Inverting recurrent neural networks for internal model control of nonlinear systems

In this paper, we show how a set of recently derived theoretical results for recurrent neural networks can be applied to the production of an internal model control system for a nonlinear plant. The results include determination of the relative order of a recurrent neural network and invertibility of such a network. A closed loop controller is produced without the need to retrain the neural network plant model. Stability of the closed-loop controller is also demonstrated.

A practical approach for training dynamic recurrent neural networks: use of Apriori information

Presents a technique for incorporating a priori knowledge from a state space system into a neural network training algorithm. The training algorithm considered is that of chemotaxis and the networks being trained are recurrent neural networks. Incorporation of the a priori knowledge ensures that the resultant network has behaviour similar to the system which it is modelling.

Internal model control of nonlinear systems through the inversion of recurrent neural networks

Recurrent neural networks can be used for both the identification and control of nonlinear systems. This paper takes a previously derived set of theoretical results about recurrent neural networks and applies them to the task of providing internal model control for a nonlinear plant. Using the theoretical results, we show how an inverse controller can be produced from a neural network model of the plant, without the need to train an additional network to perform the inverse control.

Dynamic input/output linearization using recurrent neural networks

A dynamic recurrent neural network (DRNN) is used to input/output linearize a control affine system in the globally linearizing control (GLC) structure. The network is trained as a part of a closed loop that involves a PI controller, the goal is to use the network, as a dynamic feedback, to cancel the nonlinear terms of the plant. The stability of the configuration is guarantee if the network and the plant are asymptotically stable and the linearizing input is bounded.

Identification of nonlinear systems with a dynamic recurrent neural network

Two approaches are presented to calculate the weights for a Dynamic Recurrent Neural Network (DRNN) in order to identify the input-output dynamics of a class of nonlinear systems. The number of states of the identified network is constrained to be the same as the number of states of the plant.

Relative order defines a topology for recurrent networks

This paper uses techniques from control theory in the analysis of trained recurrent neural networks. Differential geometry is used as a framework, which allows the concept of relative order to be applied to neural networks. Any system possessing finite relative order has a left-inverse. Any recurrent network with finite relative order also has an inverse, which is shown to be a recurrent network.

Stress testing credit risk: the Great Depression scenario

By employing Moody’s corporate default and rating transition data spanning the last 90 years we explore how much capital banks should hold against their corporate loan portfolios to withstand historical stress scenarios. Specifically, we will focus on the worst case scenario over the observation period, the Great Depression. We find that migration risk and the length of the investment horizon are critical factors when determining bank capital needs in a crisis. We show that capital may need to rise more than three times when the horizon is increased from 1 year, as required by current and future regulation, to 3 years. Increases are still important but of a lower magnitude when migration risk is introduced in the analysis. Further, we find that the new bank capital requirements under the so-called Basel 3 agreement would enable banks to absorb Great Depression-style losses. But, such losses would dent regulatory capital considerably and far beyond the capital buffers that have been proposed to ensure that banks survive crisis periods without government support.

Assessment of depression, anxiety and apathy in prodromal and early Huntington disease

The Functional Rating Scale Taskforce for pre-Huntington Disease (FuRST-pHD) is a multinational, multidisciplinary initiative with the goal of developing a data-driven, comprehensive, psychometrically sound, rating scale for assessing symptoms and functional ability in prodromal and early Huntington disease (HD) gene expansion carriers. The process involves input from numerous sources to identify relevant symptom domains, including HD individuals, caregivers, and experts from a variety of fields, as well as knowledge gained from the analysis of data from ongoing large-scale studies in HD using existing clinical scales. This is an iterative process in which an ongoing series of field tests in prodromal (prHD) and early HD individuals provides the team with data on which to make decisions regarding which questions should undergo further development or testing and which should be excluded. We report here the development and assessment of the first iteration of interview questions aimed to assess Depression, Anxiety and Apathy in prHD and early HD individuals.

Relationships between changes in sustained fronto-striatal connectivity and positive affect with antidepressant treatment in major depression

Objective: Deficits in positive affect and their neural bases have been associated with major depression. However, whether reductions in positive affect result solely from an overall reduction in nucleus accumbens activity and fronto-striatal connectivity or the additional inability to sustain engagement of this network over time is unknown. The authors sought to determine whether treatment-induced changes in the ability to sustain nucleus accumbens activity and fronto-striatal connectivity during the regulation of positive affect are associated with gains in positive affect. Method: Using fMRI, the authors assessed the ability to sustain activity in reward-related networks when attempting to increase positive emotion during per- formance of an emotion regulation para- digm in 21 depressed patients before and after 2 months of antidepressant treat- ment. Over the same interval, 14 healthy comparison subjects underwent scanning as well. Results: After 2 months of treatment, self-reported positive affect increased. The patients who demonstrated the largest increases in sustained nucleus accumbens activity over the 2 months were those who demonstrated the largest increases in positive affect. In addition, the patients who demonstrated the largest increases in sustained fronto-striatal connectivity were also those who demonstrated the largest increases in positive affect when control- ling for negative affect. None of these associations were observed in healthy comparison subjects. Conclusions: Treatment-induced change in the sustained engagement of fronto- striatal circuitry tracks the experience of positive emotion in daily life. Studies examining reduced positive affect in a va- riety of psychiatric disorders might benefit from examining the temporal dynamics of brain activity when attempting to under- stand changes in daily positive affect.

Increases in prefrontal cortex activity when regulating negative emotion predicts symptom severity trajectory over six months in depression

Context: Emotion regulation is critically disrupted in depression and use of paradigms tapping these processes may uncover essential changes in neurobiology during treatment. In addition, as neuroimaging outcome studies of depression commonly utilize solely baseline and endpoint data – which is more prone to week-to week noise in symptomatology – we sought to use all data points over the course of a six month trial. Objective: To examine changes in neurobiology resulting from successful treatment. Design: Double-blind trial examining changes in the neural circuits involved in emotion regulation resulting from one of two antidepressant treatments over a six month trial. Participants were scanned pretreatment, at 2 months and 6 months posttreatment. Setting: University functional magnetic resonance imaging facility. Participants: 21 patients with Major Depressive Disorder and without other Axis I or Axis II diagnoses and 14 healthy controls. Interventions: Venlafaxine XR (doses up to 300mg) or Fluoxetine (doses up to 80mg). Main Outcome Measure: Neural activity, as measured using functional magnetic resonance imaging during performance of an emotion regulation paradigm as well as regular assessments of symptom severity by the Hamilton Rating Scale for Depression. To utilize all data points, slope trajectories were calculated for rate of change in depression severity as well as rate of change of neural engagement. Results: Those depressed individuals showing the steepest decrease in depression severity over the six months were those individuals showing the most rapid increases in BA10 and right DLPFC activity when regulating negative affect over the same time frame. This relationship was more robust than when using solely the baseline and endpoint data. Conclusions: Changes in PFC engagement when regulating negative affect correlate with changes in depression severity over six months. These results are buttressed by calculating these statistics which are more reliable and robust to week-to-week variation than difference scores.