$#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
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...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
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...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></
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...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
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...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.
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...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