Around the Decidability of Reachability in Continuous Time Straight line Time-Invariant Systems – NASA/ADS

Abstract

We think about the decidability of condition-to-condition reachability in straight line time-invariant control systems over continuous time. We analyse this issue with regards to the allowable control sets, that are assumed is the image within straight line map from the unit hypercube. This naturally models bounded (sometimes known as saturated) controls. Decidability from the form of the reachability condition in which control sets are affine subspaces of $mathbb^n$ is really a fundamental lead to control theory. Our first outcome is decidability in 2 dimensions ($n=2$) when the matrix $A$ satisfies some spectral conditions, and conditional decidablility generally. When the transformation matrix $A$ is diagonal with rational records (or rational multiples of the identical algebraic number) then your reachability issue is decidable. When the transformation matrix $A$ has only real eigenvalues, the reachability issue is conditionally decidable. Time-bounded reachability issue is conditionally decidable, and unconditionally decidable in 2 dimensions. A lot of our decidability answers are conditional for the reason that they depend around the decidability of certain mathematical theories, namely the idea from the reals with exponential ($mathfrak_$) with bounded sine ($mathfrak_crime$). We get yourself a hardness result for any mild generalization from the problem in which the target is straightforward set (hypercube of dimension $n-1$ or hyperplane) rather of the point, and also the control set is really a convex bounded polytope. Within this situation, we reveal that the issue is a minimum of as hard because the emph or even the emph.

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Discrete Dynamical Systems and Difference Equations with Mathematica

Book Description

Following a work of Yorke and Li in 1975, the idea of discrete dynamical systems and difference equations developed quickly. The applying difference equations also increased quickly, particularly with the development of graphical-interface software that may plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams, and discover basins of attraction. Continue reading “Discrete Dynamical Systems and Difference Equations with Mathematica”

How illegal social structures help some but harm others

The has outraged millions, getting to light the gaps between your fortunate and fewer fortunate citizens. As being a social researcher who studies societal origins of monetary and health inequalities, it had been obvious in my experience it had become a symbol of deep structural inequalities within the U.S. social hierarchy. Such structural inequalities come in many forms, including wealth and health inequalities.

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2022 the most popular brand jeans

Every summer, the deepest impression is all kinds of cool skirts. This year is different. As soon as the weather is hot, I find that fashionable bloggers and stars at home and abroad seem to be possessed and are all wearing the same Jeans – diesel jeans online. It’s easy to wear and good-looking. It’s…

Every summer, the deepest impression is all kinds of cool skirts.

This year is different. As soon as the weather is hot, I find that fashionable bloggers and stars at home and abroad seem to be possessed and are all wearing the same Jeans – diesel jeans online.

Continue reading “2022 the most popular brand jeans”

Advanced Modeling and Simulation in Engineering Sciences

Demand Papers: Data Assimilation in Computational Mechanics – Recent Advances and New Trends

Using experimental data in colaboration with simulation models is becoming anactive research subject. Indeed, new experimental facilities (for example digital image/volume correlation (DIC/DVC)) now enable to gather a sizable and diversified quantity of data, which enables you to identify and validate complex models, in order to enhance predictions produced by simulations tools. In addition, data and models are increasingly more intertwined to enhance understanding in applications coping with structural health monitoring and control for example, with potential real-time dialogue between simulators and connected physical systems (e.g., the DDDAS concept). However, many challenges coping with data filtering, computational cost, or statistical sturdiness have to be addressed to be able to incorporate data efficiently. Continue reading “Advanced Modeling and Simulation in Engineering Sciences”