Time-optimal control of two-dimensional systems and regular synthesis.(English)Zbl 0753.49008

Summary: A time-optimal control of a system $$u'=v-F(u)$$, $$v'=-g(u)+w(t)$$, $$| w|\leq K$$, $$F$$, $$g\in C^ 1(R)$$ is studied. Pontryagin’s maximum principle is used to prove that optimal controls are piecewise constant. An optimal feedback control is studied and a construction of a locus of switching is described. Then a regular synthesis in Boltyanskij’s sense is defined and its existence is proved in special cases. In the last part the obtained results are compared with the classical ones of P. Boltyanskij, and E. B. Lee and L. Markus.

MSC:

 49K15 Optimality conditions for problems involving ordinary differential equations
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