Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 2020"
TL;DR: The proposed hierarchical least squares algorithm is effective and can generate highly accurate parameter estimates compared with the over-parametrization identification method, and can be easily extended to multi-input multi-output systems.
Abstract: This paper considers the parameter estimation problems of two-input single-output Hammerstein finite impulse response systems. A hierarchical least squares algorithm is proposed for improving the computational efficiency through combining the hierarchical identification principle and the identification model decomposition, and a multi-innovation least squares algorithm is proposed for enhancing the parameter estimation accuracy based on the multi-innovation identification theory. The key is to derive two sub-identification models, each of which contains a set of merged parameter vectors. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the over-parametrization identification method, and can be easily extended to multi-input multi-output systems. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.
157 citations
TL;DR: An unsupervised fault diagnosis method for rolling bearings is proposed, which incorporates short-time Fourier transform (STFT) as well as categorical generative adversarial networks (CatGAN) to achieve high diagnosis accuracy and strong robustness against the motor load changes.
Abstract: In recent years, the technique of machine learning or deep learning has been employed in intelligent fault diagnosis methods to achieve much success using massive labeled data. However, it is generally difficult or expensive to label the monitoring data in practical engineering due to its complex working conditions. Therefore, an unsupervised fault diagnosis method is proposed in this paper for rolling bearings, which incorporates short-time Fourier transform (STFT) as well as categorical generative adversarial networks (CatGAN). The proposed method first adopts STFT to transform raw 1-D vibration signals into 2-D time-frequency maps to serve as the input of CatGAN. Then, it obtains a CatGAN model via an adversarial training process to generate fake samples with a similar distribution to the maps extracted by STFT and cluster the input samples into certain categories. Furthermore, the performance of the proposed ST-CatGAN method is verified using a classic rotating machinery dataset, and the experimental results demonstrate its high diagnosis accuracy and strong robustness against the motor load changes.
156 citations
TL;DR: An observer-based adaptive finite-time tracking control strategy is developed by combining dynamic surface control (DSC) technique and backstepping approach and the stability of the considered system is analyzed via semi-global practical finite- time stability theory.
Abstract: This paper concentrates upon the problem of adaptive neural finite-time tracking control for uncertain nonstrict-feedback nonlinear systems with input saturation. The design difficulty of non-smooth input saturation nonlinearity is solved by applying a smooth non-affine function to approximate the saturation signal. Neural networks, as a kind of specialized function estimators, are used to estimate the uncertain function. Meanwhile, a neural network-based observer is constructed to observe the unavailable states, and thus an observer-based adaptive finite-time tracking control strategy is developed by combining dynamic surface control (DSC) technique and backstepping approach. Furthermore, the stability of the considered system is analyzed via semi-global practical finite-time stability theory. Under the proposed control method, all the signals in the closed-loop system are bounded, and the system output can almost surely track the desired trajectory within a specified bounded error in a finite time. In the end, two examples are adopted to illustrate the validity of our results.
142 citations
TL;DR: Main concepts are similar for both types of SMC, discuss new developments needed for HOSM control, compare the potential to suppress chattering, complexity of the both methods are demonstrated.
Abstract: Term “Conventional” sliding mode control (SMC) was introduced in the book Sliding Mode Control and Observation [1] by the authors, working in the area of high order sliding mode (HOSM) control The term is related to all publications on n-dimensional systems with m- dimensional control and with sliding modes and state trajectories in a manifold of order n-m Most of publications on HOSM control studied a new phenomenon for systems with a scalar control (m = 1), specifically, the existence of sliding modes in manifolds of dimension lower than n-1 with a finite reaching time Along with implementation issues, it was natural to discuss to what extent the main principles of the conventional theory were to be revised (definitions, existence conditions, motion equations), what new properties of systems with HOSM can be expected Partially these questions were discussed in [2] along with several international workshops on SMC and CDC in 2018 In this paper we demonstrate that main concepts are similar for both types of SMC, discuss new developments needed for HOSM control, compare the potential to suppress chattering, complexity of the both methods
115 citations
TL;DR: A thorough review on the development of ML-ELMs, including stacked ELM autoencoder, residual ELM, and local receptive field based ELM (ELM-LRF), as well as address their applications, and the connection between random neural networks and conventional deep learning.
Abstract: In the past decade, deep learning techniques have powered many aspects of our daily life, and drawn ever-increasing research interests. However, conventional deep learning approaches, such as deep belief network (DBN), restricted Boltzmann machine (RBM), and convolutional neural network (CNN), suffer from time-consuming training process due to fine-tuning of a large number of parameters and the complicated hierarchical structure. Furthermore, the above complication makes it difficult to theoretically analyze and prove the universal approximation of those conventional deep learning approaches. In order to tackle the issues, multilayer extreme learning machines (ML-ELM) were proposed, which accelerate the development of deep learning. Compared with conventional deep learning, ML-ELMs are non-iterative and fast due to the random feature mapping mechanism. In this paper, we perform a thorough review on the development of ML-ELMs, including stacked ELM autoencoder (ELM-AE), residual ELM, and local receptive field based ELM (ELM-LRF), as well as address their applications. In addition, we also discuss the connection between random neural networks and conventional deep learning.
112 citations
TL;DR: The inverted pendulum model is presented to demonstrate the feasibility and validity of the proposed strategies, and a more general coupling memory fuzzy sampled-data control strategy that involving time delay effect is derived.
Abstract: The present draft investigates the finite-time stabilization of T–S fuzzy semi-Markov switching systems by using a coupling memory sampled-data control approach. The main study concerned is how to effectively design the sampled-data control such that closed-loop T–S fuzzy semi-Markov switching systems is finite-time boundedness. By utilizing a Bernoulli distributed sequence, a more general coupling memory fuzzy sampled-data control strategy that involving time delay effect is derived. By virtue of fuzzy-basis-dependent membership functions, an asynchronous approach is proposed for T–S fuzzy semi-Markov switching system. Moreover, the inverted pendulum model is presented to demonstrate the feasibility and validity of the proposed strategies.
108 citations
TL;DR: The serviceability of the state estimator gains solved is finally verified, the effectiveness of the proposed design approach is further illustrated and the error dynamic obtained is globally uniformly exponentially stable and meets passive property.
Abstract: In this paper, the state estimation issue for a set of switched complex dynamic networks affected by quantization is studied, in which the switching process is assumed to follow persistent dwell-time switching regulation. Thereinto, the switching regulation aforementioned describes the switchings among different parameters on complex dynamic networks. Meanwhile, for the network-based model, in the communication channels from the sensor to the estimator, quantization is inevitable to be taken into consideration. To track partially inaccessible information in the target system, a state estimator is thoroughly reconstructed. Intensive attention is that a set of sufficient conditions can be derived by using some simple matrix transformation methods, linear matrix inequality and Lyapunov stability theory, to further assure the error dynamic obtained is globally uniformly exponentially stable and meets passive property. The serviceability of the state estimator gains solved is finally verified and the effectiveness of the proposed design approach is further illustrated.
104 citations
TL;DR: The main purpose is to design a novel memory sampled-data control scheme to ensure the synchronization of the master-slave system and achieves the stochastic stability and satisfies an extended dissipative performance index via constructing Lyapunov function.
Abstract: The work is concerned with the synchronization issue of complex dynamic networks subject to the semi-Markov process. The semi-Markov process is used to describe the switching among different modes of network topology. Meanwhile, a constant signal transmission delay is considered in the sampled-data controller when dealing with the synchronization problem. The main purpose is to design a novel memory sampled-data control scheme to ensure the synchronization of the master-slave system. With the help of some improved integral inequality techniques, several sufficient conditions are obtained to assure the error system achieves the stochastic stability and satisfies an extended dissipative performance index via constructing Lyapunov function. Finally, two simulation examples are given to verify the validity and superiority of the memory sampled-data controller designed.
102 citations
TL;DR: It is demonstrated that the follower OBFNs could enter the convex hull formed by the leader OBFN's in finite time through using the Lyapunov approach and an adaptive law is designed to compensate the upper bounds of estimation error.
Abstract: The Ocean Bottom Flying Node (OBFN) is a kind of small Autonomous Underwater Vehicle (AUV) used in detection of seabed resources. Based on directed commination topology, this paper investigates the problem of distributed finite-time fault-tolerant containment control for multiple OBFN systems in presence of model uncertainties, external disturbances, and thruster faults. By choosing the nonsingular fast terminal sliding surface and defining the containment error variables, a distributed finite-time containment control method is designed, so as to make the states of the multiple OBFN systems converge to the sliding surface in finite time. The thruster faults, model uncertainties, and external disturbances are considered together and estimated by utilizing Neural Networks (NNs). An adaptive law is designed to compensate the upper bounds of estimation error. Based on the graph theory and matrix theory, it is demonstrated that the follower OBFNs could enter the convex hull formed by the leader OBFNs in finite time through using the Lyapunov approach. Numerical simulation is presented to show the effectiveness of the proposed algorithm.
80 citations
TL;DR: An extended reciprocally convex quadratic inequality and an improvedquadratic function negative-determination condition are proposed and based on the method proposed, some less conservative criteria are derived.
Abstract: This paper studies the stability problems of linear systems with time-varying delays. Firstly, an extended reciprocally convex quadratic inequality and an improved quadratic function negative-determination condition are proposed. Based on the method proposed, some less conservative criteria are derived. Finally, a well-known numerical example is carried out to demonstrate the effectiveness and the merits of the proposed method.
77 citations
TL;DR: An improved time-dependent and fuzzy-membership-function-dependent Lyapunov–Krasovskii functional is constructed to commendably capture the available information related to the real sampling pattern to ensure that the switched sampled-data control stabilizes the fuzzy systems.
Abstract: This study focuses on the stabilization analysis for fuzzy systems with the switched sampled-data control. By utilizing the information of the membership functions, an improved time-dependent and fuzzy-membership-function-dependent Lyapunov–Krasovskii functional (LKF) is constructed to commendably capture the available information related to the real sampling pattern. Together with a switching idea and newly inequalities, further results with less conservativeness are established to ensure that the switched sampled-data control stabilizes the fuzzy systems. Moreover, the switched sampled-data controllers are devised with a larger sampling interval. Finally, the effectiveness of the presented criteria is verified by two examples.
TL;DR: This paper investigates the distributed finite-time formation tracking control problem with collision avoidance for multiple quadrotor Unmanned Aerial Vehicles subject to external disturbances and proposes a novel sliding mode surface-like variable based distributed position tracking control strategy and a fast terminal sliding mode based attitude tracking control scheme.
Abstract: In this paper, the distributed finite-time formation tracking control problem with collision avoidance is investigated for multiple quadrotor Unmanned Aerial Vehicles (UAV) subject to external disturbances. Firstly, two finite-time observers are designed to estimate the external disturbance force and torque without upper bound, respectively. Then, utilizing the precisely observed information deriving from the observers, a novel sliding mode surface-like variable based distributed position formation tracking control strategy and a fast terminal sliding mode based attitude tracking control strategy are proposed, respectively. It achieves that the multiple quadrotor UAVs can track the desired trajectory in a specific formation configuration within the safe distance and avoid dynamic obstacles. Meanwhile, the rapid attitude synchronization and tracking is also achieved. The entire multiple UAVs distributed formation tracking closed-loop control system are proved to be globally fast finite-time stable by using Lyapunov-like analysis. Finally, the effective and fine performance of the proposed schemes are demonstrated by a numerical simulation example with a group of quadrotor UAVs.
TL;DR: A finite-time trajectory tracking control for unmanned surface vessel with error constraints and input saturations is proposed, which takes the limited actuator capability into account and employs the hyperbolic tangent function to address the saturation problem.
Abstract: In this paper, a finite-time trajectory tracking control for unmanned surface vessel with error constraints and input saturations is proposed. We take the limited actuator capability into account and employ the hyperbolic tangent function to address the saturation problem, which is converted into the unknown input gains. A tan-type barrier Lyapunov function tackles the error constraints, where error variables remain within the predefined bounds. In addition, the neural networks are utilized for model uncertainties and external disturbances. We present a semi-globally uniformly bounded control method, and develop a finite-time control approach subsequently. Finally, the effectiveness of the proposed strategies is verified by the simulation studies.
TL;DR: The fuzzy asynchronous dissipative filtering issue for Markov jump discrete-time nonlinear systems subject to fading channels is discussed in this paper, where the Rice fading model is employed to characterize the fading channels phenomenon in the system measurements for the first time.
Abstract: The fuzzy asynchronous dissipative filtering issue for Markov jump discrete-time nonlinear systems subject to fading channels is discussed in this paper, where the Rice fading model is employed to characterize the fading channels phenomenon in the system measurements for the first time. The attention is focused on developing an available asynchronous filter, which can ensure that the underlying error system is dissipative. In this regard, several important performances can be investigated conveniently by introducing adjustment matrices. By means of the stochastic analysis theory and the network control technique, some sufficient conditions for the solvability of the addressed problem are presented, simultaneously, the gains of the filter desired are determined correspondingly. An illustrative example is finally exploited to explain the utilizability of the developed approach.
TL;DR: A novel approach of combining the reciprocally convex combination and weighted summation inequalities is employed to get the less conservative conditions of reachable set estimation for a class of Takagi-Sugeno fuzzy model based Markov jump inertial neural networks with time-varying delay.
Abstract: This paper addresses the problem of reachable set estimation for a class of Takagi-Sugeno fuzzy model based Markov jump inertial neural networks with time-varying delay. The objective of this paper is to obtain a compact set bounding all states of the system from some domains under initial conditions, while all the states from other domain are exponential convergence in another compact set. Primarily, on the basis of the Lyapunov-Krasovskii functional (LKF), in which both the upper and lower bounds of time-varying delay as well as the triple-summation term are considered, a novel approach of combining the reciprocally convex combination and weighted summation inequalities is employed to get the less conservative conditions. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.
TL;DR: An iterative algorithm based on the conjugate gradient method and least squares principle is presented to solve the periodic Sylvester bimatrix equations and it is shown that the iterative solutions of the algorithm converge to the exact solutions at finite steps with any initial values.
Abstract: The problem considered in this paper is to solve periodic Sylvester bimatrix equations. Based on the conjugate gradient method and least squares principle, an iterative algorithm is presented to solve the periodic Sylvester bimatrix equations. We show that the iterative solutions of the algorithm converge to the exact solutions at finite steps with any initial values. Finally, a numerical example is given to illustrate the validity and efficiency of the iterative algorithm.
TL;DR: Comprehensive simulations and comparisons conducted on CyberShip II demonstrate the effectiveness and superiority of the proposed F-PFTC and F-AFTC schemes can track exactly an ASV to the desired trajectory.
Abstract: In this paper, finite-time fault-tolerant control (FTC) for trajectory tracking of an autonomous surface vehicle (ASV) is solved. Main contributions are summarized as follows: (1) a finite-time passive FTC (F-PFTC) scheme using integral sliding mode (ISM) manifold is developed by exploiting partial knowledge on faults and disturbances, and achieves fast and accurate tracking with passive fault tolerance; (2) an online finite-time fault estimator (FFE) is devised to detect, isolate, and accommodate unknown faults and disturbances, and thereby eventually contributing to the finite-time active FTC (F-AFTC) scheme without using a priori knowledge; (3) suffering from both unknown faults and disturbances, the proposed F-PFTC and F-AFTC schemes can track exactly an ASV to the desired trajectory. Comprehensive simulations and comparisons conducted on CyberShip II demonstrate the effectiveness and superiority of the proposed schemes.
TL;DR: A novel barrier-actor-critic algorithm is presented for adaptive optimal learning while guaranteeing the full-state constraints and input saturation and it is proven that the closed-loop signals remain bounded during the online learning phase.
Abstract: This paper develops a novel adaptive optimal control design method with full-state constraints and input saturation in the presence of external disturbance. First, to consider the full-state constraints, a barrier function is developed for system transformation. Moreover, it is shown that, with the barrier-function-based system transformation, the stabilization of the transformed system is equivalent to the original constrained control problem. Second, the disturbance attenuation problem is formulated within the zero-sum differential games framework. To determine the optimal control and the worst-case disturbance, a novel barrier-actor-critic algorithm is presented for adaptive optimal learning while guaranteeing the full-state constraints and input saturation. It is proven that the closed-loop signals remain bounded during the online learning phase. Finally, simulation studies are conducted to demonstrate the effectiveness of the presented barrier-actor-critic learning algorithm.
TL;DR: A bilinear state observer is established to update the unavailable states recursively, and a new least squares based efficient estimation algorithm is presented for simultaneously estimating the unknown states, parameters and time delay.
Abstract: This paper develops a redundant recursive identification algorithm for joint estimation of states and parameters of bilinear state-space systems with time delays. In order to handle measurement delays in parameter identification and state estimation, the bilinear model is transformed to an extended identification model according to the redundant rule. In this regard, a bilinear state observer is established to update the unavailable states recursively, and a new least squares based efficient estimation algorithm is presented for simultaneously estimating the unknown states, parameters and time delay. The effectiveness of the proposed algorithm is evaluated by a numerical example.
TL;DR: By the proposed two design schemes, the impacts induced by the faults on the system is eliminated, and the entire nonlinear feedback system holds strong robustness and perfect tracking performance.
Abstract: Uncertainties and fault signals usually exist in the real systems and it is difficult to maintain stability and tracking performance for the real applications. Therefore, it is important to study the robust fault tolerant tracking control (RFTTC) for uncertain nonlinear feedback systems (NFS). Generally, the RFTTC schemes are designed for the uncertain NFS by using operator theory based robust right coprime factorization (ORRCF) method. In details, firstly, one novel RFTTC scheme is proposed for the uncertain NFS, wherein the fault tolerant controllers as well as the tracking one are designed based on the internal model. Secondly, the other new RFTTC scheme is proposed where the robust fault tolerant controllers are combined with the compensation operator and the tracking controller. By the proposed two design schemes, the impacts induced by the faults on the system is eliminated, and the entire nonlinear feedback system holds strong robustness and perfect tracking performance. Finally, simulation results of the multi-joint manipulator are used to indicate the validity of proposed two design schemes.
TL;DR: The relative attitude kinematic and dynamic models of a spacecraft are presented and a sliding mode surface and predefined-time stability theory are applied to ensure that both the tracking errors of the attitude and the angular velocity converge to zero within a prescribed time.
Abstract: This paper investigates the attitude tracking problem of a rigid spacecraft using contemporary predefined-time stability theory. To this end, the relative attitude kinematic and dynamic models of a spacecraft are presented. Then, a sliding mode surface and predefined-time stability theory are applied to ensure that both the tracking errors of the attitude, expressed by the quaternion and the angular velocity, converge to zero within a prescribed time. Simulation results demonstrate the performance of the proposed scheme.
TL;DR: Simulation results shown that the designed event-trigger based adaptive controller ensures the stability of closed-loop system and the introduction of smooth function sgi in controller make the approximation of sign(·) become more accurate.
Abstract: In this paper, an event-trigger based adaptive control scheme is developed for a class of interconnected systems with unknown external disturbance. Under the proposed control scheme, the effects caused by external disturbance and unknown measurement error can be compensated by constructing the estimator of its unknown constant upper bound. The effect caused by unknown interactions occurred in all subsystems which exist in every channel can be dealt with signals zi,1ϕi added in virtual control αi,1. In addition, the introduction of smooth function sgi(·) in controller make the approximation of sign(·) become more accurate. So that the performance of closed-loop system can be improved. Finally, The proof of avoiding the Zeno behavior under such event-trigger based adaptive controller are finished and simulation results shown that the designed event-trigger based adaptive controller ensures the stability of closed-loop system.
TL;DR: Based on the Lyapunov–Krasovskii functional theory, a new relaxed sufficient condition with fewer linear matrix inequality (LMI) constraints is derived and the IT2 fuzzy sampled-data controller is devised to ensure the closed-loop system is asymptotically stable.
Abstract: This paper is devoted to the investigation of the interval type-2 (IT2) fuzzy sampled-data stabilization problem for the controlled plant subject to nonlinearities and parameter uncertainties. Some free-weighting matrices, slack matrices, and the bound information in membership functions are used to improve the stability analysis. Based on the Lyapunov–Krasovskii functional (LKF) theory, a new relaxed sufficient condition with fewer linear matrix inequality (LMI) constraints is derived. According to this criterion, the IT2 fuzzy sampled-data controller is devised to ensure the closed-loop system is asymptotically stable. Finally, three practical examples are provided to demonstrate the effectiveness and efficiency of the proposed design. Some comparisons show that the proposed algorithm is more simple and practical.
TL;DR: A finite-time attitude synchronization tracking control scheme is developed by using neural networks and finite- time differentiator techniques, and it is shown that by using the Lyapunov method, all UAVs can track their individual attitude references, while the synchronized tracking errors among Uavs are all bounded in finite time and confined within the prescribed performance bounds.
Abstract: This paper is concerned with the decentralized finite-time fault-tolerant attitude synchronization tracking control problem for multiple unmanned aerial vehicles (multi-UAVs) with prescribed performance. Failure to counteract actuator faults in the formation flight of multi-UAVs in a limited time may lead to catastrophic consequences. By integrating the prescribed performance functions into the synchronization tracking errors, a new set of errors is defined. Based on the transformed errors, a finite-time attitude synchronization tracking control scheme is developed by using neural networks and finite-time differentiator techniques. The neural networks are utilized to identify the unknown nonlinear terms induced by uncertainties and actuator faults. To reduce the computational burden caused by estimating the weight vectors, the norms of weight vectors are used for the estimation, such that the number of adaptive parameters is significantly reduced and independent from the number of neurons. The finite-time differentiators are utilized to estimate the intermediate control signals and their derivatives. Moreover, auxiliary dynamic signals with explicit consideration of differentiator estimation errors are introduced into the control scheme to guarantee the finite-time convergences of the synchronized tracking errors. Furthermore, it is shown that by using the Lyapunov method, all UAVs can track their individual attitude references, while the synchronized tracking errors among UAVs are all bounded in finite time and confined within the prescribed performance bounds. Finally, comparative simulation studies on multi-UAVs are conducted to verify the effectiveness of the proposed scheme.
TL;DR: The barrier Lyapunov function combining exponential function is introduced to obtain better transient performance of systems by solving an output constraint problem, where the convergence rates and convergence bounds of tracking errors are precisely guaranteed.
Abstract: The problem of distributed adaptive event-triggered consensus tracking control is investigated for a class of output-constrained uncertain nonlinear multi-agent systems (MASs). With the help of fuzzy logic systems (FLSs), the unavailable states are estimated by constructing a fuzzy state observer. In order to mitigate communication burden, the adaptive event-triggered controller is presented by employing the backstepping approach and dynamics surface control (DSC) technique, which guarantees the boundedness of all system signals. In view of the possible poor transient performance resulting from discontinuous control signal under the event-triggered mechanism, the barrier Lyapunov function combining exponential function is introduced to obtain better transient performance of systems by solving an output constraint problem, where the convergence rates and convergence bounds of tracking errors are precisely guaranteed. Simulation results demonstrate the effectiveness of the presented method.
TL;DR: It is proved that the proposed fault-tolerant controller guarantees the synchronization of multi-agent systems with deception attacks and actuator bias.
Abstract: The fault tolerant control problem for multi-agent systems with deception attacks and actuator faults is studied in this paper. Under deception attacks, the false data will be injected to communication channels, and change the transmittal signals. It is extremely difficult to ensure synchronization control of multi-agent systems with deception attacks and actuator bias faults by using the existing fault-tolerant control methods. A novel distributed adaptive fault tolerant controller is constructed in physical layer, and a distributed impulsive controller is proposed to deal with deception attacks in communication layer. It is proved that the proposed fault-tolerant controller guarantees the synchronization of multi-agent systems with deception attacks and actuator bias. Simulation results verify the effectiveness of the proposed method.
TL;DR: The robustness results indicate that the FLQR and FLQG controllers under the internal and external disturbances were effective and produce much better results than the dynamic responses of the classical L QR and LQG controller, respectively.
Abstract: In this paper, a Fuzzy based Linear Quadratic Regulator (FLQR) and Linear Quadratic Gaussian (FLQG) controllers are developed for stability control of a Double Link Rotary Inverted Pendulum (DLRIP) system. The aim of this work is to study dynamic performance analysis of both FLQR and FLQG controllers and to compare them with the classical LQR and LQG controllers, respectively. A dynamic mechanical simulation model of the DLRIP was obtained using both the numerically SimMechanics toolbox in MATLAB and the analytically dynamic nonlinear equations. To determine the control performance of the controllers, Settling Time (Ts), Peak Overshoot (PO), Steady-State Error (Ess), and the total Root Mean Squared Errors (RMSEs) of the joint positions are computed. Furthermore, the dynamic responses of the controllers were compared based on robustness analysis under internal and external disturbances. To show the control performance of the controllers, several simulations were conducted. Based on the comparative results, the dynamic responses of both FLQR and FLQG controllers produce much better results than the dynamic responses of the classical LQR and LQG controllers, respectively. Moreover, the robustness results indicate that the FLQR and FLQG controllers under the internal and external disturbances were effective.
TL;DR: The finite-time fault-tolerant trajectory tracking of fully actuated marine vehicles is investigated in the presence of parametric uncertainties, external disturbances, actuator faults, and input saturation, and a novel adaptive finite- time sliding mode control scheme is proposed.
Abstract: The increasing interest in marine mechatronic systems and their applications has promoted the development of advanced control algorithms for the trajectory control of marine vehicles including ships, surface vehicles, and underwater vehicles. In this paper, the finite-time fault-tolerant trajectory tracking of fully actuated marine vehicles is investigated in the presence of parametric uncertainties, external disturbances, actuator faults, and input saturation. A novel adaptive finite-time sliding mode control scheme is proposed by combining the homogeneous integral sliding mode manifold, the fast terminal sliding mode control, and the adaptation technique. Rigorous theoretical analysis for the practical finite-time stability of the whole closed-loop system is provided. The proposed control scheme can guarantee the position and velocity tracking errors converge to the small region about zero in finite time even in the presence of actuator faults. To the best of the authors’ knowledge, there are really limited existing controllers can achieve such excellent performance in the same conditions. In addition, the proposed control scheme is structurally simple, model-independent, and continuous with chattering free, which makes it affordable for practical applications. Numerical simulations illustrate the effectiveness and superiority of the proposed control scheme.
TL;DR: This paper presents a novel adaptive neural-based control design for a robot with incomplete dynamical modeling and facing disturbances based on a simple structured PID-like control that provides proof that all signals in the closed-loop system are bounded while the constraints are not violated.
Abstract: The problem of designing an analytical gain tuning and stable PID controller for nonlinear robotic systems is a long-lasting open challenge. This problem becomes even more intricate if unknown system dynamics and external disturbances are involved. This paper presents a novel adaptive neural-based control design for a robot with incomplete dynamical modeling and facing disturbances based on a simple structured PID-like control. Radial basis function neural networks are used to estimate uncertainties and to determine PID gains through a direct Lyapunov method. The controller is further augmented to provide constrained behavior during system operation, while stability is guaranteed by using a barrier Lyapunov function. The paper provides proof that all signals in the closed-loop system are bounded while the constraints are not violated. Finally, numerical simulations provide a validation of the effectiveness of the reported theoretical developments.
TL;DR: The proposed FrPHTs and FrQP HTs are outperformed the classical polar harmonic transforms, the quaternion polar harmonic transform and the existing fractional orthogonal transforms in terms of accuracy and numerical stability, digital image reconstruction, RST invariances, robustness to noise and computational efficiency.
Abstract: A novel set of fractional orthogonal polar harmonic transforms for gray-scale and color image analysis are presented in this paper. These transforms are divided into two groups. The first group contains fractional polar complex exponential transforms (FrPCETs), fractional polar cosine transforms (FrPCTs), and fractional polar sine transforms (FrPSTs) for gray-scale images. The second group contains the fractional quaternion polar complex exponential transforms (FrQPCETs), fractional quaternion polar cosine transforms (FrQPCTs), and fractional quaternion polar sine transforms (FrQPSTs) for color images. All mathematical formulae for the basis functions, orthogonality relations and reconstruction forms are derived and their validity are proved. The required mathematical forms for invariance to rotation, scaling and translation (RST) are derived. A series of experiments is performed to test the validity of the proposed fractional polar harmonic transforms (FrPHTs) and the fractional quaternion polar harmonic transforms (FrQPHTs). The performances of the proposed FrPHTs and FrQPHTs are outperformed the classical polar harmonic transforms, the quaternion polar harmonic transforms and the existing fractional orthogonal transforms in terms of accuracy and numerical stability, digital image reconstruction, RST invariances, robustness to noise and computational efficiency.