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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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