This article investigates the system modeling problem for the dynamical process of human brain activity in human-robot cognitive interaction (HRCI). An important novelty of the proposed approaches is to build a computational model of a human-distributed robot-lumped parameter system (HDRLPS) that describes the inherent dynamical principle of human brain activity (with spatiotemporal-varying characteristic) undergoing the interaction between the intrinsic cognitive dynamics and extrinsic robot stimuli. A deterministic learning (DL)-based spatiotemporal dynamics identification scheme is proposed to accurately identify the spatiotemporal dynamics of HDRLS and obtain the associated knowledge as a constant radial basis functional neural network (RBF NN) model. A spatiotemporal dynamics estimator is designed with this model, which can accurately evaluate and monitor the dynamical process of human brain activity in real-time HRCI by the generated dynamics-synchronized state. The effectiveness and practicability of the approaches in the dynamics identification and evaluation for the human brain activity in HRCI are validated by the thorough analysis, including the mathematical proof, the simulation study, and the brain-computer interface (BCI) experiment using publicly available datasets. Our method is compared with state-of-the-art (SOTA) methods, such as LGGNet, EEGNet, Tsception, EEG-Deformer, EEG-Transformer, and EEGViT. The results show that our method can outperform these methods with better recognition accuracy and macro- $F1$ scores. The source code can be found at: https://github.com/alonexing/source_code/tree/master.

Accurate trajectory training is a challenging issue of upper-limb rehabilitation robots. This paper presents a novel discrete-time neural network control method to address the problems of system uncertainties and tracking accuracy in repetitive trajectory training. This control method consists of both an adaptive neural network controller and a learning controller. The adaptive neural network controller satisfying persistent excitation condition enables not only stable tracking control, but also accurate learning for closed-loop system dynamics. The learning controller utilizes the learned knowledge to provide high-performance control. In order to examine the effectiveness of the proposed control method, a series of simulation and real-world experiments with system uncertainties were conducted, in comparison of proportion integration differentiation control, sliding mode control and event-triggered adaptive neural control. Results substantiate that the proposed control method can precisely learn the unknown dynamics of human-robot system along the subject-specific reference trajectories, and control the robot to assist the arm for accurate and fast trajectory tracking with small control gains by reutilizing the learned knowledge. This control method may play a role in accurate trajectory training for upper-limb rehabilitation robots. Note to Practitioners—This work is motivated by the practical requirements of rehabilitation robots in repetitive motor training. Trajectory tracking is a fundamental but efficient training mode of rehabilitation robots. However, uncertainty and nonlinearity of the human-robot system dynamics may increase the difficulty of controlling the robots for accurate, efficient and reliable trajectory tracking training. To this end, this paper proposes a learning-based control method, which could learn the uncertain and nonlinear system dynamics by utilizing an elaborately designed neural network controller and thus achieve superior control performance using the learned knowledge. This control method can be potentially applied in variety of rehabilitation robots, showing advantages for repetitive trajectory training. First, it can accurately mode the uncertain dynamics of human-robot system and achieve personalized rehabilitation. Second, it does not need any parameter adaptation in the similar repeated motions, and can be more easily designed with digital implementations, thereby achieving better performance in the aspects of time saving. Third, it can ensure the tracking accuracy of the rehabilitation robot for rehabilitation efficiency and avoid secondary injury.

This article is concerned with the rapid classification issue for dynamical patterns consisting of sampling sequences in a relatively large-scale dynamical dataset constructed by benchmark Rossler systems. Specifically, based on a recently developed deterministic learning mechanism, a rapid dynamical pattern classification method is developed, which contains a modeling stage and a classification stage. In the modeling stage, a deterministic learning scheme is employed to accurately learn/model the inherent dynamics of the training dynamical patterns and store the acquired knowledge in a set of constant radial basis function (RBF) networks. In the classification stage, based on the trained RBF networks, a set of dynamical estimators is developed for real-time dynamic comparison. The generating recognition errors are then used to effectively represent the dynamic differences in real-time. To this end, the associated class label of the minimum recognition error is assigned to the test pattern also in real-time. To demonstrate the effectiveness of the proposed method, a relatively large-scale dynamical pattern dataset containing various dynamical behaviors is constructed by utilizing a deterministic chaos prospector (DCP) technique. The simulation results show that the new method achieves competitive classification performances compared to the state-of-the-art time-series classification method for the dynamical system classification task. In addition to performance advantages, the new method can perform real-time time-series classification with the first 10% of data achieving over 95% of accuracy based on the full-length data. Besides, the superiority of our method is demonstrated from various datasets in the UCR time-series classification (TSC) archive.

This study investigates a multitrajectory tracking control strategy for an unknown 2-DOF helicopter system, integrating deterministic learning (DL) and reinforcement learning (RL). Initially, DL theory is applied to identify the local unknown dynamics of a 2-DOF helicopter system using radial basis function neural networks (RBFNNs). Subsequently, the identified dynamic knowledge is expressed and stored using constant RBFNNs. To mitigate the issue of partial knowledge failure due to deviations between the actual and learned trajectories, we introduce a RL framework for dynamic compensation. Finally, a composite control strategy incorporating both nominal and auxiliary components is designed to achieve multitrajectory tracking control. The stability of the closed-loop system is analyzed and demonstrated using the Lyapunov direct method. The simulation and experimental results demonstrate the effectiveness of the proposed control strategy.

A key challenge for training control policies with imitation learning methods lies in the computational inefficiency. This inefficiency comes from an assumption that underlies these methods, assuming the policy should compute a new action for each state, which is unnecessary and costly. However, we notice the states occurring within K consecutive timesteps differ negligibly and their corresponding actions are extremely similar. Therefore, we challenge this assumption and argue that it is enough to compute an action every K states. With this argument, we propose K-Timestep Adaptive Action Approximation, which replaces the computation of K one-timestep actions approximately with that of one K-timestep action to alleviate the computational inefficiency issue. To demonstrate the theoretical validity of our method, we analyze the errors incurred by the policies learned via the method. The analysis proves these policies can converge to the optimal solution with errors no more than an upper bound dependent on K, revealing the effectiveness of our method. To avoid the difficulty of hyperparameter handcrafting on K, we design a simple but effective auto-hyperparameter tuning strategy. In the proposed strategy, K is added as an extra dimension to the action space of the policy, so it can be tuned adaptively by the policy according to the state without any user intervention. Empirical results on 4 imitation learning tasks show the superiority in computational efficiency of our method, which can effectively reduce new actions to compute in training policies.

This article investigates internal interaction-based dynamic learning control (LC) for uncertain discrete-time strict-feedback systems. On the basis of predict technology, the original system is converted into a common n -step-ahead input-output predict model. The predict model causes every estimated neural weight to converge to n different constants using the existing control framework. To solve such a problem, the predict model is further decomposed into n one-step-ahead subsystems, which can be viewed as n independent agents. Subsequently, the distributed cooperative weight adaptive laws are designed by introducing an undirected and connected interconnection topology among subsystems. By constructing the variable relationship between the subsystems and the n -step-ahead predict model, a new internal weight interaction-based neural dynamic LC framework is proposed for the whole closed-loop system, in which estimated weights at different times share their weight knowledge. The proposed framework ensures the ultimately uniform boundedness of the closed-loop system and achieves the excellent control performance. By combining the consensus theory and a cooperative persistent excitation condition, every estimated weight along the neural input orbit is verified to exponentially converge to a close vicinity of a unique ideal constant, rather than n different constants. Consequently, the developed LC framework facilitates constant weights storage, saves the knowledge storage space, and improves the robustness of knowledge utilization. These characteristics are verified by simulation results.

Rapid dynamical pattern recognition based on the deterministic learning method (DLM-based RDPR) aims to rapidly recognize the most similar dynamical pattern pair from perspectives of differences in inherent system dynamics. The basic mechanism is to use available recognition errors to reflect the differences in the dynamics of dynamical pattern pairs and then to make a decision based on a minimal recognition error (MRE) principle. This article focuses on providing a rigorous theoretical analysis of the MRE principle in DLM-based RDPR under the sampled-data framework. Specifically, we seek a unified methodology from the similarity definition to the measure implementation and then to derive general sufficient conditions and necessary conditions for the MRE principle. The main idea is to: 1) from the average signal energy aspect, define a time-dependent dynamics-based similarity in dynamical pattern pairs and reestablish the measure of recognition errors generated from the DLM-based RDPR; 2) introduce the energy-based Lyapunov method to establish the interrelation between the dynamical distance and the recognition error; and 3) derive sufficient conditions and necessary conditions from two directions of the interrelation. The proposed conditions distinguish themselves from virtually all of the existing DLM-based RDPR works with only sufficient conditions in the sense that it is shown in a rigorous analysis that under what conditions, the pattern pair recognized based on the MRE principle is indeed the most similar one. Therefore, the proposed work makes the DLM-based RDPR possess good interpretability and provides strong theoretical guidance in engineering applications.

This article investigates the leader–follower formation learning control (FLC) problem for discrete-time strict-feedback multiagent systems (MASs). The objective is to acquire the experience knowledge from the stable leader–follower adaptive formation control process and improve the control performance by reusing the experiential knowledge. First, a two-layer control scheme is proposed to solve the leader–follower formation control problem. In the first layer, by combining adaptive distributed observers and constructed$i_{n}$-step predictors, the leader’s future state is predicted by the followers in a distributed manner. In the second layer, the adaptive neural network (NN) controllers are constructed for the followers to ensure that all the followers track the predicted output of the leader. In the stable formation control process, the NN weights are verified to exponentially converge to their optimal values by developing an extended stability corollary of linear time-varying (LTV) system. Second, by constructing some specific “learning rules,” the NN weights with convergent sequences are synthetically acquired and stored in the followers as experience knowledge. Then, the stored knowledge is reused to construct the FLC. The proposed FLC method not only solves the leader–follower formation problem but also improves the transient control performance. Finally, the validity of the presented FLC scheme is illustrated by simulations.

Recently, functional brain network has been used for the classification of brain disorders, such as Autism Spectrum Disorder (ASD) and Alzheimer's disease (AD). Existing methods either ignore the non-imaging information associated with the subjects and the relationship between the subjects, or cannot identify and analyze disease-related local brain regions and biomarkers, leading to inaccurate classification results. This paper proposes a local-to-global graph neural network (LG-GNN) to address this issue. A local ROI-GNN is designed to learn feature embeddings of local brain regions and identify biomarkers, and a global Subject-GNN is then established to learn the relationship between the subjects with the embeddings generated by the local ROI-GNN and the non-imaging information. The local ROI-GNN contains a self-attention based pooling module to preserve the embeddings most important for the classification. The global Subject-GNN contains an adaptive weight aggregation block to generate the multi-scale feature embedding corresponding to each subject. The proposed LG-GNN is thoroughly validated using two public datasets for ASD and AD classification. The experimental results demonstrated that it achieves the state-of-the-art performance in terms of various evaluation metrics.

In this article, we investigate the actuator fault detection (AFD) problem for a class of closed-loop systems with nonlinear uncertain dynamics. Two AFD schemes are developed via the deterministic learning method (DLM). In the first scheme, knowledge of the system dynamics and actuator fault dynamics is extracted from state signals by using DLM. The learned knowledge is utilized to construct a bank of estimators. When the residual norm of a fault estimator becomes smaller than that of the nominal estimator, the occurrence of the actuator fault is deduced. In the second scheme, a learning controller is constructed to identify the feedback control dynamics under normal and fault conditions. The knowledge of the feedback control dynamics is utilized to construct a bank of controllers, which are embedded in a bank of estimators. When the residual norm of the estimator embedded with the matched controller becomes smaller than that of the estimator embedded with the nominal controller, the actuator fault can be detected. Finally, the properties of constant neural networks and the persistent excitation condition are exploited to derive the detectability conditions for diagnosis schemes. The attraction of this article is that two knowledge-bank-based AFD schemes are developed, in which the knowledge extracted from state and controller signals will enhance the sensitivity to actuator faults. Simulation results are also included to illustrate the effectiveness of these schemes.

This article investigates dynamical pattern recognition for a class of univariate time-series data. These data are sampled from the output of dynamical systems with uncertain dynamics. Based on deterministic learning, a rapid recognition approach is presented from the viewpoint of the sample-data observer. It comprises two phases: 1) training and 2) recognition. In the training phase, locally accurate dynamical modeling of the underlying dynamics of training time series can be accomplished by merging a sampled-data observer and radial basis function network (RBFN) identifiers. In the recognition phase, several RBFN-based estimators with non-high-gain designs are constructed. In this case, the stability analysis of the generated estimator error systems will conduce to conduct non-high-gain recognition of a test time series. We demonstrate that these estimator errors can depict dynamics differences between the dynamical patterns of the test and training time-series data. Based on the average$L_{1}$norms of the output errors, a decision-making scheme is developed to generate recognition results rapidly. More concise and relaxed recognition conditions are derived through rigorous analysis to ensure accurate recognition results. Simulation studies exemplify the effectiveness of the presented approach.

BACKGROUND: Osteoporosis is a common metabolic skeletal disease and usually lacks obvious symptoms. Many individuals are not diagnosed until osteoporotic fractures occur. Bone mineral density (BMD) measured by dual-energy X-ray absorptiometry (DXA) is the gold standard for osteoporosis detection. However, only a limited percentage of people with osteoporosis risks undergo the DXA test. As a result, it is vital to develop methods to identify individuals at-risk based on methods other than DXA. RESULTS: We proposed a hierarchical model with three layers to detect osteoporosis using clinical data (including demographic characteristics and routine laboratory tests data) and CT images covering lumbar vertebral bodies rather than DXA data via machine learning. 2210 individuals over age 40 were collected retrospectively, among which 246 individuals' clinical data and CT images are both available. Irrelevant and redundant features were removed via statistical analysis. Consequently, 28 features, including 16 clinical data and 12 texture features demonstrated statistically significant differences (p < 0.05) between osteoporosis and normal groups. Six machine learning algorithms including logistic regression (LR), support vector machine with radial-basis function kernel, artificial neural network, random forests, eXtreme Gradient Boosting and Stacking that combined the above five classifiers were employed as classifiers to assess the performances of the model. Furthermore, to diminish the influence of data partitioning, the dataset was randomly split into training and test set with stratified sampling repeated five times. The results demonstrated that the hierarchical model based on LR showed better performances with an area under the receiver operating characteristic curve of 0.818, 0.838, and 0.962 for three layers, respectively in distinguishing individuals with osteoporosis and normal BMD. CONCLUSIONS: The proposed model showed great potential in opportunistic screening for osteoporosis without additional expense. It is hoped that this model could serve to detect osteoporosis as early as possible and thereby prevent serious complications of osteoporosis, such as osteoporosis fractures.

In this article, through a combination of the deterministic learning (DL) method and the adaptive high gain observer (AHGO) technology, a fault identification approach for a class of nonlinear systems in canonical form is proposed. By using the DL method, the partial persistent excitation condition of the identification system is satisfied, and then, the AHGO technology is exploited to estimate the states and the neural network weights simultaneously. To analyze the convergence of the proposed method, we first analyze the uniformed completely observability (UCO) property of the linear part of the nonlinear identification system. Then, by using the Lipschitz property of the nonlinear item and the Bellman-Gronwall lemma, we show that the UCO property of the nonlinear identification system is depended on the UCO property of the linear part when the observer gain is chosen large. Therefore, by using the UCO property of the nonlinear identification system and the Lyapunov stability theorem, the convergence of the proposed learning observer is proven. The attraction of this article is based on the analysis of the UCO property of the identification system, and the convergence of the proposed learning observer can be directly proven. The simulation example is given to demonstrate the effectiveness of the proposed method.

In this article, a rapid sensor fault diagnosis (SFD) method is presented for a class of nonlinear systems. First, by exploiting the linear adaptive observer technology and the deterministic learning method (DLM), an adaptive neural network (NN) observer is constructed to capture the information of the unknown sensor fault function. Second, when the NN input orbit is a period or recurrent one, the partial persistent excitation (PE) condition of the NNs can be guaranteed through the DLM. Based on the partial PE condition and the uniformly completely observable property of a linear time-varying system, the accurate state estimation and the sensor fault identification can be achieved by properly choosing the observer gain. Third, a bank of dynamical observers utilizing the experiential knowledge is constructed to achieve rapid SFD and data recovery. The attractions of the proposed approach are that accurate approximations of sensor faults can be achieved through the DLM, and the data that are destroyed by the sensor faults can be recovered by using the learning results. Simulation studies of a robot system are utilized to show the effectiveness of the proposed method.

A unified approach is proposed to design sampled-data observers for a certain type of unknown nonlinear systems undergoing recurrent motions based on deterministic learning in this article. First, a discrete-time implementation of high-gain observer (HGO) is utilized to obtain state trajectory from sampled output measurements. By taking the recurrent estimated trajectory as inputs to a dynamical radial basis function network (RBFN), a partial persistent exciting (PE) condition is satisfied, and a locally accurate approximation of nonlinear dynamics can be realized along the estimated sampled-data trajectory. Second, an RBFN-based observer consisting of the obtained dynamics from the process of deterministic learning is designed. Without resorting to high gains, the RBFN-based observer is shown capable of achieving correct state observation. The novelty of this article lies in that, by incorporating deterministic learning with the discrete-time HGO, the nonlinear dynamics can be accurately approximated along the estimated trajectory, and such obtained knowledge can then be utilized to realize nonhigh-gain state estimation for the same or similar sampled-data systems. Simulation is performed to validate the effectiveness of the proposed approach.

This article first investigates the issue on dynamic learning from adaptive neural network (NN) control of discrete-time strict-feedback nonlinear systems. To verify the exponential convergence of estimated NN weights, an extended stability result is presented for a class of discrete-time linear time-varying systems with time delays. Subsequently, by combining the n -step-ahead predictor technology and backstepping, an adaptive NN controller is constructed, which integrates the novel weight updating laws with time delays and without the σ modification. After ensuring the convergence of system output to a recurrent reference signal, the radial basis function (RBF) NN is verified to satisfy the partial persistent excitation condition. By the combination of the extended stability result, the estimated NN weights can be verified to exponentially converge to their ideal values. The convergent weight sequences are comprehensively represented and stored by constructing some elegant learning rules with some novel sequences and the mod function. The stored knowledge is used again to develop a neural learning control scheme. Compared with the traditional adaptive NN control, the proposed scheme can not only accomplish the same or similar tracking tasks but also greatly improve the transient control performance and alleviate the online computation. Finally, the validity of the presented scheme is illustrated by numerical and practical examples.

In this article, we propose a learning-based fault diagnosis approach for a class of nonlinear sampled-data systems. First, the unmodeled sampled dynamics is acquired by the using deterministic learning method. The knowledge of the sampled dynamics of the normal and fault patterns is stored in the form of constant neural networks. Second, a fault detection scheme is designed in which memories of the learned knowledge can be recalled to give a rapid response to a fault. Third, analytical results concerning the fault detection condition and detection time are derived. It is shown that the mismatch function plays an important role in the performance properties of the diagnosis scheme. To analyze the effect of mismatch function on the residual, the concept of duty ratio is developed. Moreover, by comparing the constant neural networks of the normal and fault patterns, an extraction operator is designed to capture the feature of the mismatch function. By using this method, the performance of the diagnosis scheme can be improved. A simulation study is included to demonstrate the effectiveness of the approach.

This article investigates the problem of small fault detection (sFD) for discrete-time nonlinear systems with uncertain dynamics. The faults are considered to be "small" in the sense that the system trajectories in the faulty mode always remain close to those in the normal mode, and the magnitude of fault can be smaller than that of the system's uncertain dynamics. A novel adaptive dynamics learning-based sFD framework is proposed. Specifically, an adaptive dynamics learning approach using radial basis function neural networks (RBF NNs) is first developed to achieve locally accurate identification of the system uncertain dynamics, where the obtained knowledge can be stored and represented in terms of constant RBF NNs. Based on this, a novel residual system is designed by incorporating a newmechanism of absolute measurement of system dynamics changes induced by small faults. An adaptive threshold is then developed for real-time sFD decision making. Rigorous analysis is performed to derive the detectability condition and the analytical upper bound for sFD time. Simulation studies, including an application to a three-tank benchmark engineering system, are conducted to demonstrate the effectiveness and advantages of the proposed approach.

Gait is an important biometric technology for human identification at a distance. This study focuses on gait features obtained by Microsoft Kinect and proposes a new model-based gait recognition method by combining deterministic learning theory and the data stream of Kinect. Deterministic learning theory is employed to capture the gait dynamics underlying Kinect-based gait parameters. Spatial-temporal gait features can be represented as the gait dynamics underlying the trajectories of spatial-temporal parameters, which can implicitly reflect the temporal changes of silhouette shape. Kinematic gait features can be represented as the gait dynamics underlying the trajectories of kinematic parameters, which can represent the temporal changes of body structure and dynamics. Both spatial-temporal and kinematic cues can be used separately for gait recognition using the smallest error principle. They are fused on the decision level to improve the gait recognition performance. Additionally, we discuss how to eliminate the effect of view angle on the proposed method. The experimental results indicate that encouraging recognition accuracy can be achieved.

In this paper, based on the deterministic learning (DL) theory, an approach for detection for small faults in a class of nonlinear closed-loop systems is proposed. First, the DL-based neural control approach and identification approach are employed to extract the knowledge of the control effort that compensates the fault dynamics (change of the control effort) and the fault dynamics (the change of system dynamics due to fault). Second, two types of residuals are constructed. One is to measure the change of system dynamics, another one is to measure change of the control effort. By combining these residuals, an enhanced residual is generated, in which the fault dynamics and the control effort are combined to diagnose the fault. It is shown that the major fault information is compensated by the control, and the major fault information is double in the enhanced residual. Therefore, the fault information in the diagnosis residual is enhanced. Finally, an analysis of the fault detectability condition of the diagnosis scheme is given. Simulation studies are included to demonstrate the effectiveness of the approach.

This paper addresses the formation control problem for a group of mechanical systems with nonlinear uncertain dynamics under the virtual leader-following framework. New cooperative deterministic learning-based adaptive formation control algorithms are proposed. Specifically, the virtual leader dynamics is constructed as a linear system subject to unknown bounded inputs, so as to produce more diverse reference signals for formation tracking control. A cooperative discontinuous nonlinear estimation protocol is first proposed to estimate the leader's state information. Based on this, a cooperative deterministic learning formation control protocol is developed using artificial neural networks, such that formation tracking control and locally-accurate nonlinear identification with learning knowledge consensus can be achieved simultaneously. Finally, by utilizing the learned knowledge represented by constant neural networks, an experience-based distributed control protocol is further proposed to enable position-swappable formation control. Numerical simulations using a group of autonomous underwater vehicles have been conducted to demonstrate the effectiveness and usefulness of the proposed results.

This paper presents a pattern-based neural network (NN) control approach for a class of uncertain nonlinear systems. The approach consists of two phases of identification and another two phases of recognition and control. First, in the phase (i) of identification, adaptive NN controllers are designed to achieve closed-loop stability and tracking performance of nonlinear systems for different control situations, and the corresponding closed-loop control system dynamics are identified via deterministic learning. The identified control system dynamics are stored in constant radial basis function (RBF) NNs, and a set of constant NN controllers are constructed by using the obtained constant RBF networks. Second, in the phase (ii) of identification, when the plant is operated under different or abnormal conditions, the system dynamics under normal control are identified via deterministic learning. A bank of dynamical estimators is constructed for all the abnormal conditions and the learned knowledge is embedded in the estimators. Third, in the phase of recognition, when one identified control situation recurs, by using the constructed estimators, the recurred control situation will be rapidly recognized. Finally, in the phase of pattern-based control, based on the rapid recognition, the constant NN controller corresponding to the current control situation is selected, and both closed-loop stability and improved control performance can be achieved. The results presented show that the pattern-based control realizes a humanlike control process, and will provide a new framework for fast decision and control in dynamic environments. A simulation example is included to demonstrate the effectiveness of the approach.

Based on the notion of persistent excitation (PE), a deterministic learning theory is recently proposed for RBF network-based identification of nonlinear systems. In this paper, we study the relationship between the PE levels, the structures of RBF networks and the performance of deterministic learning. Specifically, given a state trajectory generated from a nonlinear dynamical system, we investigate how to construct the RBF networks in order to guarantee sufficient PE levels (especially the level of excitation) for deterministic learning. It is revealed that the PE levels decrease with the density of neural centers, denoted by explicit formulas. As an illustration, these formulas are applied to convergence analysis of deterministic learning. We present exact theoretical conclusions that a finite and definite number of centers can achieve the same performance as global centers. In addition, a tradeoff exists between a relatively high level of excitation and the good approximation capabilities of RBF networks, which indicates that we cannot always obtain better convergence accuracy by increasing the density of centers. These results provide a new perspective for performance analysis of RBF network algorithms based on the notion of PE. Simulation studies are included to illustrate the results.

This paper focuses on dynamic learning from neural control for a class of nonlinear strict-feedback systems with predefined tracking performance attributes. To reduce the number of neural network (NN) approximators used and make the convergence of neural weights verified easily, state variables are introduced to transform the state-feedback control of the original strict-feedback systems into the output-feedback control of the system in the normal form. Then, using the output error transformation based on performance functions, the constrained tracking control problem of the normal systems is transformed into the stabilization problem of an equivalent unconstrained one. By combining the backstepping method, a high-gain observer with radial basis function (RBF) NNs, a novel adaptive neural control (ANC) scheme is proposed to guarantee the predefined tracking error performance as well as the ultimate boundedness of all other closed-loop signals. In particular, only one NN is employed to approximate the lumped unknown system dynamics during the controller design. Under the satisfaction of the partial persistent excitation condition for RBF NNs, the proposed stable ANC scheme is shown to be capable of achieving knowledge acquisition, expression, and storage of unknown system dynamics. The stored knowledge is reused to develop a neural learning controller for improving the control performance of the closed-loop system. When the initial condition satisfies the predefined performance, the proposed neural learning control can still guarantee the predefined tracking performance. Simulation results on a third-order one-link robot are given to show the effectiveness of the proposed method.

Learning plays an essential role in autonomous control systems. However, how to achieve learning in the nonstationary environment for nonlinear systems is a challenging problem. In this paper, we present learning method for a class of n th-order strict-feedback systems by adaptive dynamic surface control (DSC) technology, which achieves the human-like ability of learning by doing and doing with learned knowledge. To achieve the learning, this paper first proposes stable adaptive DSC with auxiliary first-order filters, which ensures the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in a finite time. With the help of DSC, the derivative of the filter output variable is used as the neural network (NN) input instead of traditional intermediate variables. As a result, the proposed adaptive DSC method reduces greatly the dimension of NN inputs, especially for high-order systems. After the stable DSC design, we decompose the stable closed-loop system into a series of linear time-varying perturbed subsystems. Using a recursive design, the recurrent property of NN input variables is easily verified since the complexity is overcome using DSC. Subsequently, the partial persistent excitation condition of the radial basis function NN is satisfied. By combining a state transformation, accurate approximations of the closed-loop system dynamics are recursively achieved in a local region along recurrent orbits. Then, the learning control method using the learned knowledge is proposed to achieve the closed-loop stability and the improved control performance. Simulation studies are performed to demonstrate the proposed scheme can not only reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error but also greatly alleviate the computational burden because of reducing the number and complexity of NN input variables.

In this paper, we present a new method to eliminate the effect of view angle for efficient gait recognition via deterministic learning theory. The width of the binarized silhouette models the periodic deformation of human gait silhouettes. It captures the spatio-temporal characteristics of each individual, represents the dynamics of gait motion, and can sensitively reflect the variance between gait patterns across various views. The gait recognition approach consists of two phases: a training phase and a recognition phase. In the training phase, the gait dynamics underlying different individuals' gaits from different view angles are locally accurately approximated by radial basis function (RBF) neural networks. The obtained knowledge of approximated gait dynamics is stored in constant RBF networks. In order to address the problem of view change no matter the variation is small or significantly large, the training patters from different views constitute a uniform training dataset containing all kinds of gait dynamics of each individual observed across various views. In the recognition phase, a bank of dynamical estimators is constructed for all the training gait patterns. Prior knowledge of human gait dynamics represented by the constant RBF networks is embedded in the estimators. By comparing the set of estimators with a test gait pattern whose view pattern contained in the prior training dataset, a set of recognition errors are generated. The average L1norms of the errors are taken as the similarity measure between the dynamics of the training gait patterns and the dynamics of the test gait pattern. Finally, comprehensive experiments are carried out on the CASIA-B and CMU gait databases to demonstrate the effectiveness of the proposed approach.

Abstract In this paper, we extend the deterministic learning theory to sampled-data nonlinear systems. Based on the Euler approximate model, the adaptive neural network identifier with a normalized learning algorithm is proposed. It is proven that by properly setting the sampling period, the overall system can be guaranteed to be stable and partial neural network weights can exponentially converge to their optimal values under the satisfaction of the partial persistent excitation (PE) condition. Consequently, locally accurate learning of the nonlinear dynamics can be achieved, and the knowledge can be represented by using constant-weight neural networks. Furthermore, we present a performance analysis for the learning algorithm by developing explicit bounds on the learning rate and accuracy. Several factors that influence learning, including the PE level, the learning gain, and the sampling period, are investigated. Simulation studies are included to demonstrate the effectiveness of the approach.

In this paper, a rapid detection and isolation scheme for oscillation faults in a distributed nonlinear system is proposed. The distributed nonlinear system considered is modeled as a set of interconnected subsystems. First, a local learning and merging method based on deterministic learning theory is proposed to obtain knowledge of the unknown interconnections and the fault functions. Second, using learned knowledge, a bank of consensus-based dynamical estimators are constructed for each subsystem, and average L1norms of the residuals are generated to make the detection and isolation decisions. Third, a rigorous analysis for characterizing the detection and isolation capabilities of the proposed scheme is given. The attraction of the intelligence fault diagnosis approach is to give a fast response to faults using the learned knowledge and processing huge data in a dynamical and distributed manner. Simulation studies are included to demonstrate the effectiveness of the approach.

This paper studies the problem of learning from adaptive neural network (NN) control of a class of nonaffine nonlinear systems in uncertain dynamic environments. In the control design process, a stable adaptive NN tracking control design technique is proposed for the nonaffine nonlinear systems with a mild assumption by combining a filtered tracking error with the implicit function theorem, input-to-state stability, and the small-gain theorem. The proposed stable control design technique not only overcomes the difficulty in controlling nonaffine nonlinear systems but also relaxes constraint conditions of the considered systems. In the learning process, the partial persistent excitation (PE) condition of radial basis function NNs is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition and an appropriate state transformation, the proposed adaptive NN control is shown to be capable of acquiring knowledge on the implicit desired control input dynamics in the stable control process and of storing the learned knowledge in memory. Subsequently, an NN learning control design technique that effectively exploits the learned knowledge without re-adapting to the controller parameters is proposed to achieve closed-loop stability and improved control performance. Simulation studies are performed to demonstrate the effectiveness of the proposed design techniques.

This paper studies learning from adaptive neural control (ANC) for a class of pure-feedback nonlinear systems with unknown non-affine terms. The existence of the cascade structure and unknown non-affine terms makes it very difficult to achieve learning using previous methods. To overcome these difficulties, firstly, the implicit function theorem and the mean value theorem are combined to transform the closed-loop system into a semi-affine form during the control design process. Then, we decompose the stable closed-loop system into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation (PE) condition for the radial basis function (RBF) neural network (NN) is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition, accurate approximations of the closed-loop system dynamics are recursively achieved in a local region along recurrent orbits of closed-loop signals. Subsequently, the NN learning control method which effectively utilizes the learned knowledge without re-adapting to the unknown system dynamics is proposed to achieve the closed-loop stability and the improved control performance. Simulation studies are performed to demonstrate the effectiveness of the proposed scheme.

In this paper, we investigate the small fault isolation problem for a class of nonlinear uncertain systems. First, by utilizing the learned knowledge obtained through a recently proposed deterministic learning (DL) approach, a bank of estimators is constructed to represent the training normal mode and oscillation faults. Second, two isolation schemes based on the norms of residuals are provided. The occurrence of a fault can be isolated according to smallest residual principle. Rigorous analysis of the performance of the both isolation schemes is also given. The attraction of the paper lies in that an approach for fault isolation is proposed, in which the knowledge of modeling uncertainty and nonlinear faults obtained through DL is utilized to enhance the sensitivity of the isolation scheme. Simulation studies are included to demonstrate the effectiveness of the approach.

This paper presents the problems of accurate identification and learning control of ocean surface ship in uncertain dynamical environments. Thanks to the universal approximation capabilities, radial basis function neural networks (NNs) are employed to approximate the unknown ocean surface ship dynamics. A stable adaptive NN tracking controller is first designed using backstepping and Lyapunov synthesis. Partial persistent excitation (PE) condition of some internal signals in the closed-loop system is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition, the proposed adaptive NN controller is shown to be capable of accurate identification/learning of the uncertain ship dynamics in the stable control process. Subsequently, a novel NN learning control method which effectively utilizes the learned knowledge without re-adapting to the unknown ship dynamics is proposed to achieve closed-loop stability and improved control performance. Simulation studies are performed to demonstrate the effectiveness of the proposed method.

This paper studies learning from adaptive neural control (ANC) for a class of nonlinear strict-feedback systems with unknown affine terms. To achieve the purpose of learning, a simple input-to-state stability (ISS) modular ANC method is first presented to ensure the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in finite time. Subsequently, it is proven that learning with the proposed stable ISS-modular ANC can be achieved. The cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods. To overcome these difficulties, the stable closed-loop system in the control process is decomposed into a series of linear time-varying (LTV) perturbed subsystems with the appropriate state transformation. Using a recursive design, the partial persistent excitation condition for the radial basis function neural network (NN) is established, which guarantees exponential stability of LTV perturbed subsystems. Consequently, accurate approximation of the closed-loop system dynamics is achieved in a local region along recurrent orbits of closed-loop signals, and learning is implemented during a closed-loop feedback control process. The learned knowledge is reused to achieve stability and an improved performance, thereby avoiding the tremendous repeated training process of NNs. Simulation studies are given to demonstrate the effectiveness of the proposed method.

Detection of small faults is one of the most important and challenging tasks in the area of fault diagnosis. In this paper, we present an approach for the rapid detection of small oscillation faults based on a recently proposed deterministic learning (DL) theory. The approach consists of two phases: the training phase and the test phase. In the training phase, the system dynamics underlying normal and fault oscillations are locally accurately approximated through DL. The obtained knowledge of system dynamics is stored in constant radial basis function (RBF) networks. In the diagnosis phase, rapid detection is implemented. Specially, a bank of estimators are constructed using the constant RBF neural networks to represent the training normal and fault modes. By comparing the set of estimators with the test monitored system, a set of residuals are generated, and the average L(1) norms of the residuals are taken as the measure of the differences between the dynamics of the monitored system and the dynamics of the training normal mode and oscillation faults. The occurrence of a test oscillation fault can be rapidly detected according to the smallest residual principle. A rigorous analysis of the performance of the detection scheme is also given. The novelty of the paper lies in that the modeling uncertainty and nonlinear fault functions are accurately approximated and then the knowledge is utilized to achieve rapid detection of small oscillation faults. Simulation studies are included to demonstrate the effectiveness of the approach.

Recognition of temporal/dynamical patterns is among the most difficult pattern recognition tasks. In this paper, based on a recent result on deterministic learning theory, a deterministic framework is proposed for rapid recognition of dynamical patterns. First, it is shown that a time-varying dynamical pattern can be effectively represented in a time-invariant and spatially distributed manner through deterministic learning. Second, a definition for characterizing similarity of dynamical patterns is given based on system dynamics inherently within dynamical patterns. Third, a mechanism for rapid recognition of dynamical patterns is presented, by which a test dynamical pattern is recognized as similar to a training dynamical pattern if state synchronization is achieved according to a kind of internal and dynamical matching on system dynamics. The synchronization errors can be taken as the measure of similarity between the test and training patterns. The significance of the paper is that a completely dynamical approach is proposed, in which the problem of dynamical pattern recognition is turned into the stability and convergence of a recognition error system. Simulation studies are included to demonstrate the effectiveness of the proposed approach.

One of the amazing successes of biological systems is their ability to "learn by doing" and so adapt to their environment. In this paper, first, a deterministic learning mechanism is presented, by which an appropriately designed adaptive neural controller is capable of learning closed-loop system dynamics during tracking control to a periodic reference orbit. Among various neural network (NN) architectures, the localized radial basis function (RBF) network is employed. A property of persistence of excitation (PE) for RBF networks is established, and a partial PE condition of closed-loop signals, i.e., the PE condition of a regression subvector constructed out of the RBFs along a periodic state trajectory, is proven to be satisfied. Accurate NN approximation for closed-loop system dynamics is achieved in a local region along the periodic state trajectory, and a learning ability is implemented during a closed-loop feedback control process. Second, based on the deterministic learning mechanism, a neural learning control scheme is proposed which can effectively recall and reuse the learned knowledge to achieve closed-loop stability and improved control performance. The significance of this paper is that the presented deterministic learning mechanism and the neural learning control scheme provide elementary components toward the development of a biologically-plausible learning and control methodology. Simulation studies are included to demonstrate the effectiveness of the approach.