Skip to main content
Log in

Parametric optimal control problems with weighted L 1-norm in the cost function

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

Abstract

In the paper, an optimal control problem with weighted L 1-norm in the cost function is studied. The problem is considered as a parametric problem where L 1-norm weight ratio is treated as a parameter. We analyze the dependence of solution to the mentioned optimization problem on values of the parameter. A theorem that describes properties of the solution under small parameter perturbations is proved. Differential properties of the solution are investigated. Under assumption that a solution to unperturbed problem is known, rules for construction of solutions to perturbed optimization problems are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Stadler, G., Elliptic Optimal Control Problems with L 1-Control Cost and Applications for the Placement of Control Devices, Computational Optimization and Applications, 2009, vol. 44, no. 2, pp. 159–181.

    Article  MATH  MathSciNet  Google Scholar 

  2. Figueiredo, M.A.T., Nowak, R.D., and Wright, S.J., Gradient Projection for Sparse Reconstruction: Applications to Compressed Sensing and Other Inverse Problems, IEEE Journal of Selected Topics in Signal Processing, 2007, vol. 4, pp. 586–597.

    Article  Google Scholar 

  3. Fornasier, M. and Rauhut, H., Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints, SIAM Journal on Numerical Analysis, 2008, vol. 46, no. 2, pp. 577–613.

    Article  MATH  MathSciNet  Google Scholar 

  4. Daubechies, I., Fornasier, M., and Loris, I., Accelerated Projected Gradient Methods for Linear Inverse Problems with Sparsity Constraints, Journal of Fourier Analysis and Applications, 2008, vol. 14, nos. 5–6, pp. 764–792.

    Article  MATH  MathSciNet  Google Scholar 

  5. Kostyukova, O.I. and Kurdina, M.A., Asymptotic Properties of Solutions of Parametric Optimal Control Problems with Varying Index of the Singular Arcs, Differential Equaltions, 2008, vol. 44, no. 11, pp. 1510–1522.

    MathSciNet  Google Scholar 

  6. Bliss, G., Lectures on the Calculus of Variations, The University of Chicago Press, 1963.

  7. Krawczyk, D. and Rudnicki, M., Regularization Parameter Selection in Discrete Ill-posed Problems—The Use of the u-Curve, Int. J. Appl. Math. Comput. Sci.. 2007, vol. 17, no. 2, pp. 157–164.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to O. I. Kostyukova.

Additional information

Original Russian Text © O.I. Kostyukova, E.A. Kostina, N.M. Fedortsova, 2010, published in Avtomatika i Vychislitel’naya Tekhnika, 2010, No. 4, pp. 5–18.

The article was translated by the authors.

About this article

Cite this article

Kostyukova, O.I., Kostina, E.A. & Fedortsova, N.M. Parametric optimal control problems with weighted L 1-norm in the cost function. Aut. Conrol Comp. Sci. 44, 179–190 (2010). https://doi.org/10.3103/S0146411610040012

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411610040012

Key words

Navigation