Chaos control and synchronization, with input saturation, via recurrent neural networks.

This paper deals with the adaptive tracking problem of non-linear systems in presence of unknown parameters, unmodelled dynamics and input saturation. A high order recurrent neural network is used in order to identify the unknown system and a learning law is obtained using the Lyapunov methodology. Then a stabilizing control law for the reference tracking error dynamics is developed using the Lyapunov methodology and the Sontag control law. Tracking error boundedness is established as a function of a design parameter. The new approach is illustrated by examples of complex dynamical systems: chaos control and synchronization.     

Ground-based telescope pointing and tracking optimization using a neural controller.

Neural network models (NN) have emerged as important components for applications of adaptive control theories. Their basic generalization capability, based on acquired knowledge, together with execution rapidity and correlation ability between input stimula, are basic attributes to consider NN as an extremely powerful tool for on-line control of complex systems. By a control system point of view, not only accuracy and speed, but also, in some cases, a high level of adaptation capability is required in order to match all working phases of the whole system during its lifetime. This is particularly remarkable for a new generation ground-based telescope control system. Infact, strong changes in terms of system speed and instantaneous position error tolerance are necessary, especially in case of trajectory disturb induced by wind shake. The classical control scheme adopted in such a system is based on the proportional integral (PI) filter, already applied and implemented on a large amount of new generation telescopes, considered as a standard in this technological environment. In this paper we introduce the concept of a new approach, the neural variable structure proportional integral, (NVSPI), related to the implementation of a standard multi layer perceptron network in new generation ground-based Alt-Az telescope control systems. Its main purpose is to improve adaptive capability of the Variable structure proportional integral model, an already innovative control scheme recently introduced by authors [Proc SPIE (1997)], based on a modified version of classical PI control model, in terms of flexibility and accuracy of the dynamic response range also in presence of wind noise effects. The realization of a powerful well tested and validated telescope model simulation system allowed the possibility to directly compare performances of the two control schemes on simulated tracking trajectories, revealing extremely encouraging results in terms of NVSPI control robustness and reliability.     

Intelligent optimal control with dynamic neural networks.

The application of neural networks technology to dynamic system control has been constrained by the non-dynamic nature of popular network architectures. Many of difficulties are-large network sizes (i.e. curse of dimensionality), long training times, etc. These problems can be overcome with dynamic neural networks (DNN).In this study, intelligent optimal control problem is considered as a nonlinear optimization with dynamic equality constraints, and DNN as a control trajectory priming system. The resulting algorithm operates as an auto-trainer for DNN (a self-learning structure) and generates optimal feed-forward control trajectories in a significantly smaller number of iterations. In this way, optimal control trajectories are encapsulated and generalized by DNN. The time varying optimal feedback gains are also generated along the trajectory as byproducts. Speeding up trajectory calculations opens up avenues for real-time intelligent optimal control with virtual global feedback.We used direct-descent-curvature algorithm with some modifications (we called modified-descend-controller-MDC algorithm) for the optimal control computations. The algorithm has generated numerically very robust solutions with respect to conjugate points. The adjoint theory has been used in the training of DNN which is considered as a quasi-linear dynamic system. The updating of weights (identification of parameters) are based on Broyden-Fletcher-Goldfarb-Shanno BFGS method. Simulation results are given for an intelligent optimal control system controlling a difficult nonlinear second-order system using fully connected three-neuron DNN.     

Template based black-box optimization of dynamic neural fields

Due to their strong non-linear behavior, optimizing the parameters of dynamic neural fields is particularly challenging and often relies on expert knowledge and trial and error. In this paper, we study the ability of particle swarm optimization (PSO) and covariance matrix adaptation (CMA-ES) to solve this problem when scenarios specifying the input feeding the field and desired output profiles are provided. A set of spatial lower and upper bounds, called templates are introduced to define a set of desired output profiles. The usefulness of the method is illustrated on three classical scenarios of dynamic neural fields: competition, working memory and tracking.     

A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems

Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the “Single Network Adaptive Critic (SNAC)” is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.     

Control of neuromuscular stimulation for ambulation by complete paraplegics via artificial neural networks

The paper describes the application of a neural network (ANN) for controlling a functional neuromuscular stimulation (FNS) system to facilitate patient-responsive ambulation by paralyzed patients with traumatic, thoracic-level spinal cord injuries. The particular ANN that is employed is a modified Adaptive-Resonance-Theory (ART-1) network. It serves as a controller in an FNS system (the Parastep system) that is presently in use by approximately 500 patients worldwide (but still without ANN control) and which was the first and only FNS system approved by FDA. The proposed neural network discriminates above-lesion upper-trunk electromyographic (EMG) time series to activate standing and walking functions under FNS and controls FNS stimuli levels using response-EMG signals. For this particular application, several modifications are introduced into the standard ART-1 ANN. First, a modified on-line learning rule is proposed. The new rule assures bi-directional modification of the stored patterns and prevents noise interference. Second, a new reset rule is proposed, which prevents 'exact matching' when the input is a subset of the chosen pattern. A single ART-1-based structure is being applied to solving two problems, namely (1) signal pattern recognition and limb function determination, and (2) control of stimulation levels. This also facilitates ambulation of paraplegics under FNS, with adequate patient interaction in initial system training, retraining the network when needed, and in allowing patient's manual over-ride in the case of error, where any manual over-ride serves as a re-training input to the neural network. The ANN control facilitates continuous update of control settings during normal use, without formal retraining.     

Proper orthogonal decomposition based optimal neurocontrol synthesis of a chemical reactor process using approximate dynamic programming.

The concept of approximate dynamic programming and adaptive critic neural network based optimal controller is extended in this study to include systems governed by partial differential equations. An optimal controller is synthesized for a dispersion type tubular chemical reactor, which is governed by two coupled nonlinear partial differential equations. It consists of three steps: First, empirical basis functions are designed using the 'Proper Orthogonal Decomposition' technique and a low-order lumped parameter system to represent the infinite-dimensional system is obtained by carrying out a Galerkin projection. Second, approximate dynamic programming technique is applied in a discrete time framework, followed by the use of a dual neural network structure called adaptive critics, to obtain optimal neurocontrollers for this system. In this structure, one set of neural networks captures the relationship between the state variables and the control, whereas the other set captures the relationship between the state and the costate variables. Third, the lumped parameter control is then mapped back to the spatial dimension using the same basis functions to result in a feedback control. Numerical results are presented that illustrate the potential of this approach. It should be noted that the procedure presented in this study can be used in synthesizing optimal controllers for a fairly general class of nonlinear distributed parameter systems.     

Control of neuromuscular stimulation for ambulation by complete paraplegics via artificial neural networks

Abstract

The paper describes the application of a neural network (ANN) for controlling a functional neuromuscular stimulation (FNS) system to facilitate patient-responsive ambulation by paralyzed patients with traumatic, thoracic-level spinal cord injuries. The particular ANN that is employed is a modified Adaptive-ResonanceTheory (ART-1) network. It serves as a controller in an FNS system (the Parastep system) that is presently in use by approximately 500 patients worldwide (but still without ANN control) and which was the first and only FNS system approved by FDA. The proposed neural network discriminates above-lesion upper-trunk electromyographic (EMG) time series to activate standing and walking functions under FNS and controls FNS stimuli levels using response-EMG signals. For this particular application, several modifications are introduced into the standard ART-1 ANN. First, a modified on-line learning rule is proposed. The new rule assures bi-directional modification of the stored patterns and prevents noise interference. Second, a new reset rule is proposed, which prevents 'exact matching' when the input is a subset of the chosen pattern. A single ART-1-based structure is being applied to solving two problems, namely (1) signal pattern recognition and limb function determination, and (2) control of stimulation levels. This also facilitates ambulation of paraplegics under FNS, with adequate patient interaction in initial system training, retraining the network when needed, and in allowing patient's manual over-ride in the case of error, where any manual over-ride serves as a re-training input to the neural network. The ANN control facilitates continuous update of control settings during normal use, without formal retraining. [Neurol Res 2001; 23: 472-481]     

经颅磁刺激验证初级运动皮质神经活动与手指力量的相关性

A better understanding of the neural mechanisms of finger-force regulation can help to explain the relationship between the central nervous system and nerve-muscle force, as well as assist in motor functional rehabilitation and the development robot hand designs. In the present study, 11 healthy volunteers performed a different target force-tracking task, which involved the index finger alone, index and middle finger together, and the combination of four fingers (i.e., index, middle, ring, and little). The target force trace corresponded to 3 levels of 20% maximal voluntary changes (MVC), 30% MVC, and 40% MVC in 20 seconds. In the test, an unexpected single 120% motor threshold transcranial magnetic stimulation was applied to the primary motor cortex (M1) during force tracking. Results revealed that peak force changes increased with increasing background force and the number of involved task fingers. These results demonstrate that M1 neural activities correlate with finger-force production, and M1 plays a role in finger-force control. Moreover, different neuronal networks were required for different finger patterns; a complicated task required multi-finger combinations and a complicated neuronal network comprised a large number of neurons.     

Neural measures of dynamic changes in attentive tracking load

In everyday life, we often need to track several objects simultaneously, a task modeled in the laboratory using the multiple-object tracking (MOT) task [Pylyshyn, Z., & Storm, R. W. Tracking multiple independent targets: Evidence for a parallel tracking mechanism. Spatial Vision, 3, 179-197, 1988]. Unlike MOT, however, in life, the set of relevant targets tends to be fluid and change over time. Humans are quite adept at "juggling" targets in and out of the target set [Wolfe, J. M., Place, S. S., & Horowitz, T. S. Multiple object juggling: Changing what is tracked during extended MOT. Psychonomic Bulletin & Review, 14, 344-349, 2007]. Here, we measured the neural underpinnings of this process using electrophysiological methods. Vogel and colleagues [McCollough, A. W., Machizawa, M. G., & Vogel, E. K. Electrophysiological measures of maintaining representations in visual working memory. Cortex, 43, 77-94, 2007; Vogel, E. K., McCollough, A. W., & Machizawa, M. G. Neural measures reveal individual differences in controlling access to working memory. Nature, 438, 500-503, 2005; Vogel, E. K., & Machizawa, M. G. Neural activity predicts individual differences in visual working memory capacity. Nature, 428, 748-751, 2004] have shown that the amplitude of a sustained lateralized negativity, contralateral delay activity (CDA) indexes the number of items held in visual working memory. Drew and Vogel [Drew, T., & Vogel, E. K. Neural measures of individual differences in selecting and tracking multiple moving objects. Journal of Neuroscience, 28, 4183-4191, 2008] showed that the CDA also indexes the number of items being tracking a standard MOT task. In the current study, we set out to determine whether the CDA is a signal that merely represents the number of objects that are attended during a trial or a dynamic signal capable of reflecting on-line changes in tracking load during a single trial. By measuring the response to add or drop cues, we were able to observe dynamic changes in CDA amplitude. The CDA appears to rapidly represent the current number of objects being tracked. In addition, we were able to generate some initial estimates of the time course of this dynamic process.     

Fronto‐cingulate effective connectivity in obsessive compulsive disorder: A study with fMRI and dynamic causal modeling

Evidence suggests that obsessive compulsive disorder (OCD) is associated with an overactive error control system. A key role in error detection and control has been ascribed to the fronto‐cingulate system. However, the exact functional interplay between the single components of this network in OCD is largely unknown. Therefore, the present study combined a univariate data analysis and effective connectivity analysis using dynamic causal modeling (DCM) to examine error control in 21 patients with OCD and 21 matched healthy controls. All subjects performed an adapted version of the Stroop color‐word task while undergoing fMRI scans. Enhanced activation in the fronto‐cingulate system could be detected in OCD patients during the incongruent task condition. Additionally, task‐related modulation of effective connectivity from the dorsal ACC to left DLPFC was significantly stronger in OCD patients. These findings are consistent with an overactive error control system in OCD subserving suppression of prepotent responses during decision‐making. Hum Brain Mapp, 2010. © 2010 Wiley‐Liss, Inc.     

Optimal control of unknown affine nonlinear discrete-time systems using offline-trained neural networks with proof of convergence

The optimal control of linear systems accompanied by quadratic cost functions can be achieved by solving the well-known Riccati equation. However, the optimal control of nonlinear discrete-time systems is a much more challenging task that often requires solving the nonlinear Hamilton–Jacobi–Bellman (HJB) equation. In the recent literature, discrete-time approximate dynamic programming (ADP) techniques have been widely used to determine the optimal or near optimal control policies for affine nonlinear discrete-time systems. However, an inherent assumption of ADP requires the value of the controlled system one step ahead and at least partial knowledge of the system dynamics to be known. In this work, the need of the partial knowledge of the nonlinear system dynamics is relaxed in the development of a novel approach to ADP using a two part process: online system identification and offline optimal control training. First, in the system identification process, a neural network (NN) is tuned online using novel tuning laws to learn the complete plant dynamics so that a local asymptotic stability of the identification error can be shown. Then, using only the learned NN system model, offline ADP is attempted resulting in a novel optimal control law. The proposed scheme does not require explicit knowledge of the system dynamics as only the learned NN model is needed. The proof of convergence is demonstrated. Simulation results verify theoretical conjecture.     

A what-and-where fusion neural network for recognition and tracking of multiple radar emitters.

A neural network recognition and tracking system is proposed for classification of radar pulses in autonomous Electronic Support Measure systems. Radar type information is considered with position-specific information from active emitters in a scene. Type-specific parameters of the input pulse stream are fed to a neural network classifier trained on samples of data collected in the field. Meanwhile, a clustering algorithm is used to separate pulses from different emitters according to position-specific parameters of the input pulse stream. Classifier responses corresponding to different emitters are separated into tracks, or trajectories, one per active emitter, allowing for more accurate identification of radar types based on multiple views of emitter data along each emitter trajectory. Such a What-and-Where fusion strategy is motivated by a similar subdivision of labor in the brain. The fuzzy ARTMAP neural network is used to classify streams of pulses according to radar type using their functional parameters. Simulation results obtained with a radar pulse data set indicate that fuzzy ARTMAP compares favorably to several other approaches when performance is measured in terms of accuracy and computational complexity. Incorporation into fuzzy ARTMAP of negative match tracking (from ARTMAP-IC) facilitated convergence during training with this data set. Other modifications improved classification of data that include missing input pattern components and missing training classes. Fuzzy ARTMAP was combined with a bank of Kalman filters to group pulses transmitted from different emitters based on their position-specific parameters, and with a module to accumulate evidence from fuzzy ARTMAP responses corresponding to the track defined for each emitter. Simulation results demonstrate that the system provides a high level of performance on complex, incomplete and overlapping radar data.     

Neural Network–Based Event-Triggered Adaptive Control Algorithms for Uncertain Nonlinear Systems with Actuator Failures

The adaptive control for strict-feedback nonlinear systems has drawn a lot of attention in various communities. Since neural network is a useful universal-approximator to approximate unknown plant model, the neural network–based adaptive control for nonlinear systems has attracted substantial interest over decades. Furthermore, to reduce the controller updating and save the control resource, the event-triggered mechanism has been widely applied. In this paper, the RBF neural network is applied to construct the state and composite disturbance observers and the back-stepping and Lyapunov-like method are applied to design the event-triggered adaptive controller. The theoretical framework of adaptive fault-tolerant control issue for strict-feedback nonlinear system that suffer from both unknown mismatched disturbance and actuator failures is formulated. This paper comes up with a novel event-triggered control strategy to guarantee that the tracking issue is resolved with better desired performance. In this study, a unified theoretical mechanism is developed to tackle the case where some factors consisting of unknown state variables, unknown mismatched disturbance, and actuator failures as well as event-triggered effects are merged together. We expect to extend the proposed method for the self-triggered case.

     

Neurocontroller using dynamic state feedback for compensatory control

A common technique in neurocontrol is that of controlling a plant by static state feedback using the plant's inverse dynamics, which is approximated through a learning process. It is well known that in this control mode even small approximation errors or, which is the same, small perturbations of the plant may lead to instability. Here, a novel approach is proposed to overcome the problem of instability by using the inverse dynamics both for the static and for the error-compensating dynamic state feedback control. This scheme is termed SDS feedback control. It is shown that as long as the error of the inverse dynamics model is “signproper” the SDS feedback control is stable, i.e., the error of tracking may be kept small. The proof is based on a modification of Liapunov's second method. The problem of on-line learning of the inverse dynamics when using the controller simultaneously for both forward control and for dynamic feedback is dealt with, as are questions related to noise sensitivity and robust control of robotic manipulators. Simulations of a simplified sensorimotor loop serve to illustrate the approach.     

Functional networks for cognitive control in a stop signal task: independent component analysis

Cognitive control is a critical executive function of the human brain. Many studies have combined general linear modeling and the stop signal task (SST) to delineate the component processes of cognitive control. For instance, by contrasting stop success (SS) and stop error (SE) trials in the SST, investigators examined the neural processes underlying stop signal inhibition (SS > SE) and error processing (SE > SS). To complement this parameterized approach, here, we employed a data-driven method--independent component analysis (ICA)--to elucidate neural networks and the relationship between neural networks subserving cognitive control. In 59 adults performing the SST during fMRI, we characterized six independent components with ICA. These functional networks, temporally sorted for go success, SS, and SE trials as the events of interest, included a motor cortical network for motor preparation and execution; a right fronto-parietal network for attentional monitoring; a left fronto-parietal network for response inhibition; a midline cortico-subcortical network for error processing; a cuneus-precuneus network for behavioral engagement; and a "default" network for self-referential processing. Across subjects the event-associated weights of these functional networks showed a distinct pattern of correlation. These results provide new insight into the component processes of cognitive control.     

A self-stabilizing MSA algorithm in high-dimension data stream

Minor subspace analysis (MSA) is a statistical method for extracting the subspace spanned by all the eigenvectors associated with the minor eigenvalues of the autocorrelation matrix of a high-dimension vector sequence. In this paper, we propose a self-stabilizing neural network learning algorithm for tracking minor subspace in high-dimension data stream. Dynamics of the proposed algorithm are analyzed via a corresponding deterministic continuous time (DCT) system and stochastic discrete time (SDT) system methods. The proposed algorithm provides an efficient online learning for tracking the MS and can track an orthonormal basis of the MS. Computer simulations are carried out to confirm the theoretical results.     

Brain network dynamics during error commission

Previous studies suggest that the anterior cingulate and other prefrontal brain regions might form a functionally-integrated error detection network in the human brain. This study examined whole brain functional connectivity to both correct and incorrect button presses using independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data collected from 25 adolescent and 25 adult healthy participants (ages 11-37) performing a visual Go/No-Go task. Correct responses engaged a network comprising left lateral prefrontal cortex, left postcentral gyrus/inferior parietal lobule, striatum, and left cerebellum. In contrast, a similar network was uniquely engaged during errors, but this network was not integrated with activity in regions believed to be engaged for higher-order cognitive control over behavior. A medial/dorsolateral prefrontal-parietal neural network responded to all No-Go stimuli, but with significantly greater activity to errors. ICA analyses also identified a third error-related circuit comprised of anterior temporal lobe, limbic, and pregenual cingulate cortices, possibly representing an affective response to errors. There were developmental differences in error-processing activity within many of these neural circuits, typically reflecting greater hemodynamic activation in adults. These findings characterize the spatial structure of neural networks underlying error commission and identify neurobiological differences between adolescents and adults.     

Neural tracking in infants – An analytical tool for multisensory social processing in development

Humans are born into a social environment and from early on possess a range of abilities to detect and respond to social cues. In the past decade, there has been a rapidly increasing interest in investigating the neural responses underlying such early social processes under naturalistic conditions. However, the investigation of neural responses to continuous dynamic input poses the challenge of how to link neural responses back to continuous sensory input. In the present tutorial, we provide a step-by-step introduction to one approach to tackle this issue, namely the use of linear models to investigate neural tracking responses in electroencephalographic (EEG) data. While neural tracking has gained increasing popularity in adult cognitive neuroscience over the past decade, its application to infant EEG is still rare and comes with its own challenges. After introducing the concept of neural tracking, we discuss and compare the use of forward vs. backward models and individual vs. generic models using an example data set of infant EEG data. Each section comprises a theoretical introduction as well as a concrete example using MATLAB code. We argue that neural tracking provides a promising way to investigate early (social) processing in an ecologically valid setting.     

Discrete-time online learning control for a class of unknown nonaffine nonlinear systems using reinforcement learning

In this paper, a reinforcement-learning-based direct adaptive control is developed to deliver a desired tracking performance for a class of discrete-time (DT) nonlinear systems with unknown bounded disturbances. We investigate multi-input–multi-output unknown nonaffine nonlinear DT systems and employ two neural networks (NNs). By using Implicit Function Theorem, an action NN is used to generate the control signal and it is also designed to cancel the nonlinearity of unknown DT systems, for purpose of utilizing feedback linearization methods. On the other hand, a critic NN is applied to estimate the cost function, which satisfies the recursive equations derived from heuristic dynamic programming. The weights of both the action NN and the critic NN are directly updated online instead of offline training. By utilizing Lyapunov’s direct method, the closed-loop tracking errors and the NN estimated weights are demonstrated to be uniformly ultimately bounded. Two numerical examples are provided to show the effectiveness of the present approach.