attack period, and the remaining nonattacked followers can achieve cooperative control during the attack period. Finally, the effectiveness of the designed memory-event-triggered-based mixed ZS game cooperative control strategy is tested by the given simulation results.

Addressing external disturbances has been a critical issue for control design to ensure reliable operation of systems. This article investigates the tracking control problem for the uncertain nonlinear systems with the strong external disturbance and the prescribed performance. The flexible performance-based control scheme is developed by introducing an external disturbance criterion into the prescribed performance. It is capable of guaranteeing the prescribed performance if the external disturbance is less than a specified threshold and degrading that in light of the user-appointed rule otherwise. Particularly, the disturbance interval observer is synthesized to generate the boundaries of the external disturbances and realize the judgment of that criterion. With the generated boundaries, the interval-type auxiliary system is designed to provide the modified performance functions (MPFs) that characterize performance requirement and degradation rule simultaneously. Based on the positive system theory and the Lyapunov method, it is theoretically shown that the system output can always track the reference signal and satisfy the constraints of MPFs. Finally, both the numerical simulation and the application of flight control design verify that the results are effective and valid.

This article addresses the distributed zero-sum differential game adaptive control problem of six-rotor unmanned aerial vehicles under denial-of-service attacks based on the self-triggered mechanism. First, a fuzzy-logic-system-based identifier-critic framework is structured to obtain the alternative approximate solution with fewer learning parameters. Then, a novel optimal value function, considering the optimal control signal, worst disturbance signal, steady-state, and dynamic performances, is designed. Subsequently, an improved self-triggered strategy, featuring negative feedback adjustment between the threshold and system consensus error, is proposed to reduce the communication resource loss and decrease the influence of introducing the self-triggered mechanism on the system performance. Unlike the event-triggered strategy, the next trigger moment of the self-triggered strategy is determined by the current information, eliminating the need for continuous monitoring of the trigger state, which is more convenient for the physical implementation. Moreover, the connectivity-broken denial-of-service attacks on the information transmission process among unmanned aerial vehicles are considered. Next, through the transformation between stabilization control and cooperative control, the difficulty of realizing cooperative control caused by the temporarily disrupted topological relationships due to denial-of-service attacks is solved effectively. Using Lyapunov stability theory, it is proved that all signals of six-rotor unmanned aerial vehicles are bounded, and the consensus control performance is achieved. Finally, the rationality of the designed zero-sum differential game adaptive control scheme is verified by some simulation results.

In this article, an event-triggered (ET) fractional-order adaptive tracking control scheme (ATCS) is studied for the uncertain nonlinear system with the output saturation and the external disturbances by using the nonlinear disturbance observer (NDO) and the neural networks (NNs). Based on NNs, the system uncertainties are approximated. An NN-based NDO is designed to estimate the bounded disturbances. Combining the NNs, the output of the designed NDO, the fractional-order theory, and the ET mechanism, an ATCS is proposed under the output saturation. According to the stability analysis, all the closed-loop signals are semiglobally uniformly ultimately bounded based on the investigative ATCS. The simulation results and the comparative experiment verifications are shown to indicate the viability of the developed control scheme.

This paper deals with the design and the software validation of an automatic control architecture for the control of the launch vehicles' flight path slope angle in the second flight phase (after launch) by using the backstepping control approach. Starting from the nonlinear dynamics associated to the motion of the launch vehicles, the backstepping control technique and the Lyapunov theory are combined in order to obtain the general control law and the rotation angle of the rocket's reaction nozzle. The novel control scheme is software implemented in Matlab, the global stability and the effectiveness of this control architecture being proved both theoretically and by numerical simulations for the motion in vertical plane of the launch vehicle.

This paper investigates the disturbance utilization-based attitude control for the fixed-wing unmanned aerial vehicle (UAV). The disturbance utilization condition (DUC) is formed based on the Lyapunov function analysis to retain the disturbance that benefits the stability of closed-loop systems. To reduce the sign-misjudgment of disturbance coupling terms induced by the DUC, the disturbance estimation error analysis auxiliary system (DEEAAS) is designed based on the disturbance observer (DO). Combined with the DEEAAS and the DO, the boundaries of the disturbance estimation error (DEE) are derived. Subsequently, the composite DUC is proposed based on the above boundaries and the given thresholds to replace the basic DUC. Then, the boundedness of the attitude tracking errors of the fixed-wing UAV can be ensured by the controller designed with the composite DUC. And combined with the derived boundaries of the DEE and the given thresholds, the adaptive DO and the adaptive DEEAAS are also designed to avoid the use of big parameters. In addition, sufficient conditions that stabilize the attitude closed-loop system of fixed-wing UAVs equipped with the disturbance utilization-based controller (DUBC) are given. Finally, the numerical simulation for the fixed-wing UAV illustrates the effectiveness of the proposed DUBC.

The issue of modeling and fault-tolerant control (FTC) design for a class of flexible air-breathing hypersonic vehicles (FAHVs) with actuator faults is investigated in this article. Different from previous research, the shear deformation of the fuselage is considered, and an ordinary differential equations-partial differential equations (ODEs-PDEs) coupled model is established for the FAHVs. A feedback control is proposed to ensure flight stable and an adaptive FTC method is designed to deal with actuator faults while suppressing the system's vibrations. Besides, the stability analysis of the closed-loop system is given via the Lyapunov direct method and an algorithm that transfers the bilinear matrix inequalities (BMIs) feasibility problem to the linear matrix inequalities (LMIs) feasibility problem is provided for determining the control gains. Finally, the numerical simulation results show that the proposed controller can stabilize the flight states and suppresses the vibration of the fuselage efficiently.

In this article, a disturbance-observer-based adaptive fuzzy tracking control scheme is proposed for a medium-scale unmanned helicopter of six degrees of freedom in the presence of system uncertainties, flight boundary constraints, and external disturbances. A flight boundary protection algorithm is proposed to ensure its flight trajectory within the given safety range. A fuzzy logic system is utilized to estimate the system uncertainties and a nonlinear disturbance observer is adopted to handle the unknown compound terms of the external disturbances and the estimation errors resulting from the fuzzy logic system. An inverse optimal control approach is then used to avoid solving the Hamilton–Jacobi–Bellman equation in minimizing a cost function in the attitude loop. It is shown via the Lyapunov method that the desired safe tracking performance of the position loop and attitude loop of the controlled unmanned helicopter can be achieved. Simulations are provided to illustrate the effectiveness of the proposed control scheme.

To improve the safety and reliability of quadrotor unmanned aerial vehicles (QUAVs) with limited communication, system uncertainties, and unknown external disturbances in a highly uncertain and safety-critical environment, a distributed adaptive human-in-the-loop event-triggered (ET) formation controller is proposed. The nonautonomous leader is controlled by receiving control commands decided by the gesture recognition system, and the followers are controlled indirectly via the connected communication network. Thus, the safety and flexibility of the closed-loop system are improved. The designed controller is quantized and then sent to the actuator only at the ET instants to further reduce the network burden. The radial basis function neural network is used to approximate the system uncertainties. The unknown approximation error and the unknown external disturbance are viewed as a compound disturbance compensated by the high-order disturbance observer. In addition, the uniformly ultimately bounded stability of the closed-loop system is achieved through the Lyapunov method. Finally, comparative experiments are implemented on the QUAVs to demonstrate the validity of the presented control scheme.

This article proposes a fault-tolerant adaptive multigradient recursive reinforcement learning (RL) event-triggered tracking control scheme for strict-feedback discrete-time multiagent systems. The multigradient recursive RL algorithm is used to avoid the local optimal problem that may exist in the gradient descent scheme. Different from the existing event-triggered control results, a new lemma about the relative threshold event-triggered control strategy is proposed to handle the compensation error, which can improve the utilization of communication resources and weaken the negative impact on tracking accuracy and closed-loop system stability. To overcome the difficulty caused by sensor fault, a distributed control method is introduced by adopting the adaptive compensation technique, which can effectively decrease the number of online estimation parameters. Furthermore, by using the multigradient recursive RL algorithm with less learning parameters, the online estimation time can be effectively reduced. The stability of closed-loop multiagent systems is proved by using the Lyapunov stability theorem, and it is verified that all signals are semiglobally uniformly ultimately bounded. Finally, two simulation examples are given to show the availability of the presented control scheme.

In this article, an adaptive neural network (NN) tracking control scheme is proposed for uncertain multi-input-multi-output (MIMO) nonlinear system in strict-feedback form subject to system uncertainties, time-varying state constraints, and bounded disturbances. The radial basis function NNs (RBFNNs) are adopted to approximate the system uncertainties. By constructing the intermediate variables, the external disturbances that cannot be directly measured are approximated by the disturbance observers. The time-varying barrier Lyapunov function (TVBLF) is constructed to guarantee the boundedness of the errors lie in the sets. To overcome the potential singularity problem that the denominator of the barrier function term approaches zero in controller design, the adaptive NN tracking control scheme with time-varying state constraints is proposed. Based on the TVBLF, the controller will be designed to guarantee tracking performance without violating the appropriate error constraints. The analysis of TVBLF shows that all closed-loop signals remain semiglobally uniformly ultimately bounded (SGUUB). The simulation results are performed to validate the validity of the proposed scheme.

By considering the under-actuated characteristics of the quadcopter suspension transportation system and the external disturbance, the effective tracking control of the quadrotor transportation system faces great difficulties and challenges. An adaptive hierarchical sliding mode control (HSMC) scheme based on fixed-time sliding mode disturbance observer (FTSMDO) is developed for the anti-disturbance tracking control of under-actuated quadcopter suspension transportation system (UQSTS). The HSMC is used to deal with the under-actuated characteristics of the UQSTS, and the external disturbance is estimated by designing the FTSMDO. Synchronously, the disturbance estimation error is processed by designing the adaptive law. The stability analysis based on Lyapunov is applied to verify the uniform ultimate boundedness of the closed-loop system. Finally, the comparison of physical experiment upshots shows the effectiveness and potential of the proposed new control techniques.

In this article, an adaptive neural safe tracking control scheme is studied for a class of uncertain nonlinear systems with output constraints and unknown external disturbances. To allow the output to stay in the desired output constraints, a boundary protection approach is developed and utilized in the output constrained problem. Since the generated output constraint trajectory is piecewise differentiable, a dynamic surface method is utilized to handle it. For the purpose of approximating the system uncertainties, a radial basis function neural network (RBFNN) is adopted. Under the output of the RBFNN, the disturbance observer technology is employed to estimate the unknown compound disturbances of the system. Finally, the Lyapunov function method is utilized to analyze the convergence of the tracking error. Taking a two-link manipulator system, as an example, the simulation results are presented to illustrate the feasibility of the proposed control scheme.

This article studies the fixed-time fuzzy adaptive bipartite containment quantized control problem for nonlinear multiagent systems subject to unknown external disturbances and unknown Bouc–Wen hysteresis. The output and input control signals of the systems are quantized by sector-bounded quantizer. A disturbance observer and a fuzzy state observer are simultaneously designed to estimate unknown external disturbances and unmeasured states, respectively. Then, to solve the difficulty caused by Bouc–Wen hysteresis, a distributed control strategy is presented by using the disturbance observer. In addition, the bipartite containment control performance of multiagent systems can be realized, and the stability of the closed-loop multiagent systems can be proved to be the semi-global practical fixed-time stability by Lyapunov theory and fixed-time theory. Finally, a practical simulation example is shown to demonstrate the effectiveness of the proposed scheme.

In this article, an adaptive neural fault-tolerant control (FTC) scheme is proposed for the medium-scale unmanned autonomous helicopter subject to external disturbance, actuator fault, and input saturation. Multiple approximators are constructed to handle the unknown terms and promote the control design. The nonlinear coupled function terms are approximated by virtue of the radial basis function neural networks. The unknown disturbance is tackled by the developed disturbance observer. Meanwhile, two auxiliary systems are introduced to handle the actuator fault and input saturation, respectively. In the framework of the backstepping method, a multiapproximator-based adaptive FTC strategy is presented, which assures the boundedness of all closed-loop system signals. Simulation results are presented to validate the availability of the designed controller.

This article investigates the adaptive fault-tolerant tracking control problem for a class of discrete-time multiagent systems via a reinforcement learning algorithm. The action neural networks (NNs) are used to approximate unknown and desired control input signals, and the critic NNs are employed to estimate the cost function in the design procedure. Furthermore, the direct adaptive optimal controllers are designed by combining the backstepping technique with the reinforcement learning algorithm. Comparing the existing reinforcement learning algorithm, the computational burden can be effectively reduced by using the method of less learning parameters. The adaptive auxiliary signals are established to compensate for the influence of the dead zones and actuator faults on the control performance. Based on the Lyapunov stability theory, it is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, some simulation results are presented to illustrate the effectiveness of the proposed approach.

This article investigates the quantized adaptive finite-time bipartite tracking control problem for high-order stochastic pure-feedback nonlinear multiagent systems with sensor faults and Prandtl-Ishlinskii (PI) hysteresis. Different from the existing finite-time control results, the nonlinearity of each agent is totally unknown in this article. To overcome the difficulties caused by asymmetric hysteresis quantization and PI hysteresis, a new distributed control method is proposed by adopting the adaptive compensation technique without estimating the lower bounds of parameters. Radial basis function neural networks are employed to estimate unknown nonlinear functions and solve the problem of algebraic loop caused by the pure-feedback nonlinear systems. Then, an adaptive neural-network compensation control approach is proposed to tackle the problem of sensor faults. The problem of the "explosion of complexity" caused by repeated differentiations of the virtual controller is solved by using the dynamic surface control technique. Based on the Lyapunov stability theorem, it is proved that all signals of the closed-loop systems are semiglobal practical finite-time stable in probability, and the bipartite tracking control performance is achieved. Finally, the effectiveness of the proposed control strategy is verified by some simulation results.

This article studies the distributed fault estimation (DFE) and fault-tolerant control for continuous-time interconnected systems. Using associated information among subsystems to design the DFE observer can improve the accuracy of fault estimation of the interconnected systems. Based on the static output feedback (SOF), the global outputs of the interconnected systems are used to construct a distributed fault-tolerant control (DFTC). The multiconstrained methods are proposed to enhance the transient performance and ability to suppress the external disturbances simultaneously. The conditions of the presented design methods are expressed in terms of linear matrix inequalities. The simulation results are illustrated to show the feasibility of the presented approaches.

This article proposes a new implicit function-based adaptive control scheme for the discrete-time neural-network systems in a general noncanonical form. Feedback linearization for such systems leads to the output dynamics nonlinear dependence on the system states, the control input, and uncertain parameters, which leads to the nonlinear parametrization problem, the implicit relative degree problem, and the difficulty to specify an analytical adaptive controller. To address these problems, we first develop a new adaptive parameter estimation strategy to deal with all uncertain parameters, especially, those of nonlinearly parameterized forms, in the output dynamics. Then, we construct a key implicit function equation using available signals and parameter estimates. By solving the equation, a unique adaptive control law is derived to ensure asymptotic output tracking and closed-loop stability. Alternatively, we design an iterative solution-based adaptive control law which is easy to implement and ensure output tracking and closed-loop stability. The simulation study is given to demonstrate the design procedure and verify the effectiveness of the proposed adaptive control scheme.

This article proposes a high-order disturbance observer (HODO) and dynamic surface control (DSC) technique-based adaptive fuzzy control scheme for nonlinear systems subjected to input saturation and external time-varying disturbances. First, based on a Sigmoid function, the saturation input is tackled by utilizing a well-defined nonlinear smooth function. Furthermore, HODO and fuzzy logic systems are used to estimate the external disturbances and to handle the lumped unknown functions, respectively. Then, by using the backstepping method and DSC technique, a HODO-based adaptive fuzzy tracking control scheme is proposed for nonlinear systems with saturation nonlinearity, uncertainties, and external disturbances. The Lyapunov analysis method is used to prove that all signals in the entire system are semiglobally uniformly ultimately bounded (SGUUB). In addition, the tracking error converges to a compact set with a tunable error bound determined by some design parameters. Finally, a numerical simulation of two-stage chemical reactor shows the effectiveness of the developed tracking control strategy.

In this paper, a tracking flight control scheme is proposed based on a disturbance observer for a quadrotor with external disturbances. To facilitate the processing of external time-varying disturbances, it is assumed to consist of some harmonic disturbances. Then, a disturbance observer is proposed to estimate the unknown disturbance. By using the output of the disturbance observer, a flight controller of the quadrotor is developed to track the given signals which are generated by the reference model. Finally, the proposed control method is applied to flight control of the quadrotor Quanser Qball 2. The experimental results are presented to demonstrate the effectiveness of the developed control strategy.

In this article, the resilient anti-disturbance control is studied for uncertain turbofan system subject to unmeasured states and multiple disturbances. Based on four kinds of disturbances in the addressed system, some disturbances are described as an external system by using available information while the others are assumed to be energy-bounded, which are included in the system dynamics, output measurement, and controlled output, simultaneously. Initially, a state observer and a disturbance observer are jointly constructed to estimate the unmeasured state and unknown disturbance. The estimation on disturbance is used in the feedforward controller to reject the disturbances and the state estimation is applied to the resilient output feedback controller, which guarantee that the closed-loop system is asymptotically stable with the L2-L∞performance, and enhance the robustness of the uncertain turbofan system. Then, the Lyapunov stability theory and linear matrix inequality (LMI) technology are combined to obtain the algorithms on checking the controller gain and observer one. Finally, the effectiveness of our proposed methods is shown by using some numerical simulations.

In this paper, an adaptive neural discrete-time (ANDT) fractional-order tracking control scheme is proposed for an unmanned aerial vehicle system with prescribed performance in the presence of system uncertainties and unknown bounded disturbances based on a discrete-time disturbance observer (DTDO). The system uncertainties are handled using neural network (NN) approximation. To compensate for the adverse effects of unknown disturbances, an NN-based DTDO is designed. On the basis of the NN, the designed DTDO and the backstepping technology, an ANDT fractional-order control scheme with prescribed performance is developed. Then, the tracking errors are convergent under the proposed control scheme. Finally, the effectiveness of the proposed discrete-time control scheme is demonstrated by numerical simulation results.

This paper studies the relative degrees of discrete-time neural network systems in a general noncanonical form, and develops a new feedback control scheme for such systems, based on implicit function theory and feedback linearization. After time-advance operation on output of such systems, the output dynamics nonlinearly depends on the control input. To address this issue, we use implicit function theory to define the relative degrees, and to establish a normal form. Then, an implicit function equation solution-based control scheme and an iterative solution-based control scheme are proposed, which ensure not only the closed-loop stability but also the output tracking for the controlled plant. An adaptive control framework for the controlled plant with uncertainties is also presented to illustrate the basic design procedure. The simulation results are given to demonstrate the desired system performance.

In this paper, a novel adaptive fault-tolerant sliding-mode control scheme is proposed for high-speed trains, where the longitudinal dynamical model is focused, and the disturbances and actuator faults are considered. Considering the disturbances in traction force generated by the traction system, a dynamic model with actuator uncertainties modeled as input distribution matrix uncertainty is established. Then, a new sliding-mode controller with design conditions is proposed for the healthy train system, which can drive the tracking error dynamical system to a predesigned sliding surface in finite time and maintain the sliding motion on it thereafter. In order to deal with the actuator uncertainties and unknown faults simultaneously, the adaptive technique is combined with the fault-tolerant sliding-mode control design together to guarantee that the asymptotical convergence of the tracking errors is achieved. Furthermore, the proposed adaptive fault-tolerant sliding-mode control scheme is extended to the cases of the actuator uncertainties with unknown bounds and the unparameterized actuator faults. Finally, the case studies on a real train dynamic model are presented to explain the developed fault-tolerant control scheme. The simulation results show the effectiveness and feasibility of the proposed method.

This paper studies the adaptive neural control (ANC)-based tracking problem for discrete-time nonlinear dynamics of an unmanned aerial vehicle subject to system uncertainties, bounded time-varying disturbances, and input saturation by using a discrete-time disturbance observer (DTDO). Based on the approximation approach of neural network, system uncertainties are tackled approximately. To restrain the negative effects of bounded disturbances, a nonlinear DTDO is designed. Then, a backstepping technique-based ANC strategy is proposed by utilizing a constructed auxiliary system and a discrete-time tracking differentiator. The boundness of all signals is proven in the closed-loop system under the discrete-time Lyapunov analysis. Finally, the feasibility of the proposed ANC technique is further specified based on numerical simulation results.

In this paper, the suppressing problem of the cable's vibration is studied for a suspension cable system of helicopter with disturbances. The Hamilton's principle is applied to obtain a distributed parameter system of the suspension cable system which includes one partial differential equation and two ordinary differential equations. Two nonlinear disturbance observers are developed to compensate the effect of boundary disturbances. The auxiliary systems are designed to eliminate the effects of input nonlinearities. Based on the designed disturbance observer and auxiliary systems, two boundary controllers are designed at the top and bottom boundaries of the suspension cable. Under the proposed controllers, the amplitude of oscillation is proven to be uniformly ultimately bounded and converges to a small neighborhood of zero by selecting proper design parameters of the antidisturbance control scheme for the suspension cable system. Meanwhile, some sufficient conditions are provided to guarantee the effectiveness of the developed control law. Finally, simulation results show that the controllers developed in this paper work well in handling disturbances for the suspension cable system of helicopter.

This paper studies the problem of prescribed performance adaptive neural control for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems in the presence of external disturbances and input saturation based on a disturbance observer. The system uncertainties are tackled by neural network (NN) approximation. To handle unknown disturbances, a Nussbaum disturbance observer is presented. By incorporating the disturbance observer and NNs, an adaptive prescribed performance neural control scheme is further developed. Then, the expected asymptotically convergent tracking errors between system output signals and desired signals are achieved. Numerical simulation results demonstrate the effectiveness of the proposed control scheme.

This paper conducts a new study for adaptive Takagi-Sugeno (T-S) fuzzy approximation-based control of multi-input and multi-output (MIMO) noncanonical-form nonlinear systems. Canonical-form nonlinear systems have explicit relative degree structures, whose approximation models can be directly used to derive desired parameterized controllers. Noncanonical-form nonlinear systems usually do not have such a feature, nor do their approximation models, which are also in noncanonical forms. This paper shows that it is desirable to reparameterize noncanonical-form T-S fuzzy system models with smooth membership functions for adaptive control, and such system reparameterization can be realized using relative degrees, a concept yet to be studied for MIMO noncanonical-form T-S fuzzy systems. This paper develops an adaptive feedback linearization scheme for control of such general system models with uncertain parameters, by first deriving various relative degree structures and normal forms for such systems. Then, a reparameterization procedure is developed for such system models, based on which adaptive control designs are derived, with desired stability and tracking properties analyzed. A detailed example is presented with simulation results to show the new control design procedure and desired control system performance.

In this paper, an adaptive neural fault-tolerant control scheme is proposed and analyzed for a class of uncertain nonlinear large-scale systems with unknown dead zone and external disturbances. To tackle the unknown nonlinear interaction functions in the large-scale system, the radial basis function neural network (RBFNN) is employed to approximate them. To further handle the unknown approximation errors and the effects of the unknown dead zone and external disturbances, integrated as the compounded disturbances, the corresponding disturbance observers are developed for their estimations. Based on the outputs of the RBFNN and the disturbance observer, the adaptive neural fault-tolerant control scheme is designed for uncertain nonlinear large-scale systems by using a decentralized backstepping technique. The closed-loop stability of the adaptive control system is rigorously proved via Lyapunov analysis and the satisfactory tracking performance is achieved under the integrated effects of unknown dead zone, actuator fault, and unknown external disturbances. Simulation results of a mass-spring-damper system are given to illustrate the effectiveness of the proposed adaptive neural fault-tolerant control scheme for uncertain nonlinear large-scale systems.

This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.

In this paper, an adaptive neural fault-tolerant control scheme is proposed for the three degrees of freedom model helicopter, subject to system uncertainties, unknown external disturbances, and actuator faults. To tackle system uncertainty and nonlinear actuator faults, a neural network disturbance observer is developed based on the radial basis function neural network. The unknown external disturbance and the unknown neural network approximation errors are treated as a compound disturbance that is estimated by another nonlinear disturbance observer. A disturbance observer-based adaptive neural fault-tolerant control scheme is then developed to track the desired system output in the presence of system uncertainty, external disturbance, and actuator faults. The stability of the whole closed-loop system is analyzed using the Lyapunov method, which guarantees the convergence of all closed-loop signals. Finally, the simulation results are presented to illustrate the effectiveness of the new control design techniques.

In this paper, a constrained control allocation scheme is designed based on the neurodynamic model for an overactuated aircraft with system uncertainties and unknown time-varying external disturbances. To generate the control command signals, an adaptive neural attitude controller is developed, taking into consideration the nonsymmetric input saturation constraint. This control scheme can guarantee semi-global uniform ultimate boundedness for all signals in the closed-loop system. The control command signals are sent to the actuators of the overactuated aircraft via the constrained control allocation scheme. Based on the developed adaptive neural attitude control scheme, the control allocation is designed with the position and rate constraints of actuators taken into account. We pose this constrained control allocation as a convex nonlinear programming problem and use a recurrent neural network as its solver. Simulation study on a near space vehicle is conducted to illustrate the effectiveness of the developed adaptive neural attitude control scheme and the constrained control allocation scheme.

This paper presents a new study on the relative degrees of single-input and single-output T-S fuzzy systems in general noncanonical forms, and proposes a feedback linearization-based control design method for such systems. The study extends the system relative degree concepts, commonly used for the control of nonlinear systems, to general T-S fuzzy systems, derives various relative degree conditions for general T-S fuzzy systems, and establishes the relative degree dependent normal forms. A feedback linearization-based control design framework is developed for general T-S fuzzy systems using its normal form, to achieve closed-loop stability and asymptotic output tracking under relaxed design conditions. A new adaptive feedback linearization-based control scheme for T-S fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed. Some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form T-S fuzzy systems are also demonstrated. An illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme.

In this paper, a dynamic surface control (DSC) scheme is proposed for a class of uncertain strict-feedback nonlinear systems in the presence of input saturation and unknown external disturbance. The radial basis function neural network (RBFNN) is employed to approximate the unknown system function. To efficiently tackle the unknown external disturbance, a nonlinear disturbance observer (NDO) is developed. The developed NDO can relax the known boundary requirement of the unknown disturbance and can guarantee the disturbance estimation error converge to a bounded compact set. Using NDO and RBFNN, the DSC scheme is developed for uncertain nonlinear systems based on a backstepping method. Using a DSC technique, the problem of explosion of complexity inherent in the conventional backstepping method is avoided, which is specially important for designs using neural network approximations. Under the proposed DSC scheme, the ultimately bounded convergence of all closed-loop signals is guaranteed via Lyapunov analysis. Simulation results are given to show the effectiveness of the proposed DSC design using NDO and RBFNN.

In this paper, the direct adaptive neural control is proposed for a class of uncertain nonaffine nonlinear systems with unknown nonsymmetric input saturation. Based on the implicit function theorem and mean value theorem, both state feedback and output feedback direct adaptive controls are developed using neural networks (NNs) and a disturbance observer. A compounded disturbance is defined to take into account of the effect of the unknown external disturbance, the unknown nonsymmetric input saturation, and the approximation error of NN. Then, a disturbance observer is developed to estimate the unknown compounded disturbance, and it is established that the estimate error converges to a compact set if appropriate observer design parameters are chosen. Both state feedback and output feedback direct adaptive controls can guarantee semiglobal uniform boundedness of the closed-loop system signals as rigorously proved by Lyapunov analysis. Numerical simulation results are presented to illustrate the effectiveness of the proposed direct adaptive neural control techniques.

In this paper, robust adaptive neural network (NN) control is investigated for a general class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems with unknown control coefficient matrices and input nonlinearities. For nonsymmetric input nonlinearities of saturation and deadzone, variable structure control (VSC) in combination with backstepping and Lyapunov synthesis is proposed for adaptive NN control design with guaranteed stability. In the proposed adaptive NN control, the usual assumption on nonsingularity of NN approximation for unknown control coefficient matrices and boundary assumption between NN approximation error and control input have been eliminated. Command filters are presented to implement physical constraints on the virtual control laws, then the tedious analytic computations of time derivatives of virtual control laws are canceled. It is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed-loop system. Finally, simulation results are presented to illustrate the effectiveness of the proposed adaptive NN control.

A decentralized feedback control scheme is proposed to synchronize linearly coupled identical neural networks with time-varying delay and parameter uncertainties. Sufficient condition for synchronization is developed by carefully investigating the uncertain nonlinear synchronization error dynamics in this article. A procedure for designing a decentralized synchronization controller is proposed using linear matrix inequality (LMI) technique. The designed controller can drive the synchronization error to zero and overcome disruption caused by system uncertainty and external disturbance.