Parametric suboptimal control of distributed systems with pointwise state constraints

  • M.I. Sumin


The article is devoted to the suboptimal control theory for nonlinear distributed systems with infinite-dimensional parameter in pointwise state constraints. A basic "element" of this theory is a minimizing sequence of usual (Lebesgue measurable) controls but not an optimal usual or a relaxed control in contrast to the traditional optimal control theory. As a concrete controlled system a so-called characteristic Cauchy problem for the vectorial nonlinear hyperbolic equation, known also under a title of a problem of Goursat - Darboux, here is considered. We consider the following main optimization questions: 1) necessary and sufficient conditions for minimizing sequences; 2) properties of regularity and normality of the suboptimal control problem; 3) differential properties of the value function; sensitivity; 4) approximation of the problem with pointwise state constraint by similar problems with finite number of functional constraints. An application of these results for construction of suboptimal controls in the problem with pointwise state constraints is discussed also.