- 期刊
EXISTENCE AND UNIFORM BOUNDEDNESS OF OPTIMAL SOLUTIONS OF VARIATIONAL PROBLEMS
並列摘要
Given an x0 ∈ R^n we study the infinite horizon problem of minimizing the expression ∫_0^T f(t, x(t), x^1(t))dt as T grows to infinity where x : [0,∞) → Rn satisfies the initial condition x(0) = x_0. We analyse the existence and the properties of approximate solutions for every prescribed initial value x0.W e also establish that for every bounded set E ⊂ R^ n 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.
並列關鍵字
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