Stability analysis of an inverse parabolic problem with discontinuous variable coefficient

2011 ◽  
Vol 141 (5) ◽  
pp. 975-999 ◽  
Author(s):  
M. Di Cristo ◽  
S. Vessella
Keyword(s):  
Continuous Dependence ◽  
Variable Coefficient ◽  
Parabolic Problem ◽  
A Priori ◽  
Time Varying ◽  
Variable Function ◽  
Thermal Measurements ◽  
Logarithmic Type ◽  
Anomalous Region ◽  
Inverse Parabolic Problem

We consider a time-varying inclusion in a thermal conductor specimen. In particular, the thermal conductivity is a variable function depending on space and time with a jump of discontinuity along the interface of the unknown anomalous region. Provided with some a priori information on the conductivity and its support, we study the continuous dependence of the inclusion from infinitely many thermal measurements taken on an open portion of the boundary of our specimen. We prove a rate of continuity of logarithmic type showing, in addition, its optimality.

scholarly journals Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 85
Author(s):  
Andreas Rauh ◽  
Julia Kersten
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
A Priori ◽  
Real Life ◽  
Reachability Analysis ◽  
Interval Methods ◽  
Space Representation ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Similarity Transformations

Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

scholarly journals Associations Between a Priori-Defined Diet Quality Indices and Survival in a Longitudinal Cohort Study of Head and Neck Squamous Cell Carcinoma Patients

2020 ◽  
Vol 4 (Supplement_2) ◽  
pp. 336-336
Author(s):  
Christian Maino Vieytes ◽  
Alison Mondul ◽  
Katie Zarins ◽  
Gregory Wolf ◽  
Laura Rozek ◽  
...  
Keyword(s):  
Squamous Cell Carcinoma ◽  
Cohort Study ◽  
Cell Carcinoma ◽  
Head And Neck ◽  
Ketogenic Diet ◽  
Squamous Cell ◽  
Diet Quality ◽  
A Priori ◽  
Time Varying ◽  
Quality Indices

Abstract Objectives Use of diet quality indices has become increasingly common. However, there are no studies, to date, that have examined the relationship of a priori indices with prognostic outcomes in the head and neck squamous cell carcinoma (HNSCC) population. The purpose of this analysis was to examine associations between diet quality in the first two years after diagnosis and mortality in a sample of HNSCC patients. Methods This was a secondary analysis of 396 newly diagnosed HNSCC patients recruited from the University of Michigan Head and Neck Specialized Programs of Research Excellence longitudinal cohort study. Participants completed food frequency questionnaires (FFQs) and health surveys at the time of diagnosis, 1-year post-diagnosis (n = 341), and 2-years post-diagnosis (n = 217). Cox Proportional Hazards models assessed associations between diet quality index score (categorized as quintiles and modeled as a time-varying covariate), all-cause-, and cancer-specific mortality. The indices chosen for examination included the Alternative Mediterranean Diet Index (aMED), Alternate Healthy Eating Index-2010 (AHEI-2010), Dietary Approaches to Stop Hypertension (DASH), and a ketogenic diet index. All models adjusted for age, sex, BMI, HPV-status, tumor site, stage, education, smoking, drinking, and total calorie intake (modeled as time-varying). Results There were 105 total deaths and 67 cancer-related deaths, during a median follow-up time of 3 years. Higher aMED and AHEI-2010 scores were significantly inversely associated with all-cause (HRaMED 0.33, 95% CI: 0.18–0.59, ptrend < 0.0001; HRaHEI 0.34, 95% CI: 0.20–0.58, ptrend < 0.001) and cancer-related mortality (HRaMED 0.28, 95% CI: 0.13–0.59, ptrend = 0.001; HRaHEI 0.35, 95% CI: 0.18–0.71, ptrend < 0.0001). There were no significant associations found with the DASH index. The ketogenic diet index showed an attenuated significant inverse association for the fifth quintile, but there was a lack of linear trend. Conclusions Developing and testing interventions that follow food and quantity guidelines emphasized by the aMED and AHEI-2010 diet quality indices among HNSCC survivors, is warranted. Funding Sources NIH/NCI and a USDA/NIFA Hatch Project.

scholarly journals Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 228
Author(s):  
Rasoul Shafipour ◽  
Gonzalo Mateos
Keyword(s):  
Inverse Problem ◽  
Covariance Matrix ◽  
A Priori ◽  
Dynamic Network ◽  
Streaming Data ◽  
Optimal Time ◽  
Time Varying ◽  
Graph Learning ◽  
Topology Inference ◽  
Diffusion Dynamics

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

Positioning and Vibration Control of Time-Varying Vibration Systems by Means of Nonstationary Optimal Regulator

2003 ◽  
Author(s):  
Susumu Hara ◽  
Kenji Nakamura ◽  
Tatsuo Narikiyo
Keyword(s):  
Wavelet Analysis ◽  
Vibration Control ◽  
A Priori ◽  
Gain Scheduling ◽  
Time Varying ◽  
Vibration System ◽  
Line Measurement ◽  
Time Varying Parameter ◽  
On Line ◽  
Optimal Regulator

This study discusses the positioning and vibration control of time-varying vibration systems whose parameters are time-varying. We assume that the time-varying parameter of a vibration system is detected by an on-line measurement or Wavelet analysis. This paper treats two control methods based on nonstationary optimal regulators (NORs) for this problem. The first method is a gain-scheduling of NORs. An actual controller is obtained by the interpolation of plural NORs designed a priori. The other one is an NOR design based on Wavelet analysis of the vibration system. In the second case, single NOR derived from the analysis result is applied. This study shows the effectiveness of these methods by numerical calculations and experiments. From the comparison of these methods, this paper suggests suitable applications of NOR according to the characteristics of each control problem.

scholarly journals On a class of nonclassical hyperbolic equations with nonlocal conditions

2002 ◽  
Vol 15 (2) ◽  
pp. 125-140 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Continuous Dependence ◽  
Hyperbolic Equations ◽  
Initial Conditions ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
A Priori Estimate ◽  
Analysis Method ◽  
Priori Estimate ◽  
Abstract Formulation

This paper proves the existence, uniqueness and continuous dependence of a solution of a class of nonclassical hyperbolic equations with nonlocal boundary and initial conditions. Results are obtained by using a functional analysis method based on an a priori estimate and on the density of the range of the linear operator corresponding to the abstract formulation of the considered problem.

On the Design of Finite Time Settling Control for Linear Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 359-368 ◽  
Author(s):  
S. Choura
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Finite Time ◽  
Linear Time ◽  
Minimum Energy ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Final State ◽  
Variable Function ◽  
Time Varying Systems

The design of controllers combining feedback and feedforward for the finite time settling control of linear systems, including linear time-varying systems, is considered. The feedforward part transfers the initial state of a linear system to a desired final state in finite time, and the feedback part reduces the effects of uncertainties and disturbances on the system performance. Two methods for determining the feedforward part, without requiring the knowledge of the explicit state solutions, are proposed. In the first method, a numerical procedure for approximating combined controls that drive linear time-varying systems to their final state in finite time is given. The feedforward part is a variable function of time and is selected based on a set of necessary conditions, such as magnitude constraints. In the second method, an analytical procedure for constructing combined controls for linear time-invariant systems is presented, where the feedforward part is accurately determined and it is of the minimum energy control type. It is shown that both methods facilitate the design of the feedforward part of combined controllers for the finite time settling of linear systems. The robustness of driving a linear system to its desired state in finite time is analyzed for three types of uncertainties. The robustness analysis suggests a modification of the feedforward control law to assure the robustness of the control strategy to parameter uncertainties for arbitrary final times.

Structural Decomposition Approach for the Stability of Uncertain Dynamic Systems

1988 ◽  
Vol 55 (4) ◽  
pp. 992-994 ◽  
Author(s):  
Y. H. Chen ◽  
Chieh Hsu
Keyword(s):  
Dynamic Systems ◽  
A Priori ◽  
Parameter Variation ◽  
Stability Study ◽  
Fast Time ◽  
Time Varying ◽  
Decomposition Approach ◽  
New Approach ◽  
Uncertain Dynamic Systems ◽  
The Stability

The stability property for a class of dynamic systems with uncertain parameter variation is studied. The uncertainty can be fast time-varying and unpredictable. A new approach for stability study is proposed. The only required information on the uncertain variation is its possible bound as well as structure. That is, no a priori knowledge on the realization of the variation is needed.

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