Resolving Controls for the Boundary Approximate Controllability of Sandwich Beams with Uncertainties the Green’s Function Approach

Khurshudyan, Asatur Zh.; Arakelyan, Sh. Kh.

doi:10.1007/s11029-019-09794-0

Cited by 3 publications

(5 citation statements)

References 16 publications

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“…This method is referred to as heuristic method. Application of the heuristic method can be found in related articles [19][20][21][22][23].…”

Section: Heuristic Methods In Controllability Analysis Of Nonlinear S...mentioning

confidence: 99%

Archives of Control Sciences

Hossain

Khurshudyan²

2019

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In this paper, we apply the heuristic method for determination of control functions for controllability analysis of nonlinear power systems. The problem of control of quasi-linear systems under proper assumptions on the nonlinear term is considered in the general statement. Making use of the Green's function solution of nonlinear systems, the exact and approximate controllability conditions are expressed in terms of unknown controls in an explicit form. The way of resolving controls determination is discussed. As a particular application, a one-machine infinite-bus system is considered described by a coupled system of three first order ordinary differential equations. Two heuristic forms of admissible controls are considered providing approximate controllability within the same amount of time having different intensities. Results of numerical simulations are presented and discussed.

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“…This method is referred to as heuristic method. Application of the heuristic method can be found in related articles [19][20][21][22][23].…”

Section: Heuristic Methods In Controllability Analysis Of Nonlinear S...mentioning

confidence: 99%

Archives of Control Sciences

Hossain

Khurshudyan²

2019

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“…Remark 1 The advantage of representation ( 9) is that because of the Dirac function in the right hand side, the solution of ( 6), (7), whenever possible, is considerably sophisticated, while the handbooks like [22] mostly contain exact solutions of homogeneous equations like (10). Moreover, since these solutions contain some arbitrary constants, the unique solution satisying (11), in principle, can be found. It is also noteworthy that there are several approaches allowing to reduce quasi-linear PDEs to ODEs of the form (6).…”

Section: The Green's Function Approachmentioning

confidence: 99%

“…where w T is the desired value to be achieved at t = T. Control function can be determined from (12) using the heuristic method developed in [7].…”

Section: The Green's Function Approachmentioning

confidence: 99%

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Archives of Control Sciences

Klamka¹,

Avetisyan²,

Khurshudyan³

2020

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In this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green's function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca's short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis confirms theoretical derivations.

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“…One of computationally efficient analytical methods for explicit determination of resolving controls is the heuristic approach . The idea of this approach is in construction of particular admissible control functions containing a set of free parameters which are determined to satisfy the controllability constraints exactly (exact controllability) or with a required accuracy (approximate controllability).…”

Section: Remarks On Explicit Determination Of the Resolving Controlsmentioning

confidence: 99%

Exact and approximate controllability of nonlinear dynamic systems in infinite time: The Green's function approach

Avetisyan

Khurshudyan

2018

Z Angew Math Mech

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A systematic method for establishment of exact and approximate controllability of dynamic systems with nonlinear state constraints within infinite time is developed. Using the recently developed Green's function approach, we derive necessary and sufficient conditions for exact controllability, as well as sufficient conditions for approximate controllability. Conditions for null‐controllability and lack of controllability are established as well. Several possibilities of deriving explicit form for resolving controls are described. Possibilities of heuristic determination of resolving controls is studied in details. The advantages and drawbacks of the method are revealed on specific examples of nonlinear wave and diffusion equations in unbounded domains.

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Resolving Controls for the Boundary Approximate Controllability of Sandwich Beams with Uncertainties the Green’s Function Approach

Cited by 3 publications

References 16 publications

Archives of Control Sciences

Archives of Control Sciences

Archives of Control Sciences

Exact and approximate controllability of nonlinear dynamic systems in infinite time: The Green's function approach

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