Approximate solution to the resource consumption minimization problem. I. Construction of a quasioptimal control

Александров, В. М.; Dykhta, V. A.

doi:10.1134/s1990478911040016

Cited by 2 publications

(3 citation statements)

References 11 publications

(11 reference statements)

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“…In these cases, the approximate methods are used [17][18][19][20][21] for solution of optimal control problem, and the resulting solution was called quasioptimal [22].…”

Section: Methodsmentioning

confidence: 99%

Algorithms of the information stimulation system of Russian citizens’ socio-optimal actions

Geraskin¹

2017

Collection of Selected Papers of the III International Conference on Information Technology and Nanotechnology

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The problem of the development of the state information stimulation system of Russian citizens' socio-optimal actions is considered according to the optimum of collective utility function as criterion. Conceptual model of the system is formed according to the conditions of individual rationality, Pareto efficiency, nonmanipulability and dynamic quasi-optimality. The algorithms of the information system are developed such as a process of step-by-step approximations. The system's criterion on each approximation does not decrease and the constraint on the stimulation fund is fulfilled.

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“…In these cases, the approximate methods are used [17][18][19][20][21] for solution of optimal control problem, and the resulting solution was called quasioptimal [22].…”

Section: Methodsmentioning

confidence: 99%

Algorithms of the information stimulation system of Russian citizens’ socio-optimal actions

Geraskin¹

2017

Collection of Selected Papers of the III International Conference on Information Technology and Nanotechnology

View full text Add to dashboard Cite

show abstract

“…Fig. 3, a depicts the dependence of J (1) kv /J (1) opt for a series of values of μ. The greater |x 1 (t 0 )| (i.e., ξ 1 ) and the given time T (i.e., μ), the less is the difference between the quasioptimal and optimal processes.…”

Section: Estimates For the Proximity Of Quasioptimal Control To Optimmentioning

confidence: 98%

“…Therefore, this is an approximating construction which yields an approximate solution to the resource consumption minimization problem. (1) opt (the seesaw piecewise broken curve I with variable slope) for the second order systemẋ 2 = x 2 ,ẋ 2 = bu and the initial phase point lying on the axis x 1 . The region Proof.…”

Section: Fig 4 Subdivision Of the Region Of Initial Conditions Intomentioning

confidence: 99%

Approximate solution to the resource consumption minimization problem. II. Estimates for the proximity of controls

Александров

Dykhta

2012

J. Appl. Ind. Math.

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The proximity is estimated of a resource quasioptimal control to the optimal control. We give a method for subdividing the bounded region of initial conditions into subregions and bringing the quasioptimal control closer to the resource optimal control. This article continues [1]. We keep all notation and definitions of [1] and also continue the numbering of sections, propositions, formulas, and figures.In the first part of the article for the linear systeṁwith bounded control |u j | ≤ M j , j = 1, m, and fixed transition time we proposed some approximate solution method for the resource consumption minimization problem.Problem. Find an admissible control u 0 (t) taking the linear system from an initial state x(t 0 ) = x 0 to the origin x(t k ) = 0 in a fixed time T = t k − t 0 , T ≥ T 0 , and minimizing the functionalHere T 0 is the time of a reaction-speed-optimal control. For the maximal values |x i (t 0 )| max , i = 1, n, in a bounded region of initial conditions D, we find the resource optimal controls. We construct n "axial" quasioptimal controls: we take the switching moments equal to those of the optimal control for the boundary point on this axis, while the control amplitude is directly proportional to the initial condition x i (t 0 ) on the ith axis taken with some weight. We proved the independence of the switching moments of the initial conditions and their constancy for systems with constant parameters. The combined control with respect to all axes takes a linear system from an arbitrary initial point in the controllability region V of the phase space into the origin in a specified time T and approximately minimizes resource consumption. We found the region of the initial conditions for which the constraints on the control are satisfied. *

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Approximate solution to the resource consumption minimization problem. I. Construction of a quasioptimal control

Cited by 2 publications

References 11 publications

Algorithms of the information stimulation system of Russian citizens’ socio-optimal actions

Algorithms of the information stimulation system of Russian citizens’ socio-optimal actions

Approximate solution to the resource consumption minimization problem. II. Estimates for the proximity of controls

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