Optimal trajectories of infinite-horizon deterministic control systems

摘要: We study the infinite-horizon deterministic control problem of minimizingź0T L(z, ź) dt, Tźź, whereL(z, ·) is convex inź for fixedz but not necessarily jointly in (z, ź). prove existence a solution to Bellman equation and use it define differential inclusion, which reduces certain cases an ordinary equation. discuss where solutions this inclusion (equation) provide optimal (in overtaking optimality sense) optimization problem. A quantity special interest minimal long-run average-cost growth rate. compute explicitly show that equal minxL(x, 0) following two cases: one scalar casen = 1 other is' when integrand separated form $$l(x) + g(\dot x)$$