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Regular time-optimal syntheses for smooth planar systems. (English) Zbl 0912.49018
This paper concerns regular synthesis for the time optimal control problem associated with the control system $$x'=F(x)+G(x)u$$, $$u(t)\in [-1,1]$$, where $$F,G$$ are $${\mathcal C}^3$$ vector fields on the plane with $$F(0)=0$$. The main result states that under some generic assumptions on $$F,G$$ in $${\mathcal C}^3$$, there exists a regular synthesis and all time optimal trajectories are concatenations of a finite number of smooth arcs. This is related to the results of H. J. Sussmann [SIAM J. Control Optimization 25, No. 5, 1145-1162 (1987; Zbl 0701.93035)], where analytic vector fields are considered.
Reviewer: O.Cârjá (Iaşi)

MSC:
 49K15 Optimality conditions for problems involving ordinary differential equations 49N35 Optimal feedback synthesis 93C15 Control/observation systems governed by ordinary differential equations 93B52 Feedback control
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References:
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