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Robust inverse optimal control for flexible structures

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Abstract

An inverse optimal control problem is formulated to develop robust control laws for purely oscillatory systems. The optimal control solution requires output feedback with specified constraints, leading to robustness with respect to unmodeled modes and a large class of parameter variations. The robustness properties are proved directly from known properties of control laws resulting from quadratic performance indices. The control laws are useful for poorly damped flexible structures.

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References

  1. 1.

    Kalman, R. E.,When is a Linear Control System Optimal?, ASME Transactions, Journal of Basic Engineering, Series D, pp. 51–60, 1964.

  2. 2.

    Anderson, B. D. O., andMoore, J. B.,Linear Optimal Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.

  3. 3.

    Molinari, B. P.,The Stable Regulator Problem and Its Inverse, IEEE Transactions on Automatic Control, Vol. AC-18, pp. 454–459, 1973.

  4. 4.

    Moylan, P. J., andAnderson, B. D. O.,Nonlinear Regulator Theory and an Inverse Optimal Control Problem, IEEE Transactions on Automatic Control, Vol. AC-18, pp. 460–465, 1973.

  5. 5.

    Park, J. G., andLee, K. Y.,An Inverse Optimal Control Problem and Its Application to the Choice of Performance Index for Economic Stabilization Policy, IEEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-5, pp. 64–76, 1975.

  6. 6.

    Willems, J. C.,Least-Squares Stationary Optimal Control and the Algebraic Riccati Equation, IEEE Transactions on Automatic Control, Vol. AC-16, pp. 621–634, 1971.

  7. 7.

    Arbel, A., andGupta, N. K.,Optimal Actuator and Sensor Locations in Oscillatory Systems, Proceedings of the 13th Asilomar Conference, Pacific Grove, California, 1979.

  8. 8.

    Aubrun, J. N.,Theory of the Control of Structures by Low-Authority Controllers, AIAA Conference on Large Space Platforms, Los Angeles, California, 1978.

  9. 9.

    Russel, D.,Linear Stabilization of the Linear Oscillator in Hilbert Space, Journal of Mathematical Analysis and Applications, Vol. 25, pp. 663–675, 1969.

  10. 10.

    Balas, M. J.,Direct Velocity Feedback Control of Large Space Structures, Journal of Guidance and Control, Vol. 2, pp. 252–253, 1979.

  11. 11.

    Balas, M.,Modal Control of Certain Flexible Dynamic Systems, SIAM Journal on Control, Vol. 16, pp. 450–462, 1978.

  12. 12.

    Wonham, W. M.,On Pole Assignment in Multi-Input Controllable Linear Systems, IEEE Transactions on Automatic Control, Vol. AC-12, pp. 660–665, 1967.

  13. 13.

    Kwakernaak, H., andSivan, R.,Linear Optimal Control Systems, John Wiley and Sons (Interscience Publishers), New York, New York, 1972.

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Additional information

This research was supported by the Office of Naval Research, Contract No. N00014-77-C-0247.

Communicated by G. Leitmann

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Arbel, A., Gupta, N.K. Robust inverse optimal control for flexible structures. J Optim Theory Appl 35, 403–416 (1981). https://doi.org/10.1007/BF00934909

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Key Words

  • Inverse optimal control
  • robust control
  • Riccati equation
  • large space structures
  • flexible structures