Reachability and Controllability of Discrete-Time Systems under Control Actions Bounded in Magnitude and Norm

Сиротин, А. Н.; Formalskii, Аlexander М.

doi:10.1023/b:aurc.0000008423.93495.be

Cited by 20 publications

(5 citation statements)

References 6 publications

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“…In particular, it is proved that in the case of linear constraints on the control, the reachable and null-controllable sets in a finite number of steps are polyhedra [2]. For their limit analogues, necessary and sufficient conditions for the boundedness are formulated [7][8][9]. At the same time, most of the papers are either focused on studying only the general properties of reachable and nullcontrollable limit sets [8][9][10][11][12], or consider systems with unbounded control [10][11][12][13][14].…”

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

ARC

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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%

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

ARC

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“…Integral constraint on the control functions does not yield the geometric boundedness, and therefore for investigation of the control systems with integral constraint on the control functions is required to apply different approaches. In papers [1] - [5] the attainable sets of the linear systems, in papers [6] - [8] approximation of the attainable sets of the systems which are affine with respect to the control vector, and in papers [9], [10] approximation of the attainable sets of the nonlinear systems are studied. For linear and affine systems one can obtain the approximations with error evaluation.…”

Section: Introductionmentioning

confidence: 99%

Approximations of the Set of Trajectories and Integral Funnel of the Nonlinear Control Systems with Limited Control Resources

Hüseyin¹,

Hüseyin²,

Guseinov³

2022

Preprint

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In this paper approximations of the set of trajectories and integral funnel of the control system described by nonlinear ordinary differential equation with integral constraint on the control functions are considered. The set of admissible control functions is replaced by a set, consisting of a finite number of piecewise-constant control functions. It is shown that the set of trajectories generated by a finite number of piecewise-constant control functions is an internal approximation of the set of trajectories. Further, each trajectory generated by a piecewise-constant control function is substituted by appropriate Euler's broken line and it is proved that the set consisting of a finite number of Euler's broken lines is an approximation of the set of trajectories of given control system. An approximation of the system's integral funnel by a set consisting of a finite number of points is obtained.

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“…In [18], zero-controllability of linear discrete-time systems under control actions bounded in magnitude and norm was discussed analytically. The controllability of constrained nonlinear Keywords and phrases.…”

Section: Introductionmentioning

confidence: 99%

Control of constrained nonlinear uncertain discrete-time systemsviarobust controllable sets: a modal interval analysis approach

et al. 2009

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Abstract.A general framework for computing robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed robust controllable sets is introduced in this paper. The addressed one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solver of 1-dimensional quantified set inversion in modal interval analysis is extended to 2-dimensional cases for computing robust controllable sets off-line with a clear semantic interpretation, where both universal and existential quantifiers are concerned simultaneously. An interval-based solver of constrained minimax optimization is also proposed to compute one-step control inputs online in a reliable way, which guarantee to drive the system state contractively along the computed robust controllable sets to a selected terminal robust control invariant set.Mathematics Subject Classification. 65G40, 93B05, 93B51.

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Reachability and Controllability of Discrete-Time Systems under Control Actions Bounded in Magnitude and Norm

Cited by 20 publications

References 6 publications

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

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

Approximations of the Set of Trajectories and Integral Funnel of the Nonlinear Control Systems with Limited Control Resources

Control of constrained nonlinear uncertain discrete-time systemsviarobust controllable sets: a modal interval analysis approach

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