Chebyshev approximations in parametric optimization problems for controlled processes. III: Optimal control problems (Q1319736)

Some properties of extremum points in mathematical programming problems with a continuum of constraints, generalizing the known results of nonlinear Chebyshev approximation theory, have been proposed in the previous parts [Autom. Telemekh. 1992, No. 2, 60-67 (1992; Zbl 0790.49011); ibid. No. 3, 59-64 (1992; Zbl 0810.49029)]. An algorithm to find the corresponding extremals has been developed on the basis of these properties. Part III applies this technique to solve some optimal control problems with nonsmooth boundaries of feasible regions of final states in appropriate phase spaces, for which the use of the standard transversality conditions runs into difficulties. A number of related problems can be parametrized to fit the proposed scheme.