On a construction of an extension of a control problem with integral constraints. (Russian) Zbl 0707.49002

The author considers a linear control system \[ (1)\quad \dot x=A(t)x+b(t)u(t) \] where b is a discontinuous function and u is a measurable function satisfying \[ (2)\quad \int | u(t)| \lambda (dt)\leq c, \] where \(\lambda\) is the trace of the corresponding Lebesgue measure. Using a compactification procedure, a relaxation of an optimal control problem for (1), (2) is introduced and conditions for relaxation stability are derived.
Reviewer: A.L.Dontchev


49J15 Existence theories for optimal control problems involving ordinary differential equations
49J45 Methods involving semicontinuity and convergence; relaxation
49N99 Miscellaneous topics in calculus of variations and optimal control