On the Optimal Speed Problem for the Class of Linear Autonomous Infinite-Dimensional Discrete-Time Systems with Bounded Control and Degenerate Operator

Ibragimov, D. N.

doi:10.1134/s0005117919030019

Cited by 12 publications

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“…sets of initial states from which the system can be transferred to the origin, in a finite number of steps, as well as estimates of the limit reachable and null-controllable sets [1]. The null-controllable and reachable sets can be used in optimal control problems to construct positional control for discrete-time systems [2,3]. Thus it is possible to judge the solvability of these problems in principle by the apparatus of limit sets.…”

Section: Introductionmentioning

confidence: 99%

On the External Estimation of Reachable and Null-Controllable Limit Sets for Linear Discrete-Time Systems with a Summary Constraint on the Scalar Control

Ibragimov

2024

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The problem of constructing reachable and null-controllable sets for stationary linear discrete-time systems with a summary constraint on the scalar control is considered. For the case of quadratic constraints and a diagonalizable matrix of the system, these sets are built explicitly in the form of ellipsoids. In the general case, the limit reachable and null-controllable sets are represented as fixed points of a contraction mapping in the metric space of compact sets. On the basis of the method of simple iteration, a convergent procedure for constructing their external estimates with an indication of the a priori approximation error is proposed. Examples are given.

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Section: Introductionmentioning

confidence: 99%