2011
DOI: 10.1134/s1990478911040016
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Approximate solution to the resource consumption minimization problem. I. Construction of a quasioptimal control

Abstract: For linear systems with constrained control and fixed transition time, we propose two methods for solving the resource consumption minimization problem approximately. We prove that the switching moments of resource-quasioptimal controls are independent of the initial conditions and constant for autonomous systems. Some region of the initial conditions is found for which the constraints on the control are never violated.

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Cited by 2 publications
(3 citation 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%
“…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%
“…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%