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Time-optimal control under state-dependent control restraints

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We consider the control system

$$\dot x = Ax + Bu,$$

subject to the state-dependent control restraint

$$u(t) \in \Omega \cap (\mathcal{H}{\text{ + }}Cx(t)\} ,$$

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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This work was supported in part by the National Research Council of Canada, under Grant No. A4641.

Communicated by G. Leitmann

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Stern, R.J. Time-optimal control under state-dependent control restraints. J Optim Theory Appl 24, 585–606 (1978).

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Key Words

  • State-dependent control restraints
  • state restraints
  • maximality
  • time-optimal control