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Strong local optimality for a bang-bang trajectory in a Mayer problem. (English) Zbl 1230.49003

Summary: This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of those considered in A. A. Agrachev, G. Stefani, and P. Zezza [SIAM J. Control Optim., 41, pp. 991-1014, (2002, Zbl 1020.49021)], L. Poggiolini [Rend. Semin. Mat. Univ. Politec. Torino, 64, pp. 1-23, (2006, Zbl 1169.49019)], and L. Poggiolini and G. Stefani [Systems Control Lett., 53, pp. 269-279, (2004, Zbl 1157.49305)]. We require both the strict bang-bang Legendre condition and second order conditions for the finite dimensional problem obtained by moving the switching times of the reference trajectory.

MSC:

49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
49K15 Optimality conditions for problems involving ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
93C10 Nonlinear systems in control theory
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