解受限最优控制问题的混合罚函数方法

THE MIXED PENALTY FUNCTION METHODS FOR SOLVING THE CONSTRAINED OPTIMAL CONTROL PROBLEMS

中文摘要

      考虑的受控系统是关于控制向量u为线性的情形（见式（1），（2））。作者曾用同意的方法把外罚函数和内罚函数的概念作了扩展并用来解受限最优控制问题[7，8]。本文在这些工作上第一次直接地在连续最优控制系统中，把外罚函数和内罚函数联合起来，组成混合罚函数，以解决状态向量受限的最优控制问题。我们给出了在适当条件下带混合罚函数的最优控制问题，一定有非受限解并且在极限情形下等价于原来的受限最优控制问题。这就为使用混合罚函数方法来解决连续控制系统受限最优控制问题而提供了理论基础。

英文摘要

      The articles[7,8] have taken a unified approach to define the concepts of exterior and interior functions, and have taken the generalized exterior and interior penalty functions to solve the constrained optimal control problems. In this paper, our work is funded on [7,8]. We combine the exterior and interior penalty functions to produce a mixed method for solving the constrained optimal control problems in the following form: {dx/dt =g(t,x)+B(t,x)u, x(au)=x0,x(bu)=x1, x(t)∈B=B`∩B``,u(t) ∈U,au≤t≤bu, J[u]=buau{g0(t ,x)+}dt=min, Where denotes inner product; g(t,x), g0(t,x) and h0(t,x ) are n-vectors, 1-vector and r-vectors functions are continuous for (t,x) ∈[a,b]XRn and continuously differentiable for x∈Rn; u is a vector and its range is in U; U is a convex compact set in Rr with nonempty interior; B` and B`` are clased sets in Rr with nonempty interior.