关于一类连续最优控制问题的一种可实现的离散方法

本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法，此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象，文中给出这种做法的理论证明和实现方案。     

一类线性奇异摄动最优控制问题的渐近解

研究了一类线性奇异摄动最优控制问题的空间对照结构,讨论了初始点固定,终端自由的情形.首先根据变分法得到了一阶最优性条件,其次运用退化最优控制问题的解证明了异宿轨道的存在性,从而结合奇异摄动理论证明了原问题空间对照结构解的存在性.进一步根据解的结构,利用边界层函数法构造了奇异摄动最优控制问题一致有效的形式渐近解.最后,通...     

一类非线性奇异积分方程的离散近似解及其误差估计

当函数f(x,t,u)满足一些[1]中常假定的条件时,我们可借助算子S~(N)和不等式证明非线性奇异积分方程有唯一的离散近似解,这个解可用关于距离的逐次逼近法得到.     

带位移非线性奇异积分方程的离散近似解

将积分区间划分为2N 等分后,我们定义了带位移的离散奇异算子■~(N).对于广义 Hilder 空间 H_(α,β,γ)中的函数 u(x),被带位移奇异算子作用后与■(N)_u 的差在分点处是 O((ln N)/(Nγ)).算子■(N)是一致有界的。利用它,我们给出了一类带位移的非线性奇异积分(哥西核)方程的离散近似解     

一类带弱奇异核非线性偏积分微分方程的全离散有限元

1引言我们将研究下面一类带弱奇异核非线性偏积分微分方程的数值解:u_t-▽·(a(u)▽u)-integral from n=0 to tβ(t-s)△u(s)ds=f(u),x∈Ω,t∈(?),(1.1) u(·,t)=0,x∈(?)Ω,t∈J,(1.2) u(·,0)=v(x),x∈Ω,(1.3)其中Ω为平面上的凸角域,J=(0,T],α和f为R上的光滑函数,满足0相似文献   

一类非线性奇异摄动差分方程的数值解法

1 引言文章考虑如下形式的非线性奇异摄动差分方程:ε·{(g(y_(k+1))-2g(y_k)+g(y_(k-1)))/h~2}+(f(y_(k+1))-f y_k))(/h+H(x_k,y_k)=0, (1.1) y_0=α,y_N=β     

一类非线性离散系统基于有界反馈的奇异H_∞控制问题

主要研究基于有界控制律的一类非线性离散系统的奇异H∞控制问题.在系统不满足正则条件的情况下,分离出正则部分与非正则部分,给出基于有界反馈与二次Lyapunov函数的离散系统奇异H∞问题可解性的必要条件以及充分条件,求出的有界控制律能使得闭环系统在保证内稳定的条件下达到干扰衰减.     

微生物间歇发酵非线性动力系统的性质及最优控制

本文针对微生物间歇发酵制取1，3-丙二醇非线性动力系统，以产物1，3-丙二醇的生产强度最大为目标泛函，建立了最优控制模型．用不可微优化理论与方法证明了模型最优解的存在性．论述了最优性函数与一阶最优性条件的等价性．     

状态约束下的抛物控制问题的罚函数方法

该文讨论了一类状态变量约束下由发展方程导出的最优控制系统，通过原问题的扰动，得到了状态变量与控制变量分离的最优性条件．     

On Global Optimality Conditions for Nonlinear Optimal Control Problems

Let a trajectory and control pair maximize globally the functional g(x(T)) in the basic optimal control problem. Then (evidently) any pair (x,u) from the level set of the functional g corresponding to the value g( (T)) is also globally optimal and satisfies the Pontryagin maximum principle. It is shown that this necessary condition for global optimality of turns out to be a sufficient one under the additional assumption of nondegeneracy of the maximum principle for every pair (x,u) from the above-mentioned level set. In particular, if the pair satisfies the Pontryagin maximum principle which is nondegenerate in the sense that for the Hamiltonian H, we have along the pair on [0,T], and if there is no another pair (x,u) such that g(x(T))=g( (T)), then is a global maximizer.     

Deterministic Global Optimization in Nonlinear Optimal Control Problems

The accurate solution of optimal control problems is crucial in many areas of engineering and applied science. For systems which are described by a nonlinear set of differential-algebraic equations, these problems have been shown to often contain multiple local minima. Methods exist which attempt to determine the global solution of these formulations. These algorithms are stochastic in nature and can still get trapped in local minima. There is currently no deterministic method which can solve, to global optimality, the nonlinear optimal control problem. In this paper a deterministic global optimization approach based on a branch and bound framework is introduced to address the nonlinear optimal control problem to global optimality. Only mild conditions on the differentiability of the dynamic system are required. The implementa-tion of the approach is discussed and computational studies are presented for four control problems which exhibit multiple local minima.     

Dinkelbach Approach to Solving a Class of Fractional Optimal Control Problems

We consider optimal control problems with functional given by the ratio of two integrals (fractional optimal control problems). In particular, we focus on a special case with affine integrands and linear dynamics with respect to state and control. Since the standard optimal control theory cannot be used directly to solve a problem of this kind, we apply Dinkelbach’s approach to linearize it. Indeed, the fractional optimal control problem can be transformed into an equivalent monoparametric family {P_q} of linear optimal control problems. The special structure of the class of problems considered allows solving the fractional problem either explicitly or requiring straightforward classical numerical techniques to solve a single equation. An application to advertising efficiency maximization is presented. This work was partially supported by the Università Ca’ Foscari, Venezia, Italy, the MIUR (PRIN cofinancing 2005), the Council for Grants (under RF President) and State Aid to Fundamental Science Schools (Grant NSh-4113.2008.6). We thank Angelo Miele, Panos Pardalos and the anonymous referees for comments and suggestions.     

A Connection between Singular Stochastic Control and Optimal Stopping

We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions.     

A Connection between Singular Stochastic Control and Optimal Stopping

We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions.     

非线性Blasius方程求解的一种新算法

通过一半无限大平板的不可压缩的两维稳定流是一个典型的工程问题,被称为边界层流问题.它是一个由三阶非线性微分方程描述的边值问题,其微分方程称为Blasius方程.首先将该边值问题转化为一对初值问题,然后用状态方程直接积分法和Taylor级数展开法对这对初值问题进行求解.与其它算法相比,具有算法简单,精度高的优点.     

Necessary Conditions for Impulsive Nonlinear Optimal Control Problems without a priori Normality Assumptions

First-order and second-order necessary conditions of optimality for an impulsive control problem that remain informative for abnormal control processes are presented and derived. One of the main features of these conditions is that no a priori normality assumptions are required. This feature follows from the fact that these conditions rely on an extremal principle which is proved for an abstract minimization problem with equality constraints, inequality constraints, and constraints given by an inclusion in a convex cone. Two simple examples illustrate the power of the main result.The first author was partially supported by the Russian Foundation for Basic Research Grant 02-01-00334. The second author was partially supported by the Russian Foundation for Basic Research Grant 00-01-00869. The third author was partially supported by Fundacao para a Ciencia e Tecnologia and by INVOTAN Grant.     

Sufficiency for Optimal Control Problems Involving Parameters

The optimal control problem is extended to the case where the performance index, the differential constraints, and the prescribed final conditions contain parameters. The sufficient condition for a minimum is derived for nonsingular problems using the sweep method. As expected, it involves the finiteness of a matrix or the location of the conjugate point. The minimum-time navigation problem is solved as a fixed final time problem to illustrate the application of the theory.     

A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

We derive a weak Maximum Principle for nonsmooth optimal control problem involving mixed constraints under some convexity assumptions. Notably we consider problems with possibly nonsmooth mixed constraints. A nonsmooth version of the positive linear independence of the gradients with respect to the control of the mixed constraints plays a key role in validation of our main result. The first author was support by FEDER and FCT-Portugal, grants POSC/EEA/SRI/61831/2004 and SFRH/BSAB/781/2008. G.N. Silva thanks the financial support of CNPq grant 200875/06-0 and FAPESP grant 07-5226-6.