arXiv subjects

Sandra Hirche

Publications and source records attributed to Sandra Hirche.

136 records · Page 8Linked to original sources

arXiv2018

Stable Gaussian Process based Tracking Control of Lagrangian Systems

High performance tracking control can only be achieved if a good model of the dynamics is available. However, such a model is often difficult to obtain from first order physics only. In this paper, we develop a data-driven control law that ensures closed loop stability of Lagrangian systems. For this purpose, we use Gaussian Process regression for the feed-forward compensation of the unknown dynamics of the system. The gains of the feedback part are adapted based on the uncertainty of the learned model. Thus, the feedback gains are kept low as long as the learned model describes the true system sufficiently precisely. We show how to select a suitable gain adaption law that incorporates the uncertainty of the model to guarantee a globally bounded tracking error. A simulation with a robot manipulator demonstrates the efficacy of the proposed control law.

eess.SY↗

arXiv2018

Stability of Gaussian Process State Space Models

Gaussian Process State Space Models (GP-SSMs) are a non-parametric model class suitable to represent nonlinear dynamics. They become increasingly popular in data-driven modeling approaches, i.e. when no first-order physics-based models are available. Although a GP-SSM produces well-behaved approximations and gains increasing popularity, the fundamental system dynamics are just sparsely researched. In this paper, we present stability results for the GP-SSM depending on selected covariance function employing a deterministic point of view as widely done in the literature. The focus is set on the squared exponential function which is one of the most used covariance functions for nonlinear regression. We start with calculations according to the equilibrium points of GP-SSM and continue with conditions for stability.

eess.SY↗

arXiv2018

A Multi-layer Gaussian Process for Motor Symptom Estimation in People with Parkinson's Disease

The assessment of Parkinson's disease (PD) poses a significant challenge as it is influenced by various factors which lead to a complex and fluctuating symptom manifestation. Thus, a frequent and objective PD assessment is highly valuable for effective health management of people with Parkinson's disease (PwP). Here, we propose a method for monitoring PwP by stochastically modeling the relationships between their wrist movements during unscripted daily activities and corresponding annotations about clinical displays of movement abnormalities. We approach the estimation of PD motor signs by independently modeling and hierarchically stacking Gaussian process models for three classes of commonly observed movement abnormalities in PwP including tremor, (non-tremulous) bradykinesia, and (non-tremulous) dyskinesia. We use clinically adopted severity measures as annotations for training the models, thus allowing our multi-layer Gaussian process prediction models to estimate not only their presence but also their severities. The experimental validation of our approach demonstrates strong agreement of the model predictions with these PD annotations. Our results show the proposed method produces promising results in objective monitoring of movement abnormalities of PD in the presence of arbitrary and unknown voluntary motions, and makes an important step towards continuous monitoring of PD in the home environment.

cs.LG↗

arXiv2018

Parkinson's Disease Assessment from a Wrist-Worn Wearable Sensor in Free-Living Conditions: Deep Ensemble Learning and Visualization

Parkinson's Disease (PD) is characterized by disorders in motor function such as freezing of gait, rest tremor, rigidity, and slowed and hyposcaled movements. Medication with dopaminergic medication may alleviate those motor symptoms, however, side-effects may include uncontrolled movements, known as dyskinesia. In this paper, an automatic PD motor-state assessment in free-living conditions is proposed using an accelerometer in a wrist-worn wearable sensor. In particular, an ensemble of convolutional neural networks (CNNs) is applied to capture the large variability of daily-living activities and overcome the dissimilarity between training and test patients due to the inter-patient variability. In addition, class activation map (CAM), a visualization technique for CNNs, is applied for providing an interpretation of the results.

cs.CV↗

arXiv2018

Optimal LQG Control under Delay-dependent Costly Information

In the design of closed-loop networked control systems (NCSs), induced transmission delay between sensors and the control station is an often-present issue which compromises control performance and may even cause instability. A very relevant scenario in which network-induced delay needs to be investigated is costly usage of communication resources. More precisely, advanced communication technologies, e.g. 5G, are capable of offering latency-varying information exchange for different prices. Therefore, induced delay becomes a decision variable. It is then the matter of decision maker's willingness to either pay the required cost to have low-latency access to the communication resource, or delay the access at a reduced price. In this article, we consider optimal price-based bi-variable decision making problem for single-loop NCS with a stochastic linear time-invariant system. Assuming that communication incurs cost such that transmission with shorter delay is more costly, a decision maker determines the switching strategy between communication links of different delays such that an optimal balance between the control performance and the communication cost is maintained. In this article, we show that, under mild assumptions on the available information for decision makers, the separation property holds between the optimal link selecting and control policies. As the cost function is decomposable, the optimal policies are efficiently computed.

math.OC↗

arXiv2017

Data Augmentation of Wearable Sensor Data for Parkinson's Disease Monitoring using Convolutional Neural Networks

While convolutional neural networks (CNNs) have been successfully applied to many challenging classification applications, they typically require large datasets for training. When the availability of labeled data is limited, data augmentation is a critical preprocessing step for CNNs. However, data augmentation for wearable sensor data has not been deeply investigated yet. In this paper, various data augmentation methods for wearable sensor data are proposed. The proposed methods and CNNs are applied to the classification of the motor state of Parkinson's Disease patients, which is challenging due to small dataset size, noisy labels, and large intra-class variability. Appropriate augmentation improves the classification performance from 77.54\% to 86.88\%.

cs.CV↗

arXiv2017

Object Handover Prediction using Gaussian Processes clustered with Trajectory Classification

A robotic system which approximates the user intention and appropriate complimentary motion is critical for successful human-robot interaction. %While the existing wearable sensors can monitor human movements in real-time, prediction of human movement is a significant challenge due to its highly non-linear motions optimised through the redundancy in the degrees of freedom. Here, we demonstrate robustness of the Gaussian Process (GP) clustered with a stochastic classification technique for trajectory prediction using an object handover scenario. By parametrising real 6D hand movements during human-human object handover using dual quaternions, variations of handover configurations were classified in real-time and then the remaining hand trajectory was predicted using the GP. The results highlights that our method can classify the handover configuration at an average of $43.4\%$ of the trajectory and the final hand configuration can be predicted within the normal variation of human movement. In conclusion, we demonstrate that GPs combined with a stochastic classification technique is a robust tool for proactively estimating human motions for human-robot interaction.

cs.RO↗

arXiv2016

Consensus Driven by the Geometric Mean

Consensus networks are usually understood as arithmetic mean driven dynamical averaging systems. In applications, however, network dynamics often describe inherently non-arithmetic and non-linear consensus processes. In this paper, we propose and study three novel consensus protocols driven by geometric mean averaging: a polynomial, an entropic, and a scaling-invariant protocol, where terminology characterizes the particular non-linearity appearing in the respective differential protocol equation. We prove exponential convergence to consensus for positive initial conditions. For the novel protocols we highlight connections to applied network problems: The polynomial consensus system is structured like a system of chemical kinetics on a graph. The entropic consensus system converges to the weighted geometric mean of the initial condition, which is an immediate extension of the (weighted) average consensus problem. We find that all three protocols generate gradient flows of free energy on the simplex of constant mass distribution vectors albeit in different metrics. On this basis, we propose a novel variational characterization of the geometric mean as the solution of a non-linear constrained optimization problem involving free energy as cost function. We illustrate our findings in numerical simulations.

math.DS↗

arXiv2016

Stabilizing Transmission Intervals for Nonlinear Delayed Networked Control Systems [Extended Version]

In this article, we consider a nonlinear process with delayed dynamics to be controlled over a communication network in the presence of disturbances and study robustness of the resulting closed-loop system with respect to network-induced phenomena such as sampled, distorted, delayed and lossy data as well as scheduling protocols. For given plant-controller dynamics and communication network properties (e.g., propagation delays and scheduling protocols), we quantify the control performance level (in terms of Lp-gains) as the transmission interval varies. Maximally Allowable Transfer Interval (MATI) labels the greatest transmission interval for which a prescribed Lp-gain is attained. The proposed methodology combines impulsive delayed system modeling with Lyapunov-Razumikhin techniques to allow for MATIs that are smaller than the communication delays. Other salient features of our methodology are the consideration of variable delays, corrupted data and employment of model-based estimators to prolong MATIs. The present stability results are provided for the class of Uniformly Globally Exponentially Stable (UGES) scheduling protocols. The well-known Round Robin (RR) and Try-Once-Discard (TOD) protocols are examples of UGES protocols. Finally, two numerical examples are provided to demonstrate the benefits of the proposed approach.

eess.SY↗

arXiv2012

Event-Triggered Estimation of Linear Systems: An Iterative Algorithm and Optimality Properties

This report investigates the optimal design of event-triggered estimation for first-order linear stochastic systems. The problem is posed as a two-player team problem with a partially nested information pattern. The two players are given by an estimator and an event-trigger. The event-trigger has full state information and decides, whether the estimator shall obtain the current state information by transmitting it through a resource constrained channel. The objective is to find an optimal trade-off between the mean squared estimation error and the expected transmission rate. The proposed iterative algorithm alternates between optimizing one player while fixing the other player. It is shown that the solution of the algorithm converges to a linear predictor and a symmetric threshold policy, if the densities of the initial state and the noise variables are even and radially decreasing functions. The effectiveness of the approach is illustrated on a numerical example. In case of a multimodal distribution of the noise variables a significant performance improvement can be achieved compared to a separate design that assumes a linear prediction and a symmetric threshold policy.

math.OC↗