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Points used to define the shape of curves and surfaces
In computer-aided geometric design a control point is a member of a set of points used to determine the shape of a spline curve or, more generally, a
Control_point_(mathematics)
Topics referred to by the same term
control point in Wiktionary, the free dictionary. Control point may refer to: Control point (mathematics) Control point (orienteering) Control point (rail)
Control_point
Branch of engineering and mathematics
Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems. The aim is to develop a model
Control_theory
Field of knowledge
Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical
Mathematics
Fundamental object of geometry
a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces
Point_(geometry)
Broad concept generalizing scalars in mathematics and physics
In mathematics and physics, a vector is a generalization of a single number. It may denote a vector quantity, i.e., physical quantity that cannot be expressed
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Mathematical way of attaining a desired output from a dynamic system
optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies
Optimal_control
Binary feedback controller
LaSalle, Joseph P. (1969). Functional analysis and time optimal control. Mathematics in Science and Engineering. Vol. 56. New York—London: Academic Press
Bang–bang_control
Control theory for nonlinear or time-variant systems
both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs
Nonlinear_control
Basic framework of mathematics
Foundations of mathematics are the logical and mathematical frameworks that allow the development of mathematics without generating self-contradictory
Foundations_of_mathematics
A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol,
Mathematical_object
Use of various control systems for operating equipment
its set point despite disturbances. This closed-loop control is an application of negative feedback to a system. The mathematical basis of control theory
Automation
Study of discrete mathematical structures
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a one-to-one
Discrete_mathematics
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Strategies to make sure approximate calculations stay close to accurate
the error and better control the rounding in some applications, such as financial applications. Interval arithmetic is a mathematical technique used to put
Floating-point error mitigation
Floating-point_error_mitigation
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
In mathematics, straight line touching a plane curve without crossing it
limit when point B approximates or tends to A. The existence and uniqueness of the tangent line depends on a certain type of mathematical smoothness,
Tangent
Mathematics independent of applications
mathematics, pure mathematics is an informal term to describe the study of mathematical concepts independently of any application outside mathematics
Pure_mathematics
Engineering discipline that deals with control systems
on implementation of control systems mainly derived by mathematical modeling of a diverse range of systems. Modern day control engineering is a relatively
Control_engineering
Russian mathematician (born 1966)
research post in Steklov Institute of Mathematics and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the
Grigori_Perelman
Used to count, measure, and label
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth. Individual
Number
Number of times a curve wraps around a point in the plane
In mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of
Winding_number
Study of mathematical algorithms for optimization problems
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria
Mathematical_optimization
Branch of mathematics
words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved
Topology
Function whose values are sets (mathematics)
set. Set-valued functions are used in a variety of mathematical fields, including optimization, control theory and game theory. Set-valued functions are
Set-valued_function
Interdisciplinary field of research
Mathematical sociology is an interdisciplinary field of research concerned with the use of mathematics within sociological research. Starting in the early
Mathematical_sociology
Condition for a mathematical function to map some value to itself
In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some
Fixed-point_theorem
Branch of mathematics
ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy. (Strictly speaking, the point of the paradox
Mathematical_analysis
Theorem in order and lattice theory
In the mathematical areas of order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following:
Knaster–Tarski_theorem
Topics referred to by the same term
systems Control system, the ability to control some mechanical or chemical equipment Control theory, the mathematical theory about controlling dynamical
Control
Description of a system using mathematical concepts and language
mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical
Mathematical_model
For applied mathematics, in nonlinear control theory, a non-linear system of the form x ˙ = f ( x , u ) {\displaystyle {\dot {x}}=f(x,u)} is said to satisfy
Small_control_property
arise in optimal control problems that exhibit multiple optimal solutions. A Sethi-Skiba point is an indifference point in an optimal control problem such
Sethi-Skiba_point
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern
History_of_mathematics
Computer approximation for real numbers
standard mathematical notation, the digit string can be of any length, and the location of the radix point is indicated by placing an explicit "point" character
Floating-point_arithmetic
Coordinate system using perpendicular axes
In mathematics, physics, and engineering contexts, the first two axes are often defined or depicted as horizontal, with the third axis pointing up. In
Cartesian_coordinate_system
Typographical mark (^)
exponentiation operator as an upward-pointing arrow, intended to evoke the superscript notation common in mathematics. The upward-pointing arrow is now used to signify
Caret
Computer control of machine tools
numerical control (CNC) or CNC machining is the automated control of machine tools by a computer. It is an evolution of numerical control (NC), where
Computer_numerical_control
Reasoning for mathematical statements
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The
Mathematical_proof
Punctuation mark
forms of brackets are used in mathematics, with specific mathematical meanings, often for denoting specific mathematical functions and subformulas. Angle
Bracket
Topics referred to by the same term
special kind of configuration for regular polytopes Configuration space (mathematics), a space representing assignments of points to non-overlapping positions
Configuration
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Branch of topology
In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions
General_topology
mathematics. These include mathematical research, mathematics education, the history and philosophy of mathematics, public outreach, and mathematics contests
List_of_women_in_mathematics
Teaching, learning, and scholarly research in mathematics
In contemporary education, mathematics education (known in Europe as the didactics or pedagogy of mathematics) is the practice of teaching, learning, and
Mathematics_education
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
Standardized mathematics test
variety of other topics typically encountered in undergraduate mathematics courses, such as point-set topology, probability and statistics, geometry, and real
GRE_Mathematics_Test
Mathematics course taught in the Faculty of Mathematics, University of Cambridge
The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. In its classical 19th century
Mathematical_Tripos
Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods,
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Target value for the process variable of a control system
and control theory, a setpoint (SP; also set point) is the desired or target value for an essential variable, or process value (PV) of a control system
Setpoint_(control_system)
1960 article by Eugene Wigner
that mathematical concepts have applicability far beyond the context in which they were originally developed. He writes: "It is important to point out
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Development of mathematics in South Asia
The tradition of Indian mathematics flourished in South Asia from circa 1200 BCE until the late 18th century, when it merged into a global discipline
Indian_mathematics
Polish mathematician (1899–1943)
estimates Schauder fixed point theorem List of Polish mathematicians Kuratowski, Kazimierz (1980). A Half Century of Polish Mathematics : Remembrances and Reflections
Juliusz_Schauder
Technique to make a model more generalizable and transferable
In mathematics, statistics, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts
Regularization_(mathematics)
In mathematics, the Markus–Yamabe conjecture is a conjecture on global asymptotic stability. If the Jacobian matrix of a dynamical system at a fixed point
Markus–Yamabe_conjecture
Optimization. The IMA Volumes in Mathematics and its Applications, Springer. ISBN 978-1493986354. Tröltzsch, Fredi (2010). Optimal Control of Partial Differential
PDE-constrained_optimization
Measure of the shape of a function
Moments of a function in mathematics are certain quantitative measures related to the shape of the function's graph. For example, if the function represents
Moment_(mathematics)
Book on philosophy of mathematics
Mathematics, Form and Function, a book published in 1986 by Springer-Verlag, is a survey of the whole of mathematics, including its origins and deep structure
Mathematics, Form and Function
Mathematics,_Form_and_Function
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned
Mathematics_and_art
number that can be represented by a double-precision IEEE floating-point value. Mathematics: 365 ! / 365 365 {\displaystyle 365!/365^{365}} ≈ 1.45×10−157 is
Orders_of_magnitude_(numbers)
How software progresses through its implementation
when a command transfers control to another point – in which case the command is classified as a control flow command. Depending on context, other terms
Control_flow
Mathematical model of a system in control engineering
In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables
State-space_representation
Property of two varying quantities with a constant ratio
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant
Proportionality_(mathematics)
Typographic character indicating a question (?)
dot), and corresponds to Unicode code point U+0294 ʔ LATIN LETTER GLOTTAL STOP.[citation needed] In mathematics, "?" commonly denotes Minkowski's question
Question_mark
Control loop feedback mechanism
observing the system response. Control action – The mathematical model and practical loop above both use a direct control action for all the terms, which
PID_controller
Form of graphical projection where the projection lines converge to one or more points
Mathematical Gazette. 77 (479): 206. doi:10.2307/3619717. JSTOR 3619717. S2CID 195006163. Zeeman, Sir Erik Chistopher (3 December 1978). "Mathematics
Perspective_(graphical)
Computer-generated imagery Cone tracing Constructive solid geometry Control point (mathematics) Convex hull Cross section (geometry) Cube mapping Curvilinear
List of computer graphics and descriptive geometry topics
List_of_computer_graphics_and_descriptive_geometry_topics
Mathematical concept related to subsets of vector spaces
In functional analysis, a branch of mathematics, a bounding point of a subset of a vector space is a conceptual extension of the boundary of a set. Let
Bounding_point
Smallest fixed point of a function from a poset
In order theory, a branch of mathematics, the least fixed point (lfp or LFP, sometimes also smallest fixed point) of a function from a partially ordered
Least_fixed_point
Set of philosophical problems
antinomies. Zeno's paradoxes remain a pivotal reference point in the philosophical and mathematical exploration of reality, motion, and the infinite, influencing
Zeno's_paradoxes
Polish-American mathematician (born 1948)
co-editor-in-chief of two academic journals, Applied Mathematics & Optimization and Evolution Equations & Control Theory. Lasiecka earned her Ph.D. in 1975 from
Irena_Lasiecka
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or
List of mathematical constants
List_of_mathematical_constants
Branch of applied mathematics
development of mathematical ideas inspired by physics, known as physical mathematics. There are several distinct branches of mathematical physics, and these
Mathematical_physics
Indian mathematician (1887–1920)
contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered
Srinivasa_Ramanujan
Control paradigm in which errors are measured before they can affect a system
disturbance. This requires a mathematical model of the system so that the effect of disturbances can be properly predicted. A control system which has only feed-forward
Feed_forward_(control)
Length in a vector space
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance
Norm_(mathematics)
Process where information about current status is used to influence future status
in feedback control theory. This was a landmark paper on control theory and the mathematics of feedback. The verb phrase to feed back, in the sense of
Feedback
Numerical symbol
Organization-regulated air traffic control communications). In mathematics, the decimal separator is a type of radix point, a term that also applies to number
Decimal_separator
Mathematical symbols (+ and −)
The plus sign (+) and the minus sign (−) are mathematical symbols used to denote positive and negative functions, respectively. In addition, the symbol
Plus_and_minus_signs
Arithmetic operation
numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects
Addition
Point where a function crosses an axis and changes sign
A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis
Zero_crossing
Study of vector bundles, principal bundles, and fibre bundles
In mathematics, and especially differential geometry and mathematical physics, gauge theory is the general study of connections on vector bundles, principal
Gauge_theory_(mathematics)
Curve that winds around a central point
In mathematics, a spiral is a curve which emanates from a point, moving further away as it revolves around the point. It is a subtype of whorled patterns
Spiral
Mathematical definition of point elasticity
In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output) at
Elasticity_of_a_function
Curve used in computer graphics and related fields
Springer Undergraduate Mathematics Series (2nd ed.). ISBN 978-1-85233-801-5. ASIN 1852338016. Shene, C. K. "Finding a Point on a Bézier Curve: De Casteljau's
Bézier_curve
Multiple ways for multi-joint objects to realize a movement
optimal control process. Optimal control is a way of understanding motor control and the motor equivalence problem, but as with most mathematical theories
Degrees_of_freedom_problem
Anxiety towards math
Mathematical anxiety, also known as math phobia and math anxiety, is a feeling of tension and anxiety that interferes with the manipulation of numbers
Mathematical_anxiety
Ancient Greek mathematician (fl. 300 BC)
mathematicians of antiquity, and one of the most influential in the history of mathematics. Very little is known of Euclid's life, and most information comes from
Euclid
23 mathematical problems stated in 1900
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several
Hilbert's_problems
(2002). "MISER3: Optimal Control Toolbox User Manual, Matlab Beta Version 2.0". Nedlands, WA 6907, Australia: Department of Mathematics, The University of Western
PROPT
mathematical symbols International Code of Signals (using flags) International Symbol of Access Japanese punctuation Korean punctuation Media control
List of typographical symbols and punctuation marks
List_of_typographical_symbols_and_punctuation_marks
American mathematician and philosopher (1894–1964)
stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems. Wiener
Norbert_Wiener
American mathematician (1916–2001)
best subjects were science and mathematics. At home, he constructed such devices as models of planes, a radio-controlled model boat and a barbed-wire telegraph
Claude_Shannon
System that manages the behavior of other systems
and control systems. Building automation – Branch of automation Coefficient diagram method Control theory – Branch of engineering and mathematics Cybernetics –
Control_system
Branch of applied mathematics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods
Mathematical_economics
In logistics, a counting point (CP; also known as a status point, data acquisition point, check point, or control point) is a certain spot designated for
Counting_point
Additional mathematical object
In mathematics, a structure on a set (or on some sets) refers to providing or endowing it (or them) with certain additional features (e.g. an operation
Mathematical_structure
Physical quantities taking values at each point in space and time
matter caused by stress, is an example of a tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous
Field_(physics)
Process in control theory
In the subject area of control theory, an internal model is a process that simulates the response of the system in order to estimate the outcome of a
Internal model (motor control)
Internal_model_(motor_control)
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