Control relevant model reduction and controller synthesis for complex dynamical systems

Research area and Problem formulation: For the control of large scale dynamical systems, complex mathematical models are used to describe the most dominant physical phenomena in sufficient detail. The controller to be designed needs to have short computation times, since it needs to be implemented in the control loop that is running in real-time, and hence needs to have a lower complexity than the mathematical model representing the dynamical system. There are two classical approaches for obtaining low order controllers. Either by first approximating the model using model reduction strategies and inferring a low order controller based on this approximation, or by directly designing a controller for the complex model and applying a reduction strategy to reduce the controller complexity. With the common model reduction strategies, both approaches have the potential disadvantage of losing relevant information for the controller in such a way that the interconnection of the controller with the original system does not have the desired performance. Similar problems occur in the design of observers for complex dynamical systems, which are used to estimate signals that are not directly measurable, and also have to be implemented in real-time. Methodology: This research aims to develop model reduction strategies that prevent these problems by providing explicit guarantees on the performance of controlled systems. The following two methodologies have been investigated: i. This methodology involves first representing the (complex) controlled system, approximating it by an efficient reduction technique and then synthesizing a controller of low complexity. ii. This methodology develops model reduction strategies that maintain control relevant information in the approximation process in such a way that a controller (or observer) designed using the approximated system, exhibits explicit guarantees on (controlled) performance. Contributions: i. We have addressed the design of models that describe the desired closed-loop system for different control and observer design problems. ii. We have provided novel results on the representation of systems with square integrable trajectories in the behavioral framework, extended this theory to rational representations, and we have provided novel computational algorithms that can be used for the synthesis of controllers using this approach. iii. We have developed model reduction strategies that keep the design of controllers and observers invariant, and ensure that disturbances on the input of the system have no influence on measurable outputs or estimated signals of the closed-loop system. Applications Part of this research has been performed at TNO, Integrated Vehicle Safety, in Helmond, where we have shown that the problem of losing control-relevant information using the two classical approaches occurs in applications in industry. For future safety systems in cars, a complex mathematical model that describes the kinematic behavior of a driver has been developed. For this model, the active muscular behavior is included by interconnection with controllers, which are based on the derived complex model. The model describing the complete active kinematic behavior, which is the interconnection of the controllers with the complex passive model, needs to be simulated in-vehicle, and therefore needs to be fast. We have shown that our proposed methodologies result in a better performance than when compared to the classical strategies

On the problem of model reduction in the gap metric

Abstract-This paper deals with the model reduction problem where, for a given linear time-invariant dynamical system of complexity n, a simpler system of complexity r < n is desired such that the gap between their respective behaviors is minimized. We describe dynamical systems as closed, shift invariant subspaces of H + 2 , represented as kernels of rational multiplicative operators that are anti-stable rational elements of RH − ∞ . Contrary to other approaches this enables to reduce autonomous behaviors. In this paper we will give upper-and lower bounds for the minimal gap between a rational behavior and its optimal approximation in this system class. Bounds are given in terms of its Hankel Singular Values. These bounds only depend on the given system and can be computed in advance due to the use of rational operators describing the dynamical systems. This will be illustrated by a simple example. I. PRELIMINARIES In this paper, dynamical systems are described using the behavioral approach. In the general behavioral framework, introduced by Willems et. al., behaviors are represented by polynomial differential operators that impose restrictions on infinitely smooth trajectories. In this paper, trajectories do not have to be infinitely smooth, but we assume them to be square integrable and to belong to Instead of viewing trajectories in the time domain, we will use a frequency domain approach. Therefore, trajectories are equivalently viewed as elements of the Hardy space H + 2 , that is defined as |f (σ + jω)| 2 dω and where | · | denotes the Euclidean norm. This is a subspace of the Lebesgue space L 2 , which is the Laplace transform of the Hilbert space L 2 of square integrable functions on R. To be able to apply restrictions on H (1) Note that B = ker Π + P , where Π + is the canonical projection from L 2 to H + 2 . We refer to (1) as the behavior defined by P , and to P as a kernel representation of B. The class of all systems that can be represented as (1) will be denoted by B. In the frequency domain, the τ -shift operator for trajectories w ∈ H + 2 is defined as is the inverse Laplace transform of w. (2) is referred to as a left shift if τ < 0 and to a right shift if τ > 0. For B as in II. PROBLEM FORMULATION To formalize a model reduction problem, we need to have a distance measure in B between any two elements, together with a measure for complexity of dynamical systems in B. In this section, we formalize both and then formulate the problem of model reduction that is discussed in the remainder of this paper. A. Distance Measure: the Gap As shown in earlier wor

The contribution of animal models to understanding the role of the immune system in human idiopathic pulmonary fibrosis

Pulmonary fibrosis occurs in a heterogeneous group of lung disorders and is characterised by an excessive deposition of extracellular matrix proteins within the pulmonary interstitium, leading to impaired gas transfer and a loss of lung function. In the past 10 years, there has been a dramatic increase in our understanding of the immune system and how it contributes to fibrogenic processes within the lung. This review will compare some of the models used to investigate the pathogenesis and treatment of pulmonary fibrosis, in particular those used to study immune cell pathogenicity in idiopathic pulmonary fibrosis, highlighting their advantages and disadvantages in dissecting human disease

Time-of-flight electron energy loss spectroscopy using TM110 deflection cavities

We demonstrate the use of two TM110 resonant cavities to generate ultrashort\u3cbr/\u3eelectron pulses and subsequently measure electron energy losses in a time-of-flight type of setup. The method utilizes two synchronized microwave cavities separated by a drift space of 1.45 m. The setup has an energy resolution of 1262 eV FWHM at 30 keV, with an upper limit for the temporal resolution of 2.760.4 ps. Both the time and energy resolution are currently limited by the brightness of the tungsten filament electron gun used. Through simulations, it is shown that an energy resolution of 0.95 eV and a temporal resolution of 110 fs can be achieved using an electron gun with a higher brightness. With this, a new method is provided for time-resolved electron spectroscopy without the need for elaborate laser setups or expensive magnetic spectrometers

Memory complaints in patients with normal cognition are associated with smaller hippocampal volumes

We aimed to investigate volumetry of the medial temporal lobe in patients with subjective memory complaints without any cognitive impairment. This study included 20 patients with subjective memory complaints and normal cognitive function and 28 controls without memory complaints. Volumes of the hippocampus and parahippocampal gyrus (PHG) were measured using coronal T1weighted MR images. Cognitive functions were assessed us-ing the Cambridge Cognitive Examination. Depressive symptoms were assessed using the Geriatric Depression Scale. Differences between groups were analysed using T-tests. Patients with subjective memory complaints had a higher education and more depressive symptoms than controls (p < 0.01). Moreover, they had smaller left hippocampal volumes than controis (p < 0.01). There were no differences between groups in the volume of the right hippocampus or PHG. There was a moderate association between the volume of left hippocampus and left PHG and memory-score (r = 0.32, p = 0.03; r = 0.34,p = 0.02). We concluded that memory complaints in patients without any cognitive impairment were associated with smaller left hippocampal volumes and more depressive symptoms. These preliminary results suggest that memory complaints may reflect minimal brain deficits associated with impending dementia, depression or a combination of both disorders