“Robustness Analysis of a Class of Optimal Control Systems”

Authors: Ole A. Solheim,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1983, Vol 4, No 4, pp. 223-235.

Keywords: Optimal control systems, robustness analysis

Abstract: This paper deals with a class of optimal control systems, where the controller. in addition to minimizing a quadratic criterion, also shall give the closed-loop system prescribed eigenvalues. Three methods for analysing the robustness of such systems under parameter perturbations are discussed: Eigenvalue sensitivity, singular values and the block Gerschgorin theorem. Numerical examples are presented to illustrate the different methods.

PDF PDF (2297 Kb)        DOI: 10.4173/mic.1983.4.3

DOI forward links to this article:
[1] R.I. Badr, M.F. Hassan, J. Bernussou and A.Y. Bilal (1989), doi:10.1016/0005-1098(89)90060-5
[2] Olav Egeland (1987), doi:10.4173/mic.1987.3.3
[3] O. Egeland (1986), doi:10.1109/ROBOT.1986.1087605
[1] ANDERSEN, B.D.O., MOORE, J.B. (1971). Linear optimal control, Prentice-Hall.
[2] DOYLE, J.C., STEIN, G. (1981). Multivariable feedback design: Concepts for a classical/modern synthesis, IEEE Trans. autom. Control, 26,4-16 doi:10.1109/TAC.1981.1102555
[3] FADDEEV, D.K., FADDEEVA, V.N. (1963). Computational methods of linear algebra, W. H. Freeman and Ca.
[4] GRAUPE, D. (1972). Derivation of weighting matrices towards satisfying eigenvalue requirements, Int. J. Control, 16,881-888.
[5] GOURISCHANKAR, V., RAMAR, K. (1976). Pole assignment with minimum eigenvalue sensitivity to plant parameter variations, Int. J. Control, 23,493-504 doi:10.1080/00207177608922175
[6] HEGER, F., FRANK, P.M. (1982). Computer-aided pole placement for the design of robust control systems, IFAC Symposium on Computer aided design of multi-variable technological systems, Purdue Univ., Lafayette, Ind., Sept. 15-17, 1982.
[7] HOWZE, J.W., CARIN, III, R.K. (1979). Regulator design with nodal insensitivity, IEEE Trans. autom. Control, 24, 466-469 doi:10.1109/TAC.1979.1102050
[8] LEHTOMAKI, N.A., SANDELL, N.R., ATHANS, M. (1981). Robustness results in linear-quadratic Gaussian based multivariable design, IEEE Trans. autom. Control, 26, 75-93 doi:10.1109/TAC.1981.1102565
[9] LEHTOMAKI, N.A., et al. (1981). Robustness tests utilizing the structure of modelling errors, 20th CDC, San Diego, Dec. 16-18.
[10] LEE, W.H., GULLY, S.W., ETERNO, J.S., SANDELL, N.R. (1982). Structural information in robustness analysis, American Control Conference.ACC, Arlington, Va, June 14-16, 1982.
[11] MACFARLANE, A.G.J. (1981). Characteristic and principal gains and phases and their use as multivariable control design tools, AGARD Lecture series No. 117, Paper no. 2, 1-34.
[12] SAMBANDAN, A., CHANDRASEKHARAN, P. C. (1981). Design of output feedback controller with eigenvalue and eigenvector intensitivity, Int. J. Control, 33, 935-943 doi:10.1080/00207178108922965
[13] SHAH, S.L., FISHER, D.G., SEBORG, D. E. (1955). Eigenvalue invariance to system parameter variations by eigenvector assignment, Int. J. Control, 26, 871-881.
[14] SOLHEIM, O.A. (1981). On the use of a block analogue of the Gerschgorin circle theorem in the design of decentralized control of a class of large scale systems, 2nd IFAC symposium on large scale systems, Toulouse, June 24-26, 1980. Modeling, Identification and Control, 2, 107-118 doi:10.4173/mic.1981.2.5
[15] SOLHEIM, O.A. (1980). On the use of low-order Riccati equations in the design of a class of feedback controllers and state estimators, Modeling, Identification and Control, 1, 231-245 doi:10.4173/mic.1980.4.3
[16] SOLHEIM, O.A. (1972). Design of optimal control systems with prescribed eigenvalues, Int. J. Control, 15, 142-160 doi:10.1080/00207177208932136
[17] SOLHEIM, O.A., SÆLID, S. (1971). Eigenvalue sensitivity in optimal feedback control systems, 2nd IFAC Symposium on Multivariable technical control systems, Düsseldorf, Oct. 11-13, 1971.
[18] TAYLOR, J.S. TUTEUR, F.B. (1966). The use of a quadratic perturbance index to design multivariable control systems, IEEE Trans. Autom. Control, 11, 84-92 doi:10.1109/TAC.1966.1098243

  title={{Robustness Analysis of a Class of Optimal Control Systems}},
  author={Solheim, Ole A.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}