''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.
6 KB (870 words) - 06:53, 26 March 2023
...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>
2 KB (296 words) - 16:58, 1 July 2020
...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
5 KB (692 words) - 15:30, 1 July 2020
...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
$#C+1 = 69 : ~/encyclopedia/old_files/data/O068/O.0608460 Optimal programming control
...matical theory of|Optimal control, mathematical theory of]]), in which the control $ u= u( t) $
20 KB (2,978 words) - 08:04, 6 June 2020
...tion introduced by W. Hamilton (1834) to describe the motion of mechanical systems. It is used, beginning with the work of C.G.J. Jacobi (1837), in the classi
...ions for the action function (cf. [[Hamilton–Jacobi theory|Hamilton–Jacobi theory]]) can be written in terms of a Hamilton function.
5 KB (753 words) - 19:43, 5 June 2020
The Pontryagin maximum principle for discrete-time control processes. For such a process the maximum principle need not be satisfied,
For example, consider the optimal control problem
7 KB (959 words) - 03:47, 4 March 2022
...pursuer (hunter) $P$ and evader (prey) $E$, whose motions are described by systems of differential equations:
...ng a pursuit game means finding an equilibrium (cf. [[Saddle point in game theory]]).
3 KB (423 words) - 20:17, 11 January 2017
...equations may be employed to find approximate solutions of the non-linear systems.
which is typical in the theory of quasi-linear oscillations, the harmonic balance method consists in repla
4 KB (613 words) - 19:43, 5 June 2020
...nning and design. Stochastic programming methods can also be used to adapt systems and algorithms to random changes in the state of the medium in which they o
In order to construct realistic stochastic models of control processes, it is necessary to have at one's disposal not only the statistic
5 KB (768 words) - 13:11, 3 May 2016
...of the classical [[Lyapunov function|Lyapunov function]] in the theory of systems of differential equations.
...p"> V.V. Kalashnikov, "Qualitative analysis of the behaviour of complex systems by the method of test functions" , Moscow (1978) (In Russian)</TD></TR></
5 KB (718 words) - 04:11, 6 June 2020
...concerning the qualitative behaviour of linear equations and second-order systems (see [[#References|[3]]], [[#References|[4]]]).
...], and [[#References|[6]]], [[#References|[7]]]). For example, the optimum control $ u _ {0} $
8 KB (1,202 words) - 14:55, 7 June 2020
There are systems of other types, where each request must necessarily be served, such as, for
...processes. The simplest queues can be described by two-dimensional random control sequences
15 KB (2,349 words) - 09:05, 21 January 2024
...be an optimal method of controlling a system when a minimizing sequence of control functions does not have a limit in the class of Lebesgue-measurable functio
...ard to the constraining condition (2), the boundary conditions (3) and the control constraint (4), is satisfied by the trajectory
13 KB (1,801 words) - 19:58, 15 January 2024
...[3]]], [[#References|[2]]]. The equation which is most often considered in control problems is
where $x=x(t)$ is the vector function sought, while $u=u(t)$ is the control, i.e. a vector function which may be arbitrarily chosen out of all permissi
5 KB (857 words) - 15:28, 14 February 2020
...6]]]. L. Neustadt has shown the significance of these operators in control theory [[#References|[a6]]].
...on abstract Volterra operators and associated equations. However, a solid theory of this kind of operator does not yet exist.
6 KB (863 words) - 15:34, 13 July 2014
...solutions of the corresponding initial-boundary value problems for a fixed control, etc.
For example, the problem of optimal control consisting of the minimization of the functional
22 KB (3,158 words) - 19:38, 5 June 2020
...ce of a dynamical system (cf. [[Automatic control theory|Automatic control theory]]) is appraised in terms of the $ H ^ \infty $-
The theory of $ H ^ \infty $
7 KB (1,101 words) - 16:08, 27 January 2024
...f $(A,B)$ as (the essential data of) a discrete-time time-invariant linear control system:
...$R = \mathbf{R}$ or $\mathbf{C}$, a continuous-time time-invariant linear control system:
5 KB (799 words) - 20:38, 12 November 2017
''optimal singular control''
An [[Optimal control|optimal control]] for which, at a certain period of time, the conditions
17 KB (2,522 words) - 20:03, 12 January 2024
...theory of non-linear oscillations, to physics, to the theory of automatic control, to astrodynamics, and to others. Averaging methods have often provided app
1) Standard systems in the sense of N.N. Bogolyubov
5 KB (679 words) - 03:42, 21 March 2022
...l]] of small dimensions, but with constraints on the phase coordinates and control functions. After discretization of the functional and the system of differe
...ethod of]]) is difficult because of the labour involved in determining the control function.
4 KB (578 words) - 19:54, 12 January 2024
In the method of local variations the original problem of optimal control, given as a [[Lagrange problem|Lagrange problem]], is made discrete with re
6 KB (898 words) - 17:24, 31 December 2020
...ical with discrete analysis. Such structures may include certain algebraic systems, infinite graphs, certain types of calculating media (e.g. homogeneous stru
...mathematics|computational mathematics]]; [[Probability theory|probability theory]], and certain other disciplines the subject of which is discrete.
9 KB (1,264 words) - 16:56, 15 April 2012
...~/encyclopedia/old_files/data/O068/O.0608430 Optimal control, mathematical theory of
...|mathematical programming]] and game theory (cf. [[Games, theory of|Games, theory of]]).
21 KB (3,161 words) - 08:04, 6 June 2020
...the development of an analytical method for modeling and designing hybrid systems is to employ a max-plus algebra model of the manufacturing work-cell and ex
...oupling feedback. An excellent exposition of the state of the art in robot control is given in [[#References|[a5]]] and [[#References|[a4]]].
12 KB (1,887 words) - 16:55, 1 July 2020
[[Pole assignment problem|pole assignment problem]] for linear control
systems
4 KB (607 words) - 02:33, 14 September 2022
...cal systems'' , '''I: Ordinary differential equations and smooth dynamical systems''' , Springer (1988) pp. 159ff (Translated from Russian)</TD></TR></tabl
3 KB (535 words) - 21:47, 30 April 2014
...rticularly useful in the study of the "structural" properties of control systems.
.../TD> <TD valign="top"> O.E. Lupanov, "On the synthesis of some class of control problems" ''Probl. Kibernet.'' , '''10''' (1963) pp. 63–97 (In Russia
18 KB (2,608 words) - 17:21, 7 February 2011
...g the theory and the methods of solution of multi-step problems of optimal control.
...ructure of which consists of several steps, or else a process in which the control is subdivided into a sequence of successive stages (steps), which usually c
10 KB (1,500 words) - 16:50, 20 January 2024
...n the areas of flexible manufacturing, communication networks and logistic systems.
...dresses the synthesis of controllers (i.e. supervisors) for discrete event systems to satisfy a set of qualitative specifications on the admissible orderings
14 KB (2,165 words) - 19:35, 5 June 2020
...opedia/old_files/data/R081/R.0801170 Reliability and inspection of control systems,
''problems in the reliability of control systems''
23 KB (3,205 words) - 08:10, 6 June 2020
...ontrol theory|automatic control theory]]. A systematic construction of the theory of ordinary differential equations with deviated arguments was begun in 194
...h a deviation of the argument, permitting the construction of a meaningful theory, has been introduced. Several properties of such equations are directly ana
27 KB (3,819 words) - 16:54, 7 February 2011
...y–Hamilton theorem can be also extended to singular two-dimensional linear systems described by Roesser-type or Fomasini–Marchesini-type models [[#Reference
...heorems may be also extended to two-dimensional continuous-discrete linear systems [[#References|[a5]]].
15 KB (2,237 words) - 17:01, 1 July 2020
...a powerful tool for understanding the outside world and for prediction and control. The analysis of a mathematical model allows the essence of a phenomenon to
...) could not be measured, which resulted in quantitative conclusions of the theory not in proper correspondence with observations, so Copernicus was forced to
8 KB (1,318 words) - 17:29, 7 February 2011
''parametrized measure, relaxed control, stochastic kernel''
The main area where Young measures have recently been used is optimization theory. Optimization problems where a local, integral cost functional is to be min
7 KB (981 words) - 13:50, 2 July 2020
The design, development, tuning, and operation of computer and communication systems heavily rely on mathematical techniques which are usually indicated as perf
...from such areas as combinatorial optimization (scheduling) and stochastic control.
5 KB (732 words) - 08:05, 6 June 2020
This problem has been greatly generalized in the theory of stationary stochastic processes (cf. [[Stationary stochastic process|Sta
For systems of stochastic differential equations the problem of interpolation of some c
6 KB (777 words) - 08:23, 6 June 2020
$#C+1 = 33 : ~/encyclopedia/old_files/data/H046/H.0406230 Hamilton\ANDJacobi theory
...o-called Hamilton–Jacobi equation. The fundamentals of the Hamilton–Jacobi theory were developed by W. Hamilton in the 1820s for problems in wave optics and
8 KB (1,116 words) - 19:43, 5 June 2020
...assical (elementary) projective and analytic geometry one speaks of linear systems of curves, surfaces, quadrics, etc. These are families of curves, surfaces,
...heory: for linear input/output systems, linear dynamical systems or linear control system.
6 KB (855 words) - 22:17, 5 June 2020
...ems theory. For systems in the sense of logics, see [[Formal_system|formal systems]].
...cussed at the interplay between them (e.g. cybernetic models of biological systems). A more fundamental definition of a system was required encompassing the
8 KB (1,362 words) - 17:44, 25 September 2012
...heory one considers boundary value problems with a functional parameter: a control. For example, consider the equation
...align="top">[5]</TD> <TD valign="top"> V.I. Zubov, "Lectures in control theory" , Moscow (1975) (In Russian)</TD></TR><TR><TD valign="top">[6]</TD> <TD
7 KB (1,004 words) - 06:29, 30 May 2020
...a certain class. The term "absolute stability" assumes given a class of systems and an indication of the sense in which stability and uniformity are to be
Numerous studies of particular non-linear systems have led to the understanding that in the first place one should take in co
16 KB (2,300 words) - 08:22, 6 June 2020
...= 12 : ~/encyclopedia/old_files/data/K110/K.1100100 Kharitonov polynomial theory
...motivation for this theory derives from the issue of robust stability for systems of linear time-invariant differential equations. For a system of linear dif
5 KB (695 words) - 22:14, 5 June 2020
...f a priori bounds on the computational complexity). This requires that the control, information and frequency relations arising in these processes between sta
...other zones, or a hammock (a subgraph connected with the other part of the control flow graph at precisely two vertices — the input and output; the input ve
5 KB (775 words) - 17:05, 7 February 2011
...lifting theorem can also be used to solve problems in [[H^infinity-control-theory| $ H ^ \infty $
control theory]] and inverse scattering [[#References|[a1]]], [[#References|[a2]]].
6 KB (815 words) - 09:51, 26 March 2023
...rgy minimization problems is presented. For the optimal control problem of systems governed by variational inequalities see [[#References|[a13]]].
...TR><TR><TD valign="top">[a13]</TD> <TD valign="top"> V. Barbu, "Optimal control of variational inequalities" , ''Res. Notes Math.'' , '''100''' , Pitman (
5 KB (737 words) - 20:35, 18 March 2024
...ary to consider statistical states of systems; for classical (non-quantum) systems they are described by probability distributions on the phase space. The rul
...ferentiable [[Dynamical system|dynamical system]] (which includes the main systems considered in analytical mechanics and classical statistical physics), the
6 KB (906 words) - 21:49, 30 April 2014
...f natural parallelism occurring in computer-modelling and computer-control systems and processes; and b) a parallelization of information processing in multi-
...and subprograms; and independent problems and programs in multi-processor systems.
11 KB (1,714 words) - 03:17, 5 June 2016
$#C+1 = 128 : ~/encyclopedia/old_files/data/O068/O.0608500 Optimal synthesis control
...n of a positional strategy makes possible an a posteriori realization of a control $ u $,
32 KB (4,621 words) - 08:04, 6 June 2020
...op"> G.E.P. Box, G.M. Jenkins, "Time series analysis. Forecasting and control" , '''1–2''' , Holden-Day (1976)</TD></TR><TR><TD valign="top">[2]</TD>
...TD valign="top">[a5]</TD> <TD valign="top"> L. Ljung, T. Söderström, "Theory and practice of recursive identification" , M.I.T. (1983)</TD></TR></table
5 KB (645 words) - 08:01, 6 June 2020
...ies of the system itself (see also [[Oscillations, theory of|Oscillations, theory of]]). The term "auto-oscillation" was introduced by A.A. Andronov (see [[#
...mous auto-oscillating systems with one degree of freedom may be defined as systems whose equations of motion have one or more limit cycles in the phase plane
9 KB (1,404 words) - 16:55, 15 April 2012
...orks), which is oriented to the qualitative analysis and synthesis of such systems (discovering deadlocks or conflict situations and bottlenecks, computer-aid
...ine is the use of Petri nets as the basis of models for discrete dynamical systems in information technology, economics, digital engineering, etc.
6 KB (897 words) - 19:23, 16 August 2016
...ments, a rule for combining them and a means of using the structure of the control system to define the function which it realizes are given.
...s of functions. A synthesis problem originally consisted of constructing a control system realizing a given function from this class.
27 KB (4,142 words) - 14:55, 7 June 2020
...of dynamical processes with memory requires the further development of the theory of functional equations with abstract Volterra operators. Numerous applicat
...equations involving classical integral operators of Volterra type when the theory is framed in abstract spaces, see [[#References|[a2]]], [[#References|[a7]]
5 KB (745 words) - 15:29, 13 July 2014
...yclopedia/old_files/data/P071/P.0701560 Parametric resonance, mathematical theory of
The branch of the theory of ordinary differential equations that studies the phenomenon of parametri
10 KB (1,385 words) - 09:16, 13 May 2022
...at follows it will be assumed that such an extension has been made for all control sequences.
For systems in which $ \{ \tau _ {j} ^ {s} - \tau _ {j} ^ {e} \} \in G _ {I} $
24 KB (3,620 words) - 16:42, 30 December 2020
...duction, $L$-systems constituted a significant part of [[formal language]] theory, allowing one to compare parallel rewriting to a more classical sequential
...d with these notions, in particular with D$0$L-sequences, which made D$0$L-systems mathematically very fruitful. The most famous problem is the D$0$L-sequence
10 KB (1,542 words) - 11:21, 26 March 2023
...rmational processes in [[#References|[a11]]], and in networks of cognitive systems in [[#References|[a15]]] and [[#References|[a16]]].
...o be used in more complex social processes, involving many self-organizing systems.
9 KB (1,251 words) - 18:24, 14 January 2021
...of motion (understood in the same wide form). Thus, stability theory is a theory in the widest sense of this word. Among the different concepts of the stabi
...]]) and having a large intersection with the theory of linear systems, the theory of Lyapunov characteristic exponents (cf. [[Lyapunov characteristic exponen
9 KB (1,252 words) - 10:41, 15 April 2014
...cience concerned with the construction of mathematical models of dynamical systems from measured input/output data. The constructed models are mostly of finit
...tworks form an example of common non-linear black-box models for dynamical systems.
7 KB (1,131 words) - 14:45, 16 December 2023
...ried applications as system identification, adaptive control, transmission systems, adaptive filtering for signal processing, and several aspects of pattern r
The study of adaptive algorithms is generally made through the theory of [[Stochastic approximation|stochastic approximation]].
8 KB (1,242 words) - 15:31, 1 July 2020
...nsformational grammars; some of them are intended for processing component systems, others for processing hierarchy trees. As an example, one can quote the so
grammars, which are finite systems of elementary transformations of the form $ t _ {1} \Rightarrow t _ {2} \
4 KB (600 words) - 19:42, 5 June 2020
...g range of computer applications. The term is often understood to mean the theory of numerical methods and algorithms for the solution of typical mathematica
...als with the simplification of the man-computer interaction, including the theory and practice of [[Programming|programming]] computer problems and of [[Auto
13 KB (1,892 words) - 20:11, 31 December 2018
The first significant results in the theory of equations (4) were obtained in [[#References|[11]]], where an effective
...dity of the majority of results listed above has also been established for systems of equations of type (4); however, in contrast to the case of a single equa
32 KB (4,357 words) - 17:14, 7 February 2011
...f [[Orbit stability|orbit stability]] of closed trajectories of autonomous systems of differential equations one has to apply necessary and sufficient conditi
...">[10]</TD> <TD valign="top"> E. Jury, "Inners and stability of dynamic systems" , Wiley (1974)</TD></TR></table>
9 KB (1,283 words) - 14:55, 7 June 2020
...ed space]]), in problems concerning the extension of functions, and in the theory of differential equations.
In optimization over a finite or infinite horizon, e.g. in the theory of optimal economic growth, one aims to maximize a future return function
5 KB (752 words) - 08:29, 6 June 2020
A code intended for the control of the functioning of an adder. When adding numbers represented in the bina
...rror-correcting code|Error-correcting code]]). In the study of problems of control of an adder one usually considers an encoding $ f: \{ 0 \dots M - 1 \} \
8 KB (1,189 words) - 09:46, 26 March 2023
...ems, in particular, in circuit theory [[#References|[a4]]] and for control theory problems involving an $ H ^ \infty $-
...[[#References|[a1]]]. Generalizations of the Nevanlinna–Pick interpolation theory have also been developed for functions of several variables (see [[#Referen
10 KB (1,474 words) - 14:54, 7 June 2020
are obtained in a less general form than for single-server systems, and are connected with a condition on the existence of so-called renewal e
must be satisfied. If for such systems, in triangular arrays, the distributions of $ \tau _ {j} ^ {(n)} e $
18 KB (2,750 words) - 19:29, 16 January 2024
...ces|[a21]]], [[#References|[a22]]] for general surveys of linear filtering theory.
...metrization, and this has led to extensive research on characterizing such systems and exploring the connection, uncovered by R.W. Brockett and J.M.C. Clark [
15 KB (2,302 words) - 08:03, 21 January 2024
...s generalizations and modifications which reflect various features of real systems. In the case of a finite automaton $ (A, S, B, \phi , \psi ) $
..., algebraic theory of|Automata, algebraic theory of]]); problems in coding theory generate the concepts of self-regulating automata, reversible automata, etc
18 KB (2,794 words) - 10:01, 25 April 2020
...rcuit is one of the first classes of control systems (cf. [[Control system|Control system]]) considered from the mathematical point of view, as well as one of
...valign="top"> V.I. Shestakov, "On a logical calculus applicable to the theory of relay-contact circuits" ''Uchen. Zap. Moskov. Gosudarstv. Univ. Mat.''
8 KB (1,204 words) - 01:44, 5 March 2022
...te evolution of the process is observed by the controller. A corresponding
theory has also been developed in the case of partial observations (incomplete dat
...w.encyclopediaofmath.org/legacyimages/c/c026/c026010/c02601030.png" /> and
control action <img align="absmiddle" border="0" src="https://www.encyclopediaofmat
107 KB (14,649 words) - 21:43, 15 December 2020
...of finite-dimensional vector spaces, fields, algebraic systems, functional systems, etc.) which is independent of the particular computer used and which may b
...arious programming methods. A computational algorithm contains a number of control parameters, which remain indefinite in the first part, form a fixed part of
10 KB (1,642 words) - 08:41, 29 August 2014
...bjects, such as complex spaces, topological manifolds, algebras, etc. Such systems occur in may parts of mathematics both as tools and as objects to be invest
parameter systems of smooth curves $ \{ \sigma ^ {1} \dots \sigma ^ {n} \} $
20 KB (3,056 words) - 08:25, 6 June 2020
...(from their own specific standpoints). By revealing the general aspects in systems of such different nature, cybernetics provides a general and moreover new m
In many specific cybernetic systems, time is regarded as a parameter taking only a discrete set of values (usua
35 KB (5,424 words) - 11:17, 26 March 2023
...cal systems with discrete states and changes of states called events; such systems arise e.g. in digital network communication protocols.
...l calculus" D. Franke (ed.) F. Kraus (ed.) , ''Design Methods of Control Systems'' , '''2''' , Pergamon (1991) pp. 723–728</TD></TR></table>
8 KB (1,166 words) - 06:28, 30 May 2020
In control theory one studies equations $ \dot{x} = f( x, u) $
with a control parameter $ u $;
11 KB (1,659 words) - 05:14, 24 February 2022
...[[Krein space|Krein space]]). The results are used in [[H^infinity-control-theory| $ H ^ \infty $
control theory]] (see [[#References|[a8]]]), and when the data are Fourier coefficients of
11 KB (1,460 words) - 14:32, 7 June 2020
...uters and of programming them relies, to a large extent, on ideas from the theory of algorithms and mathematical cybernetics. In turn, practical work with co
Common to all abstract machines is the presence of a finite control device that may be in one of the states $ q _ {1} \dots q _ {k} $.
18 KB (2,656 words) - 04:11, 6 June 2020
The modern theory of linear inequalities has been constructed on the basis of this generaliza
...onomic technology and economic planning reduce to the solution of specific systems of linear inequalities; this has significantly determined the modern trend
14 KB (2,052 words) - 10:49, 21 March 2022
...ts. Actually, Wold introduced (a1) as a joint representation for AR and MA systems (cf. also [[Mixed autoregressive moving-average process|Mixed autoregressiv
...esponding to stable and miniphase ARMA or (finite-dimensional) state space systems is by far the most important one. In this case there is a wide class of ide
9 KB (1,297 words) - 09:30, 3 February 2024
...rators which is one of the most important classes of operators in function theory; it has many applications in different fields of mathematics and applied ma
...Hankel operators. The following realization is very important in function theory. Given a function $\phi \in L ^ { \infty }$, one defines the Hankel operato
18 KB (2,757 words) - 00:48, 15 February 2024