Interval arithmetic
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Design of interval observers for uncertain dynamical systems Open
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Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic Open
Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic. It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many speci…
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Interval Estimation Methods for Discrete-Time Linear Time-Invariant Systems Open
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Rigorous Estimation of Floating-Point Round-Off Errors with Symbolic Taylor Expansions Open
Rigorous estimation of maximum floating-point round-off errors is an important capability central to many formal verification tools. Unfortunately, available techniques for this task often provide very pessimistic overestimates, causing un…
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Towards a Compiler for Reals Open
Numerical software, common in scientific computing or embedded systems, inevitably uses a finite-precision approximation of the real arithmetic in which most algorithms are designed. In many applications, the roundoff errors introduced by …
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Interval State Estimation With Uncertainty of Distributed Generation and Line Parameters in Unbalanced Distribution Systems Open
Distribution system state estimation (DSSE), which provides critical\ninformation for system monitoring and control, is being challenged by multiple\nsources of uncertainties such as random meter errors, stochastic power output\nof distrib…
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Implementation of Interval Arithmetic in CORA 2016 Open
Interval arithmetic can be seen as one of the workhorses for formal verification approaches. The popularity of interval arithmetic stems form the fact that the possible outcomes of almost all frequently occurring mathematical expressions c…
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A Multifactorial Evolutionary Algorithm for Multitasking Under Interval Uncertainties Open
Various real-world applications with interval uncertainty, such as the path planning of mobile robot, layout of radio frequency identification readers and solar desalination, can be formulated as an interval multiobjective optimization pro…
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Extentions of Affine Arithmetic: Application to Unconstrained Global Optimization Open
Global optimization methods in connection with interval arithmetic permit to determine an accurate enclosure of the global optimum, and of all the corresponding optimizers. One of the main features of these algorithms consists in the const…
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Some recent results on the design and implementation of interval observers for uncertain systems Open
Based on the theory of positive systems, the goal of interval observers is to compute sets of admissible values of the state vector at each instant of time for systems subject to bounded uncertainties (noises, disturbances and parameters).…
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A Radical Approach to Computation with Real Numbers Open
10.14529/jsfi160203
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Interval observer versus set‐membership approaches for fault detection in uncertain systems using zonotopes Open
Summary This paper presents both analysis and comparison of the interval observer–based and set‐membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both…
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Power Pattern Sensitivity to Calibration Errors and Mutual Coupling in Linear Arrays through Circular Interval Arithmetics Open
The sensitivity to both calibration errors and mutual coupling effects of the power pattern radiated by a linear array is addressed. Starting from the knowledge of the nominal excitations of the array elements and the maximum uncertainty o…
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Implementation of Taylor models in CORA 2018 Open
Tool Presentation: Computing guaranteed bounds of function outputs when their input variables are bounded by intervals is an essential technique for many formal methods. Due to the importance of bounding function outputs, several technique…
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Robust Output Feedback MPC for LPV Systems Using Interval Observers Open
This work addresses the problem of robust output feedback model predictive control for discrete-time, constrained, linear parameter-varying systems subject to (bounded) state and measurement disturbances. The vector of scheduling parameter…
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Interval observers design for continuous-time linear switched systems Open
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Interval Observer Design and Consensus of MultiAgent Systems with Time-Varying Interval Uncertainties Open
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Interval Linear Programming under Transformations: Optimal Solutions and\n Optimal Value Range Open
Interval linear programming provides a tool for solving real-world\noptimization problems under interval-valued uncertainty. Instead of\napproximating or estimating crisp input data, the coefficients of an interval\nprogram may perturb ind…
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Is an interval the right result of arithmetic operations on intervals? Open
For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, this is not true. Interval arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithme…
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Robust propagation of probability boxes by interval predictor models Open
This paper proposes numerical strategies to robustly and efficiently propagate probability boxes through expensive black box models. An interval is obtained for the system failure probability, with a confidence level. The three proposed al…
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Interval analysis of rotor dynamic response based on Chebyshev polynomials Open
Uncertainty is extensively involved in the rotor systems of rotating machinery, which may cause an unstable vibrational response. To take the uncertainty into consideration for the uncertain rotor-bearing system, an improved unified interv…
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Interval Enclosures of Upper Bounds of Roundoff Errors Using Semidefinite Programming Open
A long-standing problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a…
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A Tchebycheffian Extension of Multidegree B-Splines: Algorithmic Computation and Properties Open
In this paper we present an efficient and robust approach to compute a\nnormalized B-spline-like basis for spline spaces with pieces drawn from\nextended Tchebycheff spaces. The extended Tchebycheff spaces and their\ndimensions are allowed…
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Interval State Estimation of Distribution Network With Power Flow Constraint Open
Currently, distribution network is faced with many problems, e.g., low automation coverage and less data acquisition. There are also lots of challenges in state estimation, such as imprecise approximation of network parameters and measurem…
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Intelligent algorithm for trapezoidal interval valued neutrosophic network analysis Open
The shortest path problem has been one of the most fundamental practical problems in network analysis. One of the good algorithms is Bellman‐Ford, which has been applied in network, for the last some years. Due to complexity in the decisio…
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Interval Observers for Linear Impulsive Systems Open
The problem of interval observer design is studied for a class of linear hybrid systems. Several observers are designed oriented on different conditions of positivity and stability for estimation error dynamics. Effciency of the proposed a…
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Actuator fault detection and interval reconstruction based on interval observers Open
This paper presents an actuator fault detection and interval reconstruction scheme based on interval observers for systems with both actuator faults and disturbances. To begin with, two full-order interval observers which are sensitive to …
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On auto‐ and cross‐interdependence in interval field finite element analysis Open
Summary This paper discusses the concepts of auto‐ and cross‐interdependence in interval field finite element analysis. In classic interval analysis, independent intervals are used to construct hyper‐rectangular input spaces that correspon…
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Abstraction based Output Range Analysis for Neural Networks Open
In this paper, we consider the problem of output range analysis for feed-forward neural networks with ReLU activation functions. The existing approaches reduce the output range analysis problem to satisfiability and optimization solving, w…
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Interval observer design for Linear Parameter-Varying systems subject to component faults Open
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