Abstract

Given an x0Rn we study the infinite horizon problem of minimizing the expression 0Tf(t,x(t),x(t))dt as T grows to infinity where x:[0,)Rn satisfies the initial condition x(0)=x0. We analyse the existence and the properties of approximate solutions for every prescribed initial value x0. We also establish that for every bounded set ERn the C([0,T]) norms of approximate solutions x:[0,T]Rn for the minimization problem on an interval [0,T] with x(0),x(T)E are bounded by some constant which does not depend on T.