''in control theory''
...ttainable from it at time $T$ has non-empty interior. For example, for the control system defined in the $(x,y)$-plane by the two fields of admissible velocit
2 KB (329 words) - 15:33, 20 November 2014
...atic control theory|Automatic control theory]]) if there is a delay in the control mechanism.
1 KB (198 words) - 17:10, 7 February 2011
...mples of complex systems are: the nervous system, the brain, a computer, a control system in human society, etc.
...ir names, such as systems analysis, system-technology, and general systems theory, among others.
4 KB (532 words) - 17:22, 7 February 2011
''for a linear stationary control system (an automatic control system)''
of the input of the system (the action, the control) $ u( t) $
4 KB (608 words) - 13:08, 18 June 2020
is described by several systems of differential equations
...etails see [[#References|[3]]]). The participation of several differential systems $ ( S _ {i} ) $
4 KB (557 words) - 08:26, 6 June 2020
...tive interpretation of them. Here are some (informal) examples of physical control system.
...attention to the more detailed internal properties. Therefore, two control systems, having in some sense identical behaviour and identical purposes, are not r
12 KB (1,844 words) - 16:56, 15 April 2012
...ion of the initial elements are such that the operation of complex control systems can be described with the aid of Boolean functions. Boolean functions are a
...cube (cf. [[Boolean functions, metric theory of|Boolean functions, metric theory of]]), as well as of the various algebras of Boolean functions (cf. [[Many-
5 KB (836 words) - 12:39, 14 February 2020
''
control''
...www.encyclopediaofmath.org/legacyimages/c/c025/c025990/c0259907.png" />. A
control is called admissible if for each <img align="absmiddle" border="0" src="htt
12 KB (1,716 words) - 17:18, 7 February 2011
$#C+1 = 62 : ~/encyclopedia/old_files/data/T092/T.0902870 Time\AAhoptimal control problem
...f. [[Optimal control, mathematical theory of|Optimal control, mathematical theory of]]), consisting in the determination of the minimum time
7 KB (997 words) - 08:25, 6 June 2020
...class of systems. However, a precise and universal definition of adaptive control is still elusive.
...hen, numerous authors have tackled and solved these problems, and adaptive control has matured.
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...it and network design; architectural design; control (cf. [[Control system|Control system]]); signal processing; selection of most reliable populations (in [[
...arametric approach for selecting the most reliable population" ''Queueing Systems'' , '''24''' (1996) pp. 169–176</td></tr></table>
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...the point of view of mathematical logic, as models of logics, that is, as systems of propositions with logical operations on them; and from the point of view
...ems of many-valued logic. Among the most important problems for functional systems are those of completeness, of the complexity of expressing some functions i
7 KB (1,087 words) - 19:40, 5 June 2020
$#C+1 = 1 : ~/encyclopedia/old_files/data/A014/A.0104080 Automata, theory of
...[[Algorithms, theory of|Algorithms, theory of]]), particularly so with the theory of abstract machines, since automata can be regarded as a special case of s
7 KB (975 words) - 18:49, 5 April 2020
...is important to note that if the equations of some of the elements of the systems are unknown, the Nyquist diagram can be constructed experimentally, by feed
...ce been developed for multivariable, infinite-dimensional and sampled-data systems, e.g. [[#References|[5]]], , , .
4 KB (619 words) - 13:06, 10 August 2014
A parametric polynomial defined by a degree $n$, and a sequence of $n + 1$ control points $P_{0}, \ldots, P_{n}$.
...that Bézier curves are a parametric vector-valued representation based on control points, whereas Bernstein polynomials are usually thought of as a sequence
5 KB (759 words) - 09:49, 27 March 2023
...at states conditions for the solvability of the Lur'e equations in control theory:
...te stability [[#References|[2]]], [[#References|[4]]]–[[#References|[6]]], control and adaptation (see, for example, [[#References|[7]]]–[[#References|[9]]]
6 KB (854 words) - 12:59, 13 January 2021
...e phase coordinates and control functions. The original problem of optimal control by discretization (with respect to time $t$ and phase vector $x$) can be re
...representation of the trajectory $x(t)$ of the original problem of optimal control. The length $I(x_0,\dots,x_N)$ of this line is the sum of the (generalized)
3 KB (447 words) - 10:39, 31 August 2014
...f. [[Optimal control, mathematical theory of|Optimal control, mathematical theory of]]), several approaches to the establishment of sufficient conditions for
Let a problem of optimal control be posed in which the minimum of the functional
10 KB (1,504 words) - 08:04, 6 June 2020
...there is also an analogue of Mikhailov's criterion for non-linear control systems (see [[#References|[6]]]).
...i, L.E. El'sgol'ts, "Mathematical foundations of the theory of control systems" , Moscow (1969) (In Russian)</td></tr><tr><td valign="top">[6]</td> <td
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...e [[Optimal control, mathematical theory of|mathematical theory of optimal control]]. It was first formulated in 1956 by L.S. Pontryagin <ref name="Pontryagin
...ntryagin maximum principle corresponds to the following problem of optimal control. Given a system of [[Differential equation, ordinary|ordinary differential
8 KB (1,238 words) - 17:21, 7 June 2016