High Order Discrete Approximations to Mayer's Problems for Linear Systems

Pietrus, Alain; Scarinci, Teresa; Veliov, Vladimir M.

doi:10.1137/16m1079142

Cited by 38 publications

(20 citation statements)

References 14 publications

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“…}, corresponding to the multiplicity of the zeros of the switching function. As argued in [23], the case κ = 1 is in a certain sense "generic" and the error estimate (3.17) is of second order in this case. Also in the case κ > 1 the order of accuracy is doubled in comparison with that proved in [26] for the Euler scheme.…”

Section: Construction Of Continuous-time Controls and Order Of Convermentioning

confidence: 77%

“…[1,2,13,18,26]). As mentioned in the introduction, in doing this we use an idea that originates from [15,28] and was implemented in [23] in the case of Mayer's problems. The approach uses second order truncated Volterra-Fliess series, as described in the next subsection.…”

Section: Discretization Schemementioning

confidence: 99%

“…As pointed out in [23], it is a matter of standard calculation to represent the set Z in the more convenient way as…”

Section: The Numerical Schemementioning

confidence: 99%

“…The construction is by idea similar to that in [23] with the essential difference that now u takes values only in the set {−1, 1} and the construction is simpler. …”

Section: Construction Of Continuous-time Controls and Order Of Convermentioning

confidence: 99%

“…A new type of discretization scheme was recently presented in [23] for Mayer's problems for linear systems. The idea behind this scheme goes back to [15,20,28] and is based on a truncated Volterra-Fliess-type expansion of the state and adjoint equations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Higher-order numerical scheme for linear quadratic problems with bang–bang controls

Scarinci

Veliov

2017

Comput Optim Appl

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This paper considers a linear-quadratic optimal control problem where the control function appears linearly and takes values in a hypercube. It is assumed that the optimal controls are of purely bang-bang type and that the switching function, associated with the problem, exhibits a suitable growth around its zeros. The authors introduce a scheme for the discretization of the problem that doubles the rate of convergence of the Euler's scheme. The proof of the accuracy estimate employs some recently obtained results concerning the stability of the optimal solutions with respect to disturbances.Keywords Optimal control · Numerical methods · Bang-bang control · Linear-quadratic optimal control problems · Time-discretization methods Mathematics Subject Classification

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Section: Construction Of Continuous-time Controls and Order Of Convermentioning

confidence: 77%

Section: Discretization Schemementioning

confidence: 99%

“…As pointed out in [23], it is a matter of standard calculation to represent the set Z in the more convenient way as…”

Section: The Numerical Schemementioning

confidence: 99%

“…The construction is by idea similar to that in [23] with the essential difference that now u takes values only in the set {−1, 1} and the construction is simpler. …”

Section: Construction Of Continuous-time Controls and Order Of Convermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Higher-order numerical scheme for linear quadratic problems with bang–bang controls

Scarinci

Veliov

2017

Comput Optim Appl

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An inertial‐like Tseng's extragradient method for solving pseudomonotone variational inequalities in reflexive Banach spaces

Mewomo,

Alakoya,

Eze

et al. 2024

Math Methods in App Sciences

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A survey of the existing results in the literature shows that several of the results on variational inequality problem were established under some stringent conditions and employed some form of linesearch technique even in the framework of Hilbert spaces. However, due to the loop nature of the linesearch technique, the implementation of such algorithms might be economically nonviable. In this article, we study the pseudomonotone variational inequality problem. We propose a new inertial‐like Tseng's extragradient method with non‐monotonic self‐adaptive step size that does not involve any linesearch technique for finding the solution of the problem in reflexive Banach spaces. Under some mild conditions, we prove a strong convergence result for the proposed method without the sequentially weakly continuity condition often assumed by authors to guarantee convergence when studying the pseudomonotone variational inequality problems. Moreover, we apply our result to study a constrained convex minimization problem. Finally, we present several theoretical and real applications to optimal control numerical experiments to illustrate and show the performance of our method in comparison with related methods in the literature.

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Error Analysis for the Implicit Euler Discretization of Linear-Quadratic Control Problems with Higher Index DAEs and Bang–Bang Solutions

Martens

Gerdts

2020

Differential-Algebraic Equations Forum

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High Order Discrete Approximations to Mayer's Problems for Linear Systems

Cited by 38 publications

References 14 publications

Higher-order numerical scheme for linear quadratic problems with bang–bang controls

Higher-order numerical scheme for linear quadratic problems with bang–bang controls

An inertial‐like Tseng's extragradient method for solving pseudomonotone variational inequalities in reflexive Banach spaces

Error Analysis for the Implicit Euler Discretization of Linear-Quadratic Control Problems with Higher Index DAEs and Bang–Bang Solutions

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