The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments benefiting from real-time feedback mechanisms. Inspired by the feedback philosophy, we present feedback neural networks, showing that a feedback loop can flexibly correct the learned latent dynamics of neural ordinary differential equations (neural ODEs), leading to a prominent generalization improvement. The feedback neural network is a novel two-DOF neural network, which possesses robust performance in unseen scenarios with no loss of accuracy performance on previous tasks. A linear feedback form is presented to correct the learned latent dynamics firstly, with a convergence guarantee. Then, domain randomization is utilized to learn a nonlinear neural feedback form. Finally, extensive tests including trajectory prediction of a real irregular object and model predictive control of a quadrotor with various uncertainties, are implemented, indicating significant improvements over state-of-the-art model-based and learning-based methods.

Due to its small size and light weight, the tiny unmanned aerial vehicle (UAV) is especially suitable for tasks that involve confined indoor space exploration. However, autonomous localization of the tiny UAV has become a great challenge in the global navigation satellite system (GNSS)-denied, unstructured, and resource-constrained environments. In this paper, an onboard ultra-wideband (UWB)-based relative localization scheme of the tiny UAV is presented, where an anchor-UAV equipped with the UWB anchors is employed to provide position reference for the tiny UAV. As the key in the proposed scheme, the state estimation algorithm should be able to overcome the joint effect of the inertial sensor bias, the UWB measurement noises, and the limited computational resources. To this end, a composite disturbance filtering (CDF) method is proposed which consists of the disturbance observer for real-time bias compensation, an improved particle filter to deal with the non-Gaussian noises, and a particle size adaptation procedure to release the computation burden. The proposed CDF method represents a refined treatment of the multi-source heterogeneous uncertainties in the relative localization system and strikes a balance between localization accuracy and computational efficiency. The effectiveness of the proposed localization method is validated via both simulation tests and flight experiments.Note to Practitioners—The tiny UAVs are capable of dexterous flight in confined indoor spaces, which makes them especially suitable for the indoor operation tasks such as environment exploration, disaster relief, gas seeking, and meteorological measurement. In these tasks, accurate localization of the tiny UAV is of vital importance. To achieve autonomous localization of the tiny UAV in the GNSS-denied, infrastructure-free, and unstructured indoor environment, an onboard inertial measurement unit (IMU)/UWB fusion-based relative localization scheme is presented. In the presented scheme, a large UAV equipped with UWB anchors is employed to provide position reference for the tiny UAV. To address the multi-source heterogeneous disturbances (the dynamic IMU biases and the non-Gaussian UWB noises) in the localization model and the limited computational resource onboard the tiny UAV, a CDF method with an adaptive sample size is proposed. As demonstrated by the simulation and experiments, the positioning accuracy and computation efficiency of the tiny UAV have been effectively enhanced with the proposed scheme.

This article focuses on the oscillation suppression-enhanced cooperative control design for the aerial co-transportation system consisting of two quadrotors and a tethered pipe. The system dynamics are analyzed in depth, which yields a decoupled model under multiple disturbances by utilizing the variation linearization technique and coordinate transformations. Based on this model, a refined cooperative disturbance estimation strategy is developed to capture the angle dynamics of the cables without direct measurements of swing angles. Then the estimation results are used for designing a cooperative control law to guarantee the performance in rapid suppression of the payload oscillation and in accurate positioning of the quadrotors under system uncertainties. The stability and convergence of the overall system is established using Lyapunov theory. Finally, experiments validate and demonstrate the superiority of the proposed method over the existing ones. Note to Practitioners—This paper is motivated by the requirement of safe control schemes for aerial co-transportation systems. The unexpected oscillation of the payload may result in serious accidents, and therefore efficiently suppressing the payload swing is the main concern of the research. Nevertheless, the cascaded underactuation property and the complicated couplings among the drones make it difficult to directly control the payload. Up till now, at the cost of additional weight and more complicated structure, most existing methods relying on extra sensors to detect the states of the payload for feedback control. Accounting for the foregoing problems, this article presents a novel sensorless control scheme for suppressing the payload oscillation. The cable angles are estimated using only the states of the drones. Moreover, cooperative control laws are designed based on the estimated results so that both antiswing and positioning performance are guaranteed. All these aspects are verified by rigorous theoretical analysis and hardware experiments.

This article addresses issues of covert attacks detection and resilient control of quadcopters. In the presence of generalized covert attacks characterized by strong stealth, passive detection techniques prove to be insufficient. Active detection methods are common solutions to this problem, but the balance between the detection capability and the stability of quadcopters still remains as a challenge. Different from the existing active attack detection methods, a coding and channel switching approach and its matched resilient controller for quadcopters are proposed. First, the design and detectability analysis of the coding-based attack detection method are given. Once covert attacks revealed, a secure channel is activated to replace the attacked channel. Second, to enhance quadcopter resilience against covert attacks, a resilient control framework is proposed. It incorporates attack effect estimation and compensation via a fixed-time observer. This framework maintains the stability of the quadcopter's control system under covert attacks. Finally, the numerical simulation and real-world experiments are conducted to evaluate the effectiveness and feasibility of the proposed scheme.

The avoidance of dynamic obstacles is a challenging issue for uncrewed aerial vehicle (UAV) due to its limited perception range.This article presents a framework including cooperative warning and risk-averse safety control for multiple UAVs. When external obstacles are discovered, the evaluation of conditional value-at-risk for the obstacles is performed by the discoverers. Whenever the risk value violates the designed safety threshold, the warning information will be transmitted to the threatened neighbors immediately. Moreover, by incorporating the event-triggered mechanism, the risk-averse safety control scheme is constructed. Consequently, multiple UAVs are able to evade dynamic obstacles from various directions with enhanced safety and reduced conservatism. The effectiveness and superiority of the proposed scheme are substantiated by comparative simulations and real-world flight experiments.

The polarization-based attitude and heading reference system (PAHRS) consisting of inertial navigation system (INS) and polarization sensor (PS) offers an effective solution for attitude and heading determination in the case of global navigation satellite system (GNSS) signal degradation. Its performance depends largely on the state estimation accuracy. In the existing work, the Kalman filtering (KF), as a low complexity scheme, is employed to achieve the state estimation of PAHRS. However, in practice, the performance of PAHRS could be affected by weather conditions and the maneuvering state of the vehicle. The accurate noise statistics of INS and PS is often encountered, which leads to a degradation of PAHRS. To improve the adaptability and accuracy of the system, in this article, we conduct a KF flow-based deep neural networks (KFDNNs), a real-time state estimator that learns from PS and INS data to carry out Kalman filter. In the constructed KFDNNs, deep neural networks (DNNs) are inserted into the flow of the KF to learn the optimal Kalman gain from PAHRS data, which we can retain data efficiency and interpretability of the classic algorithm while circumvents the dependency of the KF on knowledge of the noise statistics. Moreover, a two-stage training strategy consisting of warm-up training stage and task-oriented training stage is presented for the KFDNNs, which mitigate the gradient explosion caused by the unstable random initialization of KFDNNs while improve the flexibility of sequence length selection. Finally, the simulation and vehicle test are carried to verify the performance of PAHRS. The experimental results confirm the KFDNNs outperforms KF-based INS/PS method especially in complex weather and maneuvering scenarios.

This article proposes a novel hierarchical reinforcement learning (HRL) algorithm for unmanned aerial vehicle pursuit-evasion (UAV-PE) game systems with an alternative delay update (ADU) method. In the proposed algorithm, the approximate solutions of the UAV-PE game problem are derived from a hierarchical learning process, which relies on a zero-sum game process of kinematics and a corresponding optimal process of dynamics. In this case, deep neural networks (NNs) are used to approximate the policy and value functions of UAV-PE game systems in kinematics and dynamics level. Furthermore, the ADU method is adopted to improve the training efficiency of deep NN by fixing one player of the UAV-PE game systems to form a stable environment. The goal of this article is to develop an HRL algorithm with an ADU method for obtaining approximate Nash equilibrium (NE) solutions of the considered UAV-PE game systems which are subjected to the coupling of kinematics and dynamics. Subsequently, sufficient conditions are provided for analyzing the convergence and optimality of the proposed HRL algorithm. Moreover, the inequalities of overload are obtained to guarantee that the state of dynamics tracks with the control input of kinematics in UAV-PE game systems. Finally, simulation examples are provided to demonstrate the feasibility and usefulness of the proposed HRL algorithm and ADU method.

Precise and reliable autonomous navigation in a GPS-denied environment is critical to unmanned systems. The idea of combining SINS, the polarized navigation system (PNS), and the odometer (OD) inspired by desert ants has been proven to be effective for autonomous navigation. However, there are two major challenges for polarization navigation nowadays: inaccurate modeling and obtaining reliable heading information when some sensor channels are blocked. Aiming at these two problems, a tightly-coupled solution for SINS/PNS is proposed in this paper. To obtain a refined integrated navigation system model, the installation errors between the inertial units and PNS, and polarization angle calculation errors are analyzed and modeled for SINS/PNS. Then, to quickly gain the accurate state estimation, an improved iterative unscented filtering method is devised. In particular, the sigma-point updating step with the conditional distribution of high-dimensional Gaussian distribution random variables is developed, which employs partial states to sample in each iteration to reduce the calculation burden. Finally, a detection and elimination mechanism for the abnormal light channels is provided to enhance the reliability of the integration in the presence of a light blockage. The optical channels for navigation are chosen using this mechanism depending on the difference between the predicted and measured incident light intensities. The results in both simulations and outdoor experiments show that the proposed method provides a higher heading estimation accuracy than the traditional SINS/PNS navigation method.Note to Practitioners—This article is motivated by the inaccurate modeling and obtaining reliable heading in the presence of light occlusion for the polarization navigation. Various integrated navigation algorithms based on polarized skylight have been widely developed. However, the complex environment and inaccurate modeling limit the application of the polarization navigation. This article gives a novel accurate modeling method and reliable navigation algorithm. Tightly-coupled model with installation errors and the polarization angle error aims to improve the accuracy of the polarization navigation model. The improved iterative unscented Kalman filter is utilized to quickly obtain accurate state estimation. And the light detection and elimination mechanism is used to select normal light channels to navigate in the presence of light blockage. This navigation method can also extend the application of the polarization navigation.

This article proposes a set of novel attitude estimation algorithms for a bioinspired integrated navigation system including an insect-inspired polarization sensor, an inertial measurement unit, and a global navigation satellite system (GNSS). In particular, the biomimetic polarization sensor introduced as the new type of navigation component has an orientation performance comparable to that of a magnetometer. Moreover, this small and light sensor is immune to magnetic interference, making it highly suitable for orientation in unmanned aerial vehicles (UAVs). However, inaccurate modeling, unknown parameters, and unknown statistical characteristics of noise are common problems with the orientation solution of the sensor. Therefore, we theoretically compare various adaptive and robust filtering algorithms, select the best error prediction covariance and noise covariance correction schemes, introduce Kalman smoothers and approximate inference methods, and then propose two outlier-robust algorithms. This approach can suppress multiple outliers from the two steps of prediction and estimation. The polarization sensor and GNSS update the state and error covariance according to the asynchronous fusion mode. The prediction error covariance, the polarization measurement noise covariance, and the GNSS measurement noise covariance are approximately estimated by the variational inference method. To validate the performance of our algorithms, we collected a set of multi-rotor UAV flight data for testing. Experimental results show that the proposed algorithms have better robustness performance than existing state-of-the-art algorithms.Note to Practitioners—This article was motivated by Bioinspired autonomous navigation systems suffering from inaccurate modeling, unknown parameters, and noise with unknown statistical properties. Subject to the large uncertainty in the flight of the UAV, the traditional filtering algorithm has slow convergence or even divergence when processing such actual data. In this article, we first establish a unified state estimation framework. Then, we mathematically describe correction strategies for prediction error covariance and measurement noise covariance. Considering the need for real-time estimation, we adopted the extended Kalman filter. However, this introduces a truncation error, then, Rauch-Tung-Striebel smoothing is introduced to improve the linearized reference point. However, the role of robust filtering is limited, and the non-Gaussian state still exists. Finally, the approximate inference method is used to estimate the state. The proposed method integrates adaptability, robustness, reasoning, and smoothing, and is suitable for dealing with multi-source interference problems in multi-source information fusion.

This paper is concerned with the contact force estimation problem of robot manipulators based on imperfect dynamic models of the manipulator and the contact force. To handle the imperfect dynamic information of the manipulator, a hybrid model, consisting of the nominal model and the residual dynamics, is established for the manipulator, and the Gaussian process regression (GPR) technique is employed to learn the mean and covariance of the residual dynamics. On this basis, a virtual measurement equation is established for contact force estimation and a Gaussian process adaptive disturbance Kalman filter (GPADKF) is developed where the variational Bayes technique is employed to achieve online identification of the noise statistics in the force dynamics. The GPADKF is capable of decoupling the contact force from residual dynamics and system noises, thereby reducing the dependence on accurate dynamic models of the manipulator and the contact force. Simulation and experimental results demonstrate that the proposed scheme outperforms the state-of-art methods.Note to Practitioners—Contact force estimation for robot manipulators can be achieved by fusing the dynamic models of the manipulator and the contact force. When both models are imprecise, the traditional inverse dynamics-based and disturbance Kalman filter-based approaches can no longer provide accurate force estimates. To handle this challenge, a computationally efficient hybrid dynamic model is established for the manipulator, which consists of the nominal model and a residual dynamics compensation term learned from offline data via the GPR. On this basis, an adaptive disturbance Kalman filter is constructed by using the variational Bayes technique to deal with the inaccurate noise covariance matrix in the force dynamic model. Compared with the existing approaches, the force estimate obtained via the proposed scheme is more accurate and reliable, as refined noise covariance matrices (provided by both the GPR and the variational Bayes procedure) have been adopted in the Kalman gain calculation. The proposed GPADKF method is the extension of the composite disturbance filtering (CDF) framework. With the proposed scheme, the dependency on the perfect dynamic models in contact force estimation can be significantly reduced, and this makes our approach especially suitable for contact force estimation problems under unfamiliar and complicated environments.

This article presents a bio-inspired safety control scheme for unmanned aerial vehicles (UAVs) in confined environments with disturbance. Although there has been some existing research on the effect of disturbance for a single UAV, multi-UAV formation under external wind disturbances remains challenging, especially in a tight and confined environment. Inspired by nature, this study concentrates on an anti-disturbance mechanism for safe multi-UAV formation in a tight environment. The presented safety control system combines disturbance observer-based control (DOBC), bionic formation switching (BFS) strategy, and safety evaluation. Two safety issues are considered in this article. For a single UAV, the estimated disturbance is compensated in the inner-loop controller. While for multi-UAV formation, the BFS strategy attenuates the effect of external wind disturbance leveraging the formation configuration. The so-called group perturbation immune factor (GPIF) is designed to analyze and evaluate the safety of the overall formation. The experimental results validate the comprehensiveness and anti-disturbance capability of the system.

High-precision and safety control in face of disturbances and uncertainties is a challenging issue of both theoretical and practical importance. In this article, new adaptive anti-disturbance control schemes are proposed for a class of uncertain nonlinear systems with composite disturbances, including additive disturbances, multiplicative actuator faults, and implicit disturbances deeply coupled with system states. Both the cases with known and unknown control/fault directions are investigated. By properly fusing the techniques of disturbance observers and adaptive compensation, it is shown that all closed-loop signals are globally uniformly bounded and the tracking error converges to zero asymptotically, no matter the control/fault directions are known or not. In the case of known directions, the proposed control scheme, for the first time, guarantees asymptotic tracking andL$_{\infty}$tracking performance simultaneously in face of disturbances and actuator faults. Moreover, novel Nussbaum functions and a contradiction argument are introduced, which allow the system to have multiple unknown nonidentical control directions and unknown time-varying fault direction. Simulation results illustrate the effectiveness of the proposed control schemes.

Images captured in underwater environments often suffer from color distortion, low contrast, and reduced visual quality. Most existing methods solve underwater image enhancement (UIE) by applying supervised training on synthetic images or pseudo references. However, the synthetic paired data fail to accurately replicate real-world data due to the inherent differences, and the quantity and quality of pseudo references are limited, which seriously reduces the generalization ability and performance of the model when testing on real underwater images. In contrast, unsupervised-based method is not constrained by paired data, which is more robust and potentially more promising for practical applications. Nevertheless, existing unsupervised-based methods cannot effectively constrain the network to train a model that can adapt to various degradation. Inspired by the fact that people often resolve problems from opposing but complementary perspectives, we maintain that there is implicit cooperation between the removal and generation of water layers, as they can constrain and promote each other at the same time. Based on the above analysis, a new unsupervised-based UIE framework that jointly learns water layer generation and removal based on disentangled representations is proposed. Specifically, we propose a bidirectional disentangling network in which each unidirectional network contains a loop consisting of water layer removal and generation, and restricts the image to remain consistent after a loop. Meanwhile, a novel double-order contrastive loss is proposed to improve the ability of disentanglement by utilizing the joint implicit constraint of first-order features and second-order features. Extensive experimental results demonstrate that the model outperforms the state-of-the-art methods in both qualitative and quantitative evaluation with a relatively high processing speed. The experimental results of the ablation study demonstrate the usefulness of the various components.

Underwater autonomous navigation has long been a challenging problem due to the scarcity of information sources. The polarization navigation offers a feasible solution to this problem. The existing polarization navigation schemes, however, require that the horizontal attitude is known, which can only be used for 2-D orientation. To address the limitation, a 3-D attitude determination strategy is developed in this article by exploiting the underwater downwelling radiance fields (light intensity and polarization). In particular, the horizontal attitude information contained in the Snell's window, a unique underwater optical phenomenon induced by refraction, is extracted via an improved edge recognition method. On this basis, underwater polarization is exploited to calculate solar position for orientation. By this means, the 3-D attitude is acquired independently using underwater downwelling radiance fields. The effectiveness of the proposed strategy is validated via experiments in both the water tank and open sea environments.

The safety and high-precision attitude control of launch vehicles are threatened by degradation fault and multiple disturbances (such as model uncertainty, uncertain inertia, and external disturbance) during the reentry stage. To address these challenges, an adaptive sliding mode observer (ASMO)-based composite control scheme is proposed in this article for launch vehicles to achieve simultaneous compensation and suppression of the degradation fault and multiple disturbances. Since the mismatched model uncertainty that coupled with the system state exhibits strong uncertainty, an ASMO is designed to estimate it by adaptively learning the upper bound of the derivative of the mismatched model uncertainty. In order to attenuate the effect of the degradation fault, uncertain inertia, and external disturbance, three adaptive laws are accordingly designed to identify them online. By combining the ASMO and the designed adaptive laws, a composite controller is constructed, and the degradation fault and multiple disturbances are simultaneously compensated and suppressed. The coordinated optimization performance and refinement of antidisturbance control and fault-tolerant control are effectively enhanced. Moreover, by introducing a prescribed performance function, the attitude tracking error response is constrained within a predefined range. Simulation and experiments validate the effectiveness of the proposed scheme.

Polarization navigation is an emerging autonomous navigation technology suitable for unmanned underwater vehicles (UUVs). Nonetheless, light refraction poses challenges for underwater polarization navigation as it alters the direction and amplitude of the polarization electric vector (E-vector). In this article, we propose a novel underwater heading determination method with inertial navigation system/polarization sensor integration in consideration of light refraction. In view of light deflection and energy attenuation under refraction, the direction correction matrix and amplitude compensation factor are established for the E-vector. On this basis, the refracted E-vector is introduced into the heading measurement model, which can reduce modeling errors induced by refraction, thereby producing a better prediction of heading information. In addition, a dual-filter algorithm is constructed to handle fusion models with different characteristics, improving the reliability and efficiency of heading estimation. Numerical simulation is conducted to confirm the feasibility of the proposed method, while ocean navigation experiments on UUV are carried out to evaluate its accuracy.

Accurate and reliable polarization information is extremely important as heading cues in underwater low-light environments, especially in the presence of hybrid refraction/scattering dynamic effects. In this article, a bio-inspired antagonistic differential polarization algorithm (ADPA) is proposed for polarization perception, enhancing the resolution and contrast of polarization signals in underwater low-light environments. Starting from the analysis of disturbances in underwater polarization measurements, the wavelet denoising algorithm is introduced to extract the effective light intensity. Subsequently, the antagonistic differential measurement equation is derived by mimicking biological antagonistic differential mechanisms, improving the polarization contrast from orthogonal photoreceptors. The proposed ADPA exhibits the capability to effectively handle consistent interference while dampening time-varying nonlinear disturbances. On this basis, a bio-inspired navigation strategy using ADPA is presented for heading determination. The mapping relationship between underwater polarization information and spatial motion information is revealed. Underwater navigation experiments in real oceans are carried out to manifest the effectiveness of the investigated ADPA-based method. In comparison with existing polarization methods, the proposed method can significantly improve the reliability, adaptability, and robustness of underwater polarization-based navigation.

Solar-tracking is one of the key issues in underwater polarization navigation. Most existing studies are based on the Angle of Underwater Polarization (AoUP). As water depth increases, however, the AoUP is disturbed by multiple scattering, while the Degree of Underwater Polarization (DoUP) maintains a stable relative relationship. To address the less robustness of polarization navigation, a solar-tracking and integrated orientation method based on DoUP is proposed. In consideration of the refraction, the relationship between the solar position and DoUP is established based on the maximum Degree of Polarization. Moreover, an integrated navigation model is developed aided by the solar position. Results from the static experiment in water tank and dynamic sea trials demonstrate that the proposed method exhibits improved accuracy and robustness compared to the AoUP method. This article presents a potential approach to improve the adaptability of underwater autonomous orientation.

In nature, when encountering unexpected uncertainty, animals tend to react quickly to ensure safety as the top priority, and gradually adapt to it based on recent valuable experience. We present a framework, namely EVOLutionarymodel-baseduncertainty obserVER (EVOLVER), to mimic the bio-behavior for robotics to achieve rapid transient reaction ability and high-precision steady-state performance simultaneously. In particular, the Koopman operator is leveraged to explore the latent structure of internal and external disturbances, which is subsequently utilized in anevolutionarymodel-based disturbance observer to estimate the eventual disturbance. The resulting observer can guarantee a provable convergence in optimal conditions. Several practical considerations, including construction of a training dataset, data noise handling, and lifting functions selection, are elaborated in pursuit of the theoretical optimality in real applications. The lightweight feature of our framework enables online computation, even on a microprocessor (STM32F7 with 100 Hz control frequency). The framework is thoroughly evaluated by one simulation and three experiments. The experimental scenarios include: 1) Trajectory prediction of an irregular free-flying object subject to aerodynamic drag, 2) indoor and outdoor agile flights of a quadrotor subject to wind gust, and 3) high-precision end-effector control of a manipulator subject to base moving disturbance. Comparison results show that the performance of our proposed EVOLVER is superior to several state-of-the-art model-based and learning-based schemes.

Achieving accurate control performance of the end-effector is critical for practical applications of aerial manipulator. However, due to the presence of floating-base disturbance from the unmanned aerial vehicle (UAV) platform and the kinematic error amplification effect from multilink structure of the manipulator, it is extremely challenging to ensure the high-precision performance of aerial manipulator. Building upon the philosophy of disturbance rejection, we propose a predictive optimization scheme that allows aerial manipulator to successfully execute millimeter-level flying pick and peg-in-hole task. First, the error amplification effect of the floating base is quantitatively analyzed by virtue of the aerial manipulator kinematics. Intuitively, it is found that if the further motion of the UAV platform is well predicted, the manipulator can directly counteract the floating disturbance by following a modified reference trajectory. Hence, a learning-based prediction approach is leveraged to rapidly forecast the UAV platform motion online. Subsequently, an optimization controller is formulated to follow the reference trajectory by incorporating multiple practical constraints of aerial manipulator. Flight tests demonstrate that this study goes a step further to achieve higher accuracy of the end-effector than the existing results (centimeter-level).

This article aims to investigate the security consensus and composite anti-disturbance problems for a class of nonlinear multi-agent systems subjected to stochastic false data injection attacks (FDIAs) and multiple disturbances under a directed communication topology. To attenuate and reject of the negative effects of two types of disturbances, a disturbance observer (DO) is designed to counteract the disturbance produced by exogenous system, and the$\mathcal {H}_\infty $control method is adopted to attenuate the bounded errors and variables caused by the other type of disturbances and FDIAs simultaneously. To ensure the consensus performance of MASs, an observer-based control strategy is designed, and a novel adaptive compensation technique is proposed to not only evaluate the upper bounds of the unknown but bounded disturbances but also improve the accuracy of the state observer. Furthermore, a novel event-triggered mechanism (ETM) without requiring continuous communication among neighboring agents is developed to reduce the controller update frequency and the communication burden. Meanwhile, Zeno behavior is excluded. Finally, numerical simulations are provided to verify the availability of the designed method. Note to Practitioners—In multi-agent systems, network security is very important. For example, in smart power grid systems, it is necessary to use the method of state estimation to observe the system to guarantee its safe operation. However, the measured value of the instrument may be affected by FDIAs in the transmission process, thus changing the result of state estimation and causing misjudgment of the system. Similarly, in multi-vehicle systems, FDIAs may destroy the location information of vehicles and cause serious accidents. In addition, the system will be subjected to different types of disturbances in practice, thus reducing the performance of the system. In view of the threat of FDIAs and disturbances to the MAS, a composite anti-disturbance method and an observer-based control strategy are proposed. Meanwhile, to avoid the limitation of communication bandwidth in reality, a novel ETM is developed to save network resources.

This article considers the safety control problem of a quadrotor unmanned aerial vehicle (UAV) subject to actuator faults and external disturbances, based on the quantization of system capability and safety margin. First, a trajectory function is constructed online with backpropagation of system dynamics. Therefore, a degraded trajectory is gracefully regenerated, via the tradeoff between the remaining system capability and the expected derivatives (velocity, jerk, and snap) of the trajectory. Second, a control-oriented model is established into a form of strict feedback, integrating actuator malfunctions and disturbances. Therefore, a retrofit dynamic surface control (DSC) scheme based on the control-oriented model is developed to improve the tracking performance. When comparing to the existing control methods, the compensation ability is analyzed to determine whether the faults and disturbances can be handled or not. Finally, simulation and experimental studies are conducted to highlight the efficiency of the proposed safety control scheme.

Malware, exposed on the ground control station, can tamper with the unmanned aerial vehicles (UAVs) interaction information. It makes UAVs vulnerable to the desired trajectory attacks, which deteriorates the flight safety if no timely action is taken. Therefore, this article focus on fast reactive mechanism for desired trajectory attacks on UAVs. A fixed-time detection scheme is proposed based on fixed-time unknown inputs observer and trajectory tracking errors. Subsequently, a fixed-time sliding mode attack observer is developed to compensate the effect caused by attacks. Meanwhile, the estimation errors of attacks can be stabilized within fixed time. Finally, experiment tests are presented to demonstrate the effectiveness of the proposed methods.

The polarization-based attitude and heading reference system (PAHRS) provides an effective solution for attitude and heading information acquisition. Its practical performance, however, will be degraded due to partial loss and/or occlusion of the optical signal. To improve the adaptivity of PAHRS, in this article, we establish a polarization-based tightly coupled model (PTCM) and propose a reliable fusion strategy for information extraction from the polarization sensor (PS) and inertial navigation system (INS). As compared to the existing PS/INS fusion model, the proposed PTCM directly adopt PS raw observations (polarized skylight intensity) to compensate for the accumulation errors of INS, thereby removing the constraints on the least number of PS observation channels and avoiding nonlinear transformation of PS noises. Moreover, the reliable fusion strategy consists of a reliable observation channel selection step followed by a nonlinear filtering step, which can reduce the effect of unreliable polarized skylight intensity measurement. Finally, the simulation, static and semi-physical vehicle-mounted tests confirm the effectiveness of the proposed PTCM and fusion strategy.

The proportional-integral (PI) controller has proven to be a remarkably effective control strategy in the servo field. However, it is difficult for PI to handle the problem of multiple disturbances degrading the velocity-tracking capability of the gimbal system in the control moment gyro (CMG). In this article, we propose a solution to this problem while preserving the advantages of PI from an engineering standpoint. Starting from the refined disturbance analysis based on a 5 Nms CMG gimbal system experimental tests, multiple disturbances of the gimbal system can be classified according to frequency distribution in terms of 0$\sim $5 and 128 Hz. Subsequently, under the composite hierarchical anti-disturbance control frame, a peak filter and a disturbance observer addition improve the anti-disturbance capability of the PI-based gimbal system at the frequencies of 0$\sim $5 and 128 Hz. Notably, the proposed method has a relatively low order, which is appropriate for the processing power limit. Finally, the experimental results reveal that compared to three effective control schemes (PI, extended state observer-based composite controller, and PI-resonant controller), the proposed method can strikingly enhance the anti-disturbance ability and velocity-tracking performance of the gimbal system.

In this article, the event-triggered$\epsilon $-Nash equilibrium ($\epsilon $-NE) seeking problem is investigated for a class of$n$-integrator multiagent systems with the consideration of multisource disturbances and measurement outliers. In the game setup, the partial information case is considered where each player/agent is only capable of obtaining information from its neighbors. For the purpose of saving network resources, the event-triggered mechanism is utilized which could schedule the signal transmission. In order to suppress the measurement outliers and estimate the disturbances, a stubborn extended-state observer (ESO) is developed by utilizing a saturation-type gain function. The estimates provided by the stubborn ESO act as a feedforward term to offset the disturbances. Then, by integrating the feedforward term with the feedback term, a composite event-triggered NE seeking strategy is developed such that the states of the noncooperative agents could converge to the${\epsilon }$-NE solution. In the end, a numerical example is given to verify the validity of our methodology.

This article is concerned with a quasiperiodic disturbance estimation problem for dynamic control systems without prior knowledge on frequency. As a major challenge of our work, the quasiperiodic disturbance to be treated is always submerged by untargeted waves, leading to complicated coupling between disturbance separation and frequency identification. Existing approaches on quasiperiodic disturbance rejection have circumvented, rather than overcome, this challenge by assuming either a known frequency or a measurable disturbance signal. In this work, an expectation-maximization (EM) framework is proposed where disturbance signal separation and frequency identification are carried out in an iterative manner. In the E-step, the expected log-likelihood function is evaluated via reconstruction of the quasiperiodic signal based on the latest frequency estimate; and in the M-step, the frequency estimate is updated by maximizing the log-likelihood function obtained in the E-step. To facilitate recursive frequency estimation, an online EM algorithm is also developed based on the forward-only smoothing techniques. Furthermore, we show that the proposed method can be easily extended to deal with nonlinear system models and time-varying frequencies.

In this article, a novel control algorithm is developed for a class of nonlinear stochastic systems subject to multiple disturbances, including exogenous dynamic disturbance and general non-Gaussian noise. An observer is designed to estimate the exogenous disturbance, and then the disturbance compensation is incorporated into a feedback control strategy for the non-Gaussian system. Considering the ability of entropy in randomness quantification, a performance index is established based on the generalized entropy optimization principle. Furthermore, it is adjusted to be available for the controller solution, which also solves the coupling between two kinds of disturbances. On this basis, the optimal controller is provided in a recursive way, with which the closed-loop stability and good antidisturbance ability can be guaranteed simultaneously. Compared with the existing studies on the non-Gaussian stochastic systems, the proposed control algorithm has merits in multiple disturbances decoupling and enhanced antidisturbance performance. Finally, a simulation example is given to demonstrate the effectiveness of theoretical results.

In this article, under directed graphs, an adaptive consensus tracking control scheme is proposed for a class of nonlinear multiagent systems with completely unknown control coefficients. Unlike the existing results, here, each agent is allowed to have multiple unknown nonidentical control directions, and continuous communication between neighboring agents is not needed. For each agent, we design a group of novel Nussbaum functions and construct a monotonously increasing sequence in which the effects of our Nussbaum functions reinforce rather than counteract each other. With these efforts, the obstacle caused by the unknown control directions is successfully circumvented. Moreover, an event-triggering mechanism is introduced to determine the time instants for communication, which considerably reduces the communication burden. It is shown that all closed-loop signals are globally uniformly bounded and the tracking errors can converge to an arbitrarily small residual set. Simulation results illustrate the effectiveness of the proposed scheme.

In this article, a novel composite hierarchical antidisturbance control (CHADC) algorithm aided by the information-theoretic learning (ITL) technique is developed for non-Gaussian stochastic systems subject to dynamic disturbances. The whole control process consists of some time-domain intervals called batches. Within each batch, a CHADC scheme is applied to the system, where a disturbance observer (DO) is employed to estimate the dynamic disturbance and a composite control strategy integrating feedforward compensation and feedback control is adopted. The information-theoretic measure (entropy or information potential) is employed to quantify the randomness of the controlled system, based on which the gain matrices of DO and feedback controller are updated between two adjacent batches. In this way, the mean-square stability is guaranteed within each batch, and the system performance is improved along with the progress of batches. The proposed algorithm has enhanced disturbance rejection ability and good applicability to non-Gaussian noise environment, which contributes to extending CHADC theory to the general stochastic case. Finally, simulation examples are included to verify the effectiveness of theoretical results.

For high-resolution imaging implementations, the spacecraft attitude tracking control accuracy is crucial to determining the imaging quality. This investigation addresses the attitude tracking issue of imaging spacecraft subject to system uncertainties (unavailable inertia tensor, unexpected disturbances, and actuator faults). An adaptive sliding mode control (SMC) strategy is proposed to guarantee practical fixed-time closed-loop stability even in the presence of system uncertainties. Unlike existing methodologies, the sliding mode surface is developed to satisfy a novel sufficient condition of fixed-time stability. The sliding manifold design also circumvents the unwinding phenomenon arising in quaternion representations. Particularly, this controller is developed to generate a smooth control profile by using a new parameter update law. Rigorous Lyapunov analyses are further employed to ensure the fixed-time closed-loop stability irrespective of the system initial states. Finally, numerical examples are performed to demonstrate the feasibility and highlight the inherent features of the derived control law.

Singularly perturbed systems (SPSs) wildly exist in practical engineering practice; however, the disturbance rejection in SPSs is still a problem. As well-known disturbance rejection methods, composite hierarchical anti-disturbance control (CHADC) can effectively compensate and suppress disturbance, which improves the control performances of complex systems. To enhance the capability of anti-disturbance and control precision, this article proposes a novel composite hierarchical anti-disturbance (CHAD) dynamic surface control (DSC) for the fast subsystem considering highly dynamic disturbance, and CHAD proportion-integration (PI) control for the slow subsystem with slow-varying harmonic disturbance. The disturbances are supposed to be generated by an exogenous system based on partially known information with model uncertainty, and the stabilities of both fast and slow closed-loop subsystems are analyzed. Meanwhile, the compensability of disturbances is discussed. Finally, simulations for an F-8 aircraft are given to demonstrate the effectiveness of the proposed methods.

In this article, a composite anti-disturbance control of disturbance rejection and attenuation for a class of nonlinear positive systems is proposed for the first time to achieve both positivity and stability. The disturbance observer-based control (DOBC) method is utilized to compensate for the effects of the modeled disturbances, while the$L_{1}$control strategy is adopted to suppress the effects of the disturbances which are not compensable to satisfy the$L_{1}$index performance. Besides, two analysis schemes of the closed-loop system are presented. The first scheme is commonly used and is easy for analysis, but it has some conservativeness. The second scheme is proposed novelly with less conservativeness, which releases the positivity constraint of disturbance estimation errors. The corresponding theorems and algorithms are proposed for necessary conditions and solutions. Finally, two examples are presented to illustrate the effectiveness of the proposed control schemes.

In this paper, a composite velocity-tracking control scheme is presented for improving dynamics response and control accuracy of the flexible gimbal system in the control moment gyro (CMG). Specifically, an${H}_{\infty } $optimal vibration controller (HOVC) is developed to weigh multi-performance of the gimbal system, such as stability, fast-tracking performance, and attenuation ability of multi-frequency-band disturbances. Meanwhile, a robust disturbance observer (RDO) designed on optimization technology is utilized to improve the nonlinear friction rejection ability of the gimbal system. Moreover, rigorous theoretical analysis based on the small-gain theory is provided to demonstrate the stability of the closed-loop gimbal system under multiple disturbances. Finally, experimental studies are presented to verify the effectiveness of the proposed method.

In this article, the cooperative control problem is investigated for the nonlinear multiagent system (MAS). For the purpose of avoiding possible data collisions, the stochastic communication protocol (SCP) is adopted to schedule the data transmission at each time instant. To deal with the unmatched disturbances, the composite control strategy is put forward which integrates the model predictive control (MPC) and the integral sliding-mode control methods. The sufficient conditions are established to guarantee the cooperative behavior of the MAS subjected to SCP scheduling. Furthermore, the parameters of the MPC scheme are selected such that the recursive feasibility and mean-square practical stability are guaranteed. Finally, the numerical simulation on the satellites is conducted to verify the effectiveness of the proposed methodology.

This paper investigates the dynamic event-triggered fault-tolerant optimal control strategy for a class of output feedback nonlinear discrete-time systems subject to actuator faults and input saturations. To save the communication resources between the sensor and the controller, the so-called dynamic event-triggered mechanism is adopted to schedule the measurement signal. A neural network-based observer is first designed to provide both the system states and fault information. Then, with consideration of the actuator saturation phenomenon, the adaptive dynamic programming (ADP) algorithm is designed based on the estimates provided by the observer. To reduce the computational burden, the optimal control strategy is implemented via the single network adaptive critic architecture. The sufficient conditions are provided to guarantee the boundedness of the overall closed-loop systems. Finally, the numerical simulations on a two-link flexible manipulator system are provided to verify the validity of the proposed control strategy.

Agriculture is facing severe challenges from crop stresses, threatening its sustainable development and food security. This article exploits aerial visual perception for yellow rust disease monitoring, which seamlessly integrates state-of-the-art techniques and algorithms, including unmanned aerial vehicle sensing, multispectral imaging, vegetation segmentation, and deep learning U-Net. A field experiment is designed by infecting winter wheat with yellow rust inoculum, on top of which multispectral aerial images are captured by DJI Matrice 100 equipped with RedEdge camera. After image calibration and stitching, multispectral orthomosaic is labeled for system evaluation by inspecting high-resolution RGB images taken by Parrot Anafi Drone. The merits of the developed framework drawing spectral-spatial information concurrently are demonstrated by showing improved performance over purely spectral-based classifier by the classical random forest algorithm. Moreover, various network input band combinations are tested, including three RGB bands and five selected spectral vegetation indices, by sequential forward selection strategy of wrapper algorithm.

This article proposes a robust particle filtering (PF) approach for a generic class of nonlinear systems with both additive time-varying uncertainty (ATVU) in the state transition equation and inaccurate process noise covariance matrices. To avoid sampling efficiency degradation of the PF approach caused by ATVU, we employ the disturbance observer-based PF (DOBPF) approach where the effect of ATVU is compensated in the particle generation stage. Different from the existing DOBPF method where disturbance estimation is achieved via the Kalman filter, the disturbance observer adopted in this article is in the form of variational Bayesian adaptive Kalman filter (VBAKF) which deals with the inaccurate process noise covariance matrices in both the dynamic models of the state and the ATVU. Compared with conventional PF approaches, the proposed method, named VBAKF-PF, exhibits enhanced robustness against both the ATVU in the state transition equation and the uncertainties of process noise covariance matrices. The simulation results demonstrate the superiority of VBAKF-PF over both the VBAKF and DOBPF methods.

In this article, the optimal operational control problem is considered for complex industrial processes with stochastic disturbances. The performance index is optimized by set points reselection on the operational control layer together with controllers design on the loop control layer. First, the operational indices are obtained through some optimization algorithms. Second, the controllers are designed in the ideal situation to ensure that the controlled variables can track desired set points. To minimize the performance deterioration caused by non-Gaussian stochastic noises or disturbances, a novel Pareto distribution estimation (Pareto DE)-based intelligent set-points reselection approach is proposed to optimize entropy and expectation simultaneously. In the proposed method, entropy is formulated in a recursive way basing on joint PDFs which are obtained through multivariate kernel density and bandwidth selection. Meanwhile, both the controller structure and controller parameters are fixed for whatever disturbances acting on the system. Finally, simulations are given to illustrate the effectiveness of the proposed strategy.

The resilient control refers to the control methodology which provides an interdisciplinary solution to secure the control system. In this paper, the resilient control problem is investigated for a class of wireless networked control systems (WNCS) under a denial-of-service (DoS) attack. In the presence of the DoS attacker, the control command sent by the transmitter may be interfered, which can cause the degradation of the signal-to-interference-plus-noise ratio and further lead to packet dropout phenomenon. Such a packet dropout phenomenon is described by a two-state Markov-chain. A cross-layer view is adopted toward the security issue of the considered WNCS. The Nash power strategies and optimal control strategy in the delta-domain are obtained in the cyber- and physical-layer, respectively. Based on the obtained strategies, the coupled-design problem is solved which aims to drive the underlying control performance to the desired security region by dynamically manipulating the cyber-layer pricing parameters. Finally, a numerical simulation is conducted to verify the validity of the proposed methodology.

In this paper, a novel adaptive neural network (NN) control scheme is proposed for a class of nonlinear systems with unknown control direction. By introducing some differentiable functions and high-order Lyapunov functions, the obstacle caused by unknown control direction in NN control is successfully circumvented and all closed-loop signals are shown to be uniformly bounded up to infinite time. Meanwhile, by introducing an error transformation technique, it is rigorously proved that the argument of the unknown nonlinearities remains within a compact set which can be explicitly calculated a priori, making the NN approximation always valid. Moreover, with the aid of a bound estimation approach, we effectively compress the impact of approximation errors and external disturbances and steer the tracking error into a predefined small residual set. Simulation results illustrate the effectiveness of the proposed scheme.

This paper addresses the fault tolerant control problem for high-speed trains in case of multiple possible failures. A new multiple point-mass model with system faults is built based on a stochastic jump system model approach. A novel active fault tolerant composite hierarchical anti-disturbance control strategy based on the disturbance observer is proposed such that the resulting composite system is stochastically stable with position and velocity tracking performance. According to whether the transition probabilities (TPs) of the failure and fault detection and isolation process can be accessed completely, three different cases (TPs are completely known, partially known, and completely unknown) are analyzed. For each case, based on the Lyapunov functional approach, a composite hierarchical controller is synthesized via a convex optimization problem. Finally, the simulations are given to illustrate the performance of the proposed methodologies.

One of the key problems for space vehicles is how to deal with the contradiction between the control constraints and the disturbances from multiple resources. This paper focuses on the adaptive full state constrained controller design problem for the flexible air-breathing hypersonic vehicles with multisource uncertainties. In simultaneous presence of the aerodynamical uncertainties, the modeling errors, the external disturbances, and the contingent actuator failures, an adaptive fault-tolerant control scheme is put forward in the context of dynamic surface control. Then, the barrier Lyapunov functions are utilized to guarantee that the constraints on the velocity, the flight path angle, the altitude, and the pitch rate are never violated. In virtue of the bound estimation approach, the multisource disturbances are effectively dealt with. Finally, a number of illustrative examples are provided to demonstrate the effectiveness of the proposed methodology.

In this paper, the force reflection control problem is addressed for a bilateral teleoperation system with time-varying delays. A dynamic gain force observer is proposed to obtain the force information for the force reflection control scheme. In virtue of the adaptive law, the internal uncertainties can be estimated based on the prescribed performance functions. The corrective wave variable method is utilized such that the bilateral teleoperation system could achieve a satisfactory control performance. A number of practical experiments are implemented on the bilateral teleoperation system to demonstrate the validation of the proposed methodology.

In this paper, we develop robust adaptive nonsingular terminal sliding mode (NTSM) control methodologies to solve the position and the velocity tracking control problem of the automatic train operation (ATO) system subject to unknown parameters, model uncertainty, and external disturbances. A novel nonlinear nonsingular terminal sliding manifold is proposed by considering that its parameter is unknown, which need to be estimated via a proposed non-negative adaptive law. And a corresponding novel robust adaptive NTSM control strategy, which enables the position tracking error and the velocity tracking error of the ATO system to converge to zero, and eliminates the singularity caused by terminal sliding mode controller, is proposed. Furthermore, unknown parameters of the sliding manifold and the ATO system can be estimated online by the proposed methodology. Simulation results show the effectiveness of the proposed methodologies in this paper.

In this paper, the event-triggered strategy design problem is addressed for a class of discrete-time nonlinear quadratic noncooperative games subject to matched disturbances. The event-triggered scheme is proposed based on the relative error of the input signals with aim to determine whether such signals should be transmitted to the actuator or not. The disturbance-observer-based game strategy is put forward to compensate the matched disturbance and also optimize the individual cost function for each player. The main purpose of the addressed problem is to design the time-varying strategy parameters such that the upper bound of the individual cost function of each player is minimized unilaterally over a finite horizon [0,N]. Sufficient conditions are first established for the existence and uniqueness of the game strategies through backward Riccati-like recursions and then the desired strategy parameters are computed iteratively by utilizing the Moore-Penrose pseudo inverse. Finally, a simulation example is provided to verify the effectiveness of the proposed design method.

The flight of unmanned aerial vehicle (UAV) is vulnerable to various disturbances and faults. In this paper, the small damage of the wing of an unmanned aerial vehicle is taken into consideration. The UAV control framework consists of force loop and torque loop, where the nonlinear disturbance observer (NDO) based dynamic inverse (DI) control and the extended state observer (ESO) based dynamic inverse control are employed respectively to control these two loops. The required force and moment are allocated to the steering gear and thrust vector of the UAV. The designed control law can not only make the UAV fly effectively in the presence of a fault, but also meet the demand of UAV for high maneuver flight. Finally, simulation results verify the effectiveness of the proposed method.

In this brief, the problem of composite anti-disturbance tracking control for a class of strict-feedback systems with unmatched unknown nonlinear functions and external disturbances is investigated. A disturbance-observer-based control (DOBC) in combination with a neural network scheme and back-stepping method is developed to achieve a composite anti-disturbance controller design that provides guaranteed performance. In the proposed method, a conventional disturbance observer and a radial basis function neural network (RBFNN) are combined into a new disturbance observer to estimate the unmatched disturbances. As compared with conventional DOBC methods, the primary merit of the proposed method is that the unknown nonlinear functions are approximated using the RBFNN technique, and not regarded as part of the disturbances or estimated by a conventional disturbance observer. Hence, the proposed method can obtain higher control accuracy than the conventional DOBC methods. This advantage is validated by simulation studies.

A design method of low-dimensional disturbance rejection fuzzy control (DRFC) via multiple observers is proposed for a class of nonlinear parabolic partial differential equation (PDE) systems, where the disturbance is modeled by an exosystem of ordinary differential equations (ODEs) and enters into the PDE system through the control channel. In the proposed scheme, the modal decomposition technique is initially applied to the PDE system to derive a slow subsystem of low-dimensional nonlinear ODEs, which accurately captures the dominant dynamics of the PDE system. The resulting nonlinear slow subsystem is subsequently represented by a Takagi-Sugeno (T-S) fuzzy model. From the T-S fuzzy model and the exosystem, a fuzzy slow mode observer and a fuzzy disturbance observer are constructed to estimate the slow mode and the disturbance, respectively. Furthermore, a nonlinear observation spillover observer is proposed to compensate the effect of observation spillover. Then, based on these observers, a low-dimensional DRFC design is developed in terms of linear matrix inequalities to guarantee the exponential stability of the closed-loop PDE system in the presence of the disturbance. Finally, the effectiveness of the proposed design method is demonstrated on the control of one-dimensional Burgers-KPP-Fisher diffusion-reaction system and the temperature profile of a catalytic rod.

This paper presents a novel non-Gaussian stochastic control framework for the problem of disturbance estimation and rejection by combining fuzzy identification technology with disturbance observer design. First, fuzzy logic models are used to approximate the output probability density functions (PDFs) of non-Gaussian processes such that the task of PDF shape control can be reduced to a fuzzy weight dynamics modeling and control problem. Next, Takagi-Sugeno fuzzy models with multiple disturbances are employed to describe the nonlinear relations between fuzzy weight dynamics and the control input, in which a novel disturbance-observer-based PI-type fuzzy feedback controller is designed to ensure the system stability and convergence of the tracking error to zero. Meanwhile, the disturbance estimation and attenuation performance as well as the state constrained requirement can also be guaranteed. Moreover, the novel composite observer is constructed by augmenting the disturbance estimation into the full-state estimation. The satisfactory tracking performance and full-state observation effect can be achieved by the designed optimization algorithm. Finally, simulations for paper-making process are given to show the efficiency of the proposed approach.

We consider the problem of resilient control of networked control system (NCS) under denial-of-service (DoS) attack via a unified game approach. The DoS attacks lead to extra constraints in the NCS, where the packets may be jammed by a malicious adversary. Considering the attack-induced packet dropout, optimal control strategies with multitasking and central-tasking structures are developed using game theory in the delta domain, respectively. Based on the optimal control structures, we propose optimality criteria and algorithms for both cyber defenders and DoS attackers. Both simulation and experimental results are provided to illustrate the effectiveness of the proposed design procedure.

This paper studies the finite-horizon optimal guaranteed cost control (GCC) problem for a class of time-varying uncertain nonlinear systems. The aim of this problem is to find a robust state feedback controller such that the closed-loop system has not only a bounded response in a finite duration of time for all admissible uncertainties but also a minimal guaranteed cost. A neural network (NN) based approximate optimal GCC design is developed. Initially, by modifying the cost function to account for the nonlinear perturbation of system, the optimal GCC problem is transformed into a finite-horizon optimal control problem of the nominal system. Subsequently, with the help of the modified cost function together with a parametrized bounding function for all admissible uncertainties, the solution to the optimal GCC problem is given in terms of a parametrized Hamilton-Jacobi-Bellman (PHJB) equation. Then, a NN method is developed to solve offline the PHJB equation approximately and thus obtain the nearly optimal GCC policy. Furthermore, the convergence of approximate PHJB equation and the robust admissibility of nearly optimal GCC policy are also analyzed. Finally, by applying the proposed design method to the entry guidance problem of the Mars lander, the achieved simulation results show the effectiveness of the proposed controller.

A novel robust fuzzy disturbance observer-based control (DOBC) design methodology with adaptive bounding is proposed for the longitudinal dynamics of a generic hypersonic vehicle (HV) with modeled and unmodeled disturbances. A Takagi-Sugeno (T-S) fuzzy model is first employed to approximate the nonlinear dynamics of an HV. Subsequently, a new fuzzy disturbance observer is constructed to estimate the modeled disturbance. An augmented system with multiple disturbances is thus obtained by combining the dynamics of HV and the state estimation error of the modeled-disturbance generator. Then, a robust L∞ -gain fuzzy DOBC design with adaptive bounding is developed to guarantee that the closed-loop augmented system is semiglobally input-to-state practically stable (ISpS) with an L∞-gain performance. In the proposed control scheme, the compound disturbance, including the unmodeled disturbance and the approximation error in fuzzy modeling procedure, is divided into the matched part and the mismatched one, which are attenuated by adaptive bounding control and L∞ -gain control, respectively. The outcome of the robust L∞-gain fuzzy DOBC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by means of the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of L∞-gain, meanwhile a control constraint is respected. Finally, simulation results demonstrate the effectiveness of the proposed controller.

In this paper, two types of linearly coupled neural networks with reaction-diffusion terms are proposed. We respectively investigate the adaptive synchronization of these two types of complex network models. With local information of node dynamics, some novel adaptive strategies to tune the coupling strengths among network nodes are designed. By constructing appropriate Lyapunov functionals and using inequality techniques, several sufficient conditions are given for reaching synchronization by using the designed adaptive laws. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

This paper is concerned with the passivity and stability problems of reaction-diffusion neural networks (RDNNs) in which the input and output variables are varied with the time and space variables. By utilizing the Lyapunov functional method combined with the inequality techniques, some sufficient conditions ensuring the passivity and global exponential stability are derived. Furthermore, when the parameter uncertainties appear in RDNNs, several criteria for robust passivity and robust global exponential stability are also presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.

In this paper, an adaptive fuzzy fault accommodation (FA) control design with a guaranteed L(∞)-gain performance is developed for a class of nonlinear time-delay systems with persistent bounded disturbances. Using the Lyapunov technique and the Razumikhin-type lemma, the existence condition of the L(∞) -gain adaptive fuzzy FA controllers is provided in terms of linear matrix inequalities (LMIs). In the proposed FA scheme, a fuzzy logic system is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown fault function; a continuous-state feedback control strategy is adopted for the control design to avoid the undesirable chattering phenomenon. The resulting FA controllers can ensure that every response of the closed-loop system is uniformly ultimately bounded with a guaranteed L(∞)-gain performance in the presence of a fault. Moreover, by the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L(∞)-gain. Finally, the achieved simulation results on the FA control of a continuous stirred tank reactor (CSTR) show the effectiveness of the proposed design procedure.

This paper presents a new type of control framework for dynamical stochastic systems, called statistic tracking control (STC). The system considered is general and non-Gaussian and the tracking objective is the statistical information of a given target probability density function (pdf), rather than a deterministic signal. The control aims at making the statistical information of the output pdfs to follow those of a target pdf. For such a control framework, a variable structure adaptive tracking control strategy is first established using two-step neural network models. Following the B-spline neural network approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. The dynamic neural network (DNN) is employed to identify the unknown nonlinear dynamics between the control input and the weights related to the integrated function. To achieve the required control objective, an adaptive controller based on the proposed DNN is developed so as to track a reference trajectory. Stability analysis for both the identification and tracking errors is developed via the use of Lyapunov stability criterion. Simulations are given to demonstrate the efficiency of the proposed approach.

In this paper, a new optimal fault-detection (FD) problem is addressed for a class of non-Gaussian stochastic systems called stochastic distribution systems (SDSs). For an SDS, the available information for the FD system may be the measured output probability density function. A sufficient existence condition of guaranteed cost filters is presented by constructing an augmented Lyapunov functional approach. In order to improve the detection sensitivity performance, an optimization algorithm, with linear matrix inequality constraints, is presented to minimize the threshold value. An example is given to demonstrate the effectiveness of the proposed approach.

Stochastic distribution control systems aims at the controller design so as to realize a shape control of the distributions of certain random variables in the process. Once the probability density functions (PDFs) of these variables are used to describe their distributions, the control task is to obtain control signals so that the output PFDs of the system are made to follow their target PDFs. In this paper a survey of the recent developments on the research of stochastic distribution control systems will be made.

In this paper, robust minimum entropy tracking control problem is considered for nonlinear stochastic systems. The controlled systems are described by nonlinear non-Gaussian difference equations with the un-modeled uncertainty and modeling error, as well as time delays. Entropy is adopted to characterize the uncertainty of the tracking error. The nonlinear multi-step-ahead predictive cost function is used and the relationship between the probability density functions of the input and the tracking error via the uncertain mapping is established. With these formulations, the cost function can be bounded as a nonlinear functional of the control input and the known bounds of the errors. Explicit design algorithms are presented for the robust suboptimal controller and further for the stabilization controllers. The Renyi's entropy has also been used to simplify the cost function. Simulations are given to demonstrate the effectiveness of the proposed control algorithm.

In this brief paper, an augmented Lyapunov functional, which takes an integral term of state vector into account, is introduced. Owing to the functional, an improved delay-dependent asymptotic stability criterion for delayed neural networks (NNs) is derived in term of linear matrix inequalities (LMIs). It is shown that the obtained criterion can provide less conservative result than some existing ones. When linear fractional uncertainties appear in NNs, a new robust delay-dependent stability condition is also given. Numerical examples are given to demonstrate the applicability of the proposed approach.

This paper presents a pseudo proportional-integral-derivative (PID) tracking control strategy for general non-Gaussian stochastic systems based on a linear B-spline model for the output probability density functions (PDFs). The objective is to control the conditional PDFs of the system output to follow a given target function. Different from existing methods, the control structure (i.e., the PID) is imposed before the output PDF controller design. Following the linear B-spline approximation on the measured output PDFs, the concerned problem is transferred into the tracking of given weights which correspond to the desired PDF. For systems with or without model uncertainties, it is shown that the solvability can be casted into a group of matrix inequalities. Furthermore, an improved controller design procedure based on the convex optimization is proposed which can guarantee the required tracking convergence with an enhanced robustness. Simulations are given to demonstrate the efficiency of the proposed approach and encouraging results have been obtained.