Abstract
We consider the control system
subject to the state-dependent control restraint
where Ω is a compact convex set, ℋ is a subspace, andC is a matrix. The existence of time-optimal maximal controls is proven. A natural application of this result is in solving time-optimal problems under the control restraintu(t)∈Ω and the requirement that the outputy=Sx be maintained at zero during the transfer, whereS is a given matrix. An example is provided.
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References
Lee, E. B., andMarkus, L.,Foundations of Optimal Control Theory, John Wiley and Sons, New York, New York, 1967.
Strauss, A.,An Introduction to Optimal control Theory, Springer-Verlag, New York, New York, 1968.
Basile, G., andMarro, G.,Controlled and Conditioned Invariant Subspaces in Linear System Theory, Journal of Optimization Theory and Applications, Vol. 3, pp. 306–315, 1969.
Wonham, W., andMorse, A. S.,Decoupling and Pole Assignment in Linear Multivariable Systems: A Geometric Approach, SIAM Journal on Control, Vol. 8, pp. 1–18, 1970.
Pachter, M., andStern, R. J.,The Controllability Problem for Affine Targets (to appear).
Pachter, M., andStern, R. J.,On State-Restrained Linear-Quadratic Control Problems, Journal of Mathematical Analysis and Applications (to appear).
Heymann, M.,Control Dominance, Weak Invariance and Feedback, Journal of Mathematical Analysis and Applications (to appear).
Hájek, O.,Cores of Targets in Linear Control Systems, Mathematical Systems Theory, Vol. 8, pp. 203–206, 1974.
Morse, A. S., andWonham, W.,Decoupling and Pole Assignment by Dynamic Compensation, SIAM Journal on Control, Vol. 8, pp. 317–337, 1970.
Valentine, F. A.,Convex Sets, McGraw-Hill Book Company, New York, New York, 1964.
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Communicated by G. Leitmann
This work was supported in part by the National Research Council of Canada, under Grant No. A4641.
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Stern, R.J. Time-optimal control under state-dependent control restraints. J Optim Theory Appl 24, 585–606 (1978). https://doi.org/10.1007/BF00935301
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DOI: https://doi.org/10.1007/BF00935301