Abstract
The asymptotic solution of the linear quadratic state regulator problem is obtained as the cost of the control tends to zero. Matrix Riccati gains are obtained via singular perturbations theory and are used to asymptotically calculate the optimal control and the corresponding trajectories. Several cases are distinguished and applications are discussed.
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Communicated by J. L. Lions
Work supported by the U.S. Atomic Energy Commission under Contract No. AT(11-1)-3077.
Work supported by the Office of Naval Research under Contract No. N00014-67-A-0209-0022.
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Jameson, A., O'Malley, R.E. Cheap control of the time-invariant regulator. Appl Math Optim 1, 337–354 (1975). https://doi.org/10.1007/BF01447957
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DOI: https://doi.org/10.1007/BF01447957