【摘要】 本文提供的基础定理可用于各类无界最优控制问题。我们已将之用于快速控制问题、二次不定判据最优控制问题和固定时间的一般指标无界最优控制问题。更多还原

【Abstract】 In this paper, some theorems underlying the discussion of unbounded control for distributed parameter systems are obtained.Let be a triple structure in which V embeds compactly in H and is an Hermite elliptic continuous sesquilinear form on V. Operator is defined by a Let A be the restriction of on (A) = .Theorem 1 -(?) is a n infinitesimal generator of Co equi-bounded operator semigroup e-t on the dual space V’ with propertiescomst/t t>0.2) the restriction of e-t on H is e-At,t≥0. Theorem Ⅱ Let , Z being a Banach space. Linear evolution equation on v’ of first and second order admits mild solutions respectively given by , where , and . where C(t)0and S(f)are corresponding generalized cosine and sine operator families, x(·) ∈C((0, + ∞);H).We have applied the above results to tackle problems such as time optimal control and quadratic cost optimal control of linear evolution systems, their settings being pointwise or boundary control of parabolic and hyperbolic systems.更多还原