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On the existence of the optimal control for linear uncontrollable systems

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Abstract

The optimal control of time-invariant, uncontrollable linear systems with respect to an integral quadratic performance index over an infinite time interval is considered. It is proved that the asymptotic stability of the uncontrollable part of the system is a necessary and sufficient condition for the existence of the solution.

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References

  1. 1.

    Athans, M., andFalb, P. L.,Optimal Control, McGraw-Hill Book Company, New York, 1966.

  2. 2.

    Gilbert, E. G.,Controllability and Observability in Multivariable Control Systems, SIAM Journal on Control, Vol. 1, No. 2, 1963.

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Additional information

This research was supported by the CNR (Consiglio Nazionale delle Ricerche), Rome, Italy.

Communicated by R. Conti

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Guardabassi, G., Locatelli, A. & Rinaldi, S. On the existence of the optimal control for linear uncontrollable systems. J Optim Theory Appl 3, 72–75 (1969). https://doi.org/10.1007/BF00929542

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Keywords

  • Linear System
  • Performance Index
  • Asymptotic Stability
  • Infinite Time
  • Quadratic Performance