Achim Hekler

Optimal sequence-based LQG control over TCP-like networks subject to random transmission delays and packet losses

This paper addresses the problem of sequence-based controller design for Networked Control Systems (NCS), where control inputs and measurements are transmitted over TCP-like network connections that are subject to random transmission delays and packet losses. To cope with the network effects, the controller not only sends the current control input to the actuator, but also a sequence of predicted control inputs at every time step. In this setup, we derive an optimal solution to the Linear Quadratic Gaussian (LQG) control problem and prove that the separation principle holds. Simulations demonstrate the improved performance of this optimal controller compared to other sequence-based approaches.

Sequence-based control for networked control systems based on virtual control inputs

In this paper, we address the problem of controlling a system over an unreliable UDP-like network that is affected by time-varying delays and randomly occurring packet losses. A major challenge of this setup is that the controller just has uncertain information about the control inputs actually applied by the actuator. The key idea of this work is to model the uncertain control inputs by random variables, the so-called virtual control inputs, which are characterized by discrete probability density functions. Subject to this probabilistic description, a novel, easy to implement sequence-based control approach is proposed that extends any given state feedback controller designed without consideration of the network-induced disturbances. The high performance of the proposed controller is demonstrated by means of Monte Carlo simulation runs with an inverted pendulum on a cart.

Stochastic nonlinear model predictive control based on progressive density simplification

Increasing demand for Nonlinear Model Predictive Control with the ability to handle highly noise-corrupted systems has recently given rise to stochastic control approaches. Besides providing high-quality results within a noisy environment, these approaches have one problem in common, namely a high computational demand and, as a consequence, generally a short prediction horizon. In this paper, we propose to reduce the computational complexity of prediction and value function evaluation within the control horizon by simplifying the system progressively down to the deterministic case. Approximation of occurring probability densities by a specific representation, the deterministic Dirac mixture density, with a decreasing resolution (i.e., approximation quality) leads via natural decomposition to a point estimate and thus, can be treated in a deterministic manner. Hence, calculation of the remaining time steps requires considerably less computation time.

Open-loop feedback control of nonlinear stochastic systems based on deterministic dirac mixture densities

The main problem of stochastic nonlinear model predictive control (SNMPC) is that the equations for state prediction and calculation of the expected reward are in general not solvable in closed form. A popular approach is to approximate the occurring continuous probability density functions by a discrete density representation, which allows an analytical solution of the SNMPC equations. In this paper, we propose to draw the samples not randomly as in Monte Carlo based methods, but systematically by minimizing a distance measure. In doing so, fewer components are generally required to represent the underlying probability density while achieving the same approximation quality. Especially if the evaluation of the expected reward is computationally expensive, this property affects the complexity of computation significantly. By means of a path planning problem, we have substantiated this statement with several simulation runs.

Robust model predictive control with least favorable measurements

Closed-loop model predictive control of nonlinear systems, whose internal states are not completely accessible, incorporates the impact of possible future measurements into the planning process. When planning ahead in time, those measurements are not known, so the closed-loop controller accounts for the expected impact of all potential measurements. We propose a novel conservative closed-loop control approach that does not calculate the expected impact of all measurements, but solely considers the single future measurement that has the worst impact on the control objective. In doing so, the model predictive controller guarantees robustness even in the face of high disturbances acting upon the system. Moreover, by considering only a single dedicated measurement, the complexity of closed-loop control is reduced significantly. The capabilities of our approach are evaluated by means of a path planning problem for a mobile robot.

Detection of ectopic beats in single channel electrocardiograms

Automatic detection of ectopic beats is an important procedure for electrocardiogram (ECG) processing and analysis. This paper presents a new method for detection of ventricular (VEB) and supraventricular (SVEB) ectopic beats in single channel electrocardiograms. To extract morphological and rhythmical features we approximated the signal of each heartbeat using a sum of three Gaussians and rotated the Poincare plot by −45 degrees. The nine parameters of the Gaussians and the new coordinates of the rotated Poincare plot formed together the feature vector. At the beginning of the classification a test was carried out, whether the ECG signal included cardiac arrhythmias like atrial fibrillation. If this was the case, agglomerative hierarchical clustering would be applied on the approximated signals of heartbeats. Then the clusters were classified according to different aspects. If the result of the test was negative, a threshold algorithm exclusively based on rhythmical information would be performed. In contrast to other studies the proposed approach weights rhythmical and morphological parameters depending on the existence of arrhythmia. We tested our approach on 44 files of the MIT/BIH arrhythmia database providing an annotated collection of normal and ectopic beats. The sensitivity of our method is 96.9% for VEB and 90.9% for SVEB, the specificity 97.6%.

Stochastic nonlinear open-loop feedback control with guaranteed error bounds using compactly supported wavelets

In model predictive control, a high quality of control can only be achieved if the model of the system reflects the real-world process as precisely as possible. Therefore, the controller should be capable of both handling a nonlinear system description and systematically incorporating uncertainties affecting the system. Since stochastic nonlinear model predictive control (SNMPC) problems in general cannot be solved in closed form, either the system model or the occurring densities have to be approximated. In this paper, we present an SNMPC framework that approximates the densities and the reward function by their wavelet expansions. Due to the few requirements on the shape and family of the densities or reward function, the presented technique can be applied to a large class of SNMPC problems. For accelerating the optimization, we additionally present an efficient technique, so-called dynamic thresholding, which neglects insignificant coefficients, while at the same time guaranteeing that the optimal control input is still obtained. The capabilities of the proposed approach are demonstrated by simulations and comparisons to a particle-based SNMPC method are conducted.