A new solution property in optimal control: The lens

We consider a new property of an optimal control problem called a lens.A lens is an interior point in the state-control phase plane where—given the value of the state variable—there is only one control value satisfying the necessary optimality conditions and—given the value of the control variable—there is only one state value satisfying the necessary optimality conditions.We build a simple model that generates a lens and give necessary and sufficient conditions under which a lens occurs.     

Using continuous features in the maximum entropy model

We investigate the problem of using continuous features in the maximum entropy (MaxEnt) model. We explain why the MaxEnt model with the moment constraint (MaxEnt-MC) works well with binary features but not with the continuous features. We describe how to enhance constraints on the continuous features and show that the weights associated with the continuous features should be continuous functions instead of single values. We propose a spline-based solution to the MaxEnt model with non-linear continuous weighting functions and illustrate that the optimization problem can be converted into a standard log-linear model at a higher-dimensional space. The empirical results on two classification tasks that contain continuous features are reported. The results confirm our insight and show that our proposed solution consistently outperforms the MaxEnt-MC model and the bucketing approach with significant margins.     

连续小波变换用于解析“电化学噪音”信号的初步研究

用连续小波变换的方法将原始的电化学噪音信号转换到一时 频相平面 ,揭示出隐含于其中的混沌行为。     

具有状态约束的最大值原理在水库调度中的应用

提出采用最优控制理论来描述水库调度中的连续变化特性,建立了水库调度的最优控制模型．利用具有状态约束的最大值原理对模型进行求解,给出了水库调度最优控制策略需要满足的必要条件,分析了不同条件和环境下水库调度最优控制策略的特性和具体表示形式．某具体水库调度问题的数值算例验证了上述方法的有效性．     

一种新的相平面分区控制器的分析与仿真

通过对相平面分区控制方式的分析,为扩大控制器适用范围和降低系统参数整定难度,提出了控制器的一种改进措施,引入分段相平面分区控制方法.采用了控制力的确定方法以及改进相平面分区控制器参数整定原则,并对系统稳定性进行了分析.通过高阶系统仿真示例,分析了改进相平面分区控制系统中的第一控制器参数、第二控制器参数、作用时间这三类控制参数对系统性能的影响.仿真结果表明,该方法能较好的兼顾系统的动态、稳态特性,并具有较好的抗干扰能力.     

Towards the optimal control of Markov chains with constraints

An optimal control problem with constraints is considered on a finite interval for a non-stationary Markov chain with a finite state space. The constraints are given as a set of inequalities. The optimal solution existence is proved under a natural assumption that the set of admissible controls is non-empty. The stochastic control problem is reduced to a deterministic one and it is shown that the optimal solution satisfies the maximum principle, moreover it can be chosen within a class of Markov controls. On the basis of this result an approach to the numerical solution is proposed and its implementation is illustrated by examples.     

On the optimal control of a hydroelectric power plant

A class of optimal control problems with phase restrictions is investigated whose performance index and state equation are linear in the control variable. First some necessary conditions for optimality are proved and then they are used to get the optimal solution.     

Maximum principle for the optimal control of an ablation-transpiration cooling system with free final time and phase constraints

This paper is concerned with an optimal control problem of an abhtion-transpiration cooling control system with Stefan-Signorini boundary condition. As the continuation of the authors＇previous paper, the Dubovits Rii-Milyutin fimctional approach is again adopted in investigation of the Pontryagin＇ s maximun principle of the system. The necessary optimality condition is presented for the problem with free final horizon and phase constraints.     

Some second-order necessary conditions in optimal control

In optimal control problems any extremal arc which trivially satisfies the Maximum Principle, that is a first-order control variation produces no change in cost, is called singular. Higher-order conditions are then needed to check the optimality of such arcs. Using the Volterra series associated with the variation of the cost functional gives a new context for analyzing singular optimal control problems. A basic optimality criterion for a fixed terminal time Mayer problem is obtained which allows one to derive the necessary conditions for optimality in terms of Lie brackets of vector fields associated with the dynamics of the problem.     

Maxi mumprinciple for the optimal control of an ablation-transpiration cooling system with free final time and phase constraints

paper is concerned with an optimal co nt rol problem of an ablation-transpiration cooling control system with Stefan-Sig norini boundary condition.As the continuation of the authors'previous paper,the Dubovits Rii-Milyutin functional approach is again adopted in investigation of t he Pontryagin's maximun principle of the system.The necessary optimality condit ion is presented for the problem with free final horizon and phase constraints.     

Stochastic maximum principle for SPDEs with noise and control on the boundary

In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problem can be interpreted as a stochastic control problem for an evolution system in a Hilbert space. The regularity of the solution of the adjoint equation, that is a backward stochastic equation in infinite dimension, plays a crucial role in the formulation of the maximum principle.     

Near optimality conditions in stochastic control of jump diffusion processes

This paper is concerned with necessary as well as sufficient conditions for near-optimality of controlled jump diffusion processes. Necessary conditions for a control to be near-optimal are derived, using Ekeland’s variational principle and some stability results on the state and adjoint processes, with respect to the control variable. In a second step, we show that the necessary conditions for near-optimality, are in fact sufficient for near-optimality provided some concavity conditions are fulfilled. Finally, as an illustration some examples are solved explicitly.     

New results on the relationship between dynamic programming and the maximum principle

The dynamic programming approach to optimal control theory attempts to characterize the value functionV as a solution to the Hamilton-Jacobian-Bellman equation. Heuristic arguments have long been advanced relating the Pontryagin maximum principle and dynamic programming according to the equation (H(t, x ^* (t), u ^* (t), p(t)),−p(t))=√V(t,x ^* (t)), where (x^*, u^*) is the optimal control process under consideration,p(t), is the coextremal, andH is the Hamiltonian. The relationship has previously been verified under only very restrictive hypotheses. We prove new results, establishing the relationship, now expressed in terms of the generalized gradient ofV, for a large class of nonsmooth problems.     

动画广告塑造品牌模式及原则研究

动画广告是现今企业在品牌塑造过程中运用的一种重要手段。本文通过对企业运用中的大量实例为基础进行分析归纳出动画广告在品牌塑造过程中的三种实战模式。通过对之进行优劣分析,总结出一些指导原则。简要分析动画广告的产业适用范围。     

Optimal control of dilute acid pretreatment and enzymatic hydrolysis for processing lignocellulosic feedstock

Lignocellulosic feedstock is one of the potential renewable sources for producing ethanol for transportation. The process steps viz., acid pretreatment and enzymatic hydrolysis in bio-chemical process route are intended to produce fermentable sugars, which can be readily fermented for producing ethanol. However, the dilute acid pre-treatment and enzymatic hydrolysis process steps are found to be economically inefficient. The present work aims at optimizing these process steps for improving the process performance. Such optimization is expected to increase conversion, reduce energy or material requirement, thereby improving the economics. The kinetic models of acid pretreatment and enzymatic hydrolysis for lignocellulosic feedstock processing are adapted from literature. Subsequently, these kinetic models are augmented by associated mass and energy balances, to develop a batch reactor model and fed-batch reactor model for dilute acid pretreatment and enzymatic hydrolysis processes, respectively. Optimal control with Pontryagin's maximum principle has been implemented to determine the optimal time dependent profiles of heating and cooling fluid flow rates and operating temperatures for acid pretreatment and substrate feed rate profile for enzymatic hydrolysis to optimize the respective processes performance. Different objective functions such as maximizing concentration of desired product, minimizing the batch time, and maximizing profit have been considered. The simulation results yielded an increase of 6.7% and 8.8% in final concentration of desired product; 43% and 42.5% reduction in batch processing time for pretreatment and enzymatic hydrolysis processes, respectively. Finally, the simulation results have also provided optimal operating policies which have increased the profit of pretreatment by 124% and enzymatic hydrolysis by 150%, thereby improving the techno-economic feasibility for processing lignocellulosic feedstock.     

State constraints in optimal control. The degeneracy phenomenon

In this paper we study the degeneracy phenomenon arising in optimal control problems with state constraints. It is shown that this phenomenon occurs because of the incompleteness of the standard variants of Pontryagin's maximum principle for problems with state constraints. The new maximum principle containing some additional information about the behavior of the Hamiltonian at the endtimes is developed. As application we obtain some sufficient and necessary conditions for nondegeneracy and pointwise nontriviality of the maximum principle. The results obtained envelope the optimal control problems with systems described by differential inclusions and ordinary differential equations.     

Maximum principle for the stochastic optimal control problem with delay and application

In this paper, we consider an optimal control problem for the stochastic system described by stochastic differential equations with delay. We obtain the maximum principle for the optimal control of this problem by virtue of the duality method and the anticipated backward stochastic differential equations. Our results can be applied to a production and consumption choice problem. The explicit optimal consumption rate is obtained.     

Computing stability domains in the space of time delay and controller coefficients for FOPDT and SOPDT systems

In this paper, a method is proposed to compute the maximum allowable time delay for first-order plus dead time and second-order plus dead time systems, in order to maintain stability. Designing first order controllers for such systems to preserve stability for a longer time delay is the main aim of this paper. The procedure uses the properties of the phase diagram of the open-loop transfer functions of such systems. The effects of the variation of the controller coefficients on the maximum allowable time delay of the systems are investigated and the stability domains in the space of the uncertain delay and the controller coefficients are computed. The results can be used to design first-order robust controllers for first and second order processes containing uncertain delays.     

稀薄大气层反作用控制系统设计方法

针对高层大气中反作用控制系统和气动舵的面对称飞行器控制问题,提出了反作用控制系统(RCS)的设计方法。为实现姿态的稳定控制,利用舵前馈进行力矩配平,并针对新系统提出了反作用控制系统的构成和功能。分别对关键子系统进行设计。在刚体状态估计器中,分别利用高通滤波器和低通滤波器进行姿态和角速度反馈信号的处理。根据高层大气中姿态控制系统的需求,采用最优控制方法进行相平面逻辑的设计和优化。根据动态处理方法给出了推力器选择逻辑。建立数学模型,通过仿真验证了方法的可行性和有效性。说明控制器满足高层大气中姿态控制系统的性能指标,稳态精度小于0.50。     

Fuzzy homogeneity and scale-space approach to color image segmentation

Image segmentation is the procedure in which the original image is partitioned into homogeneous regions, and has many applications. In this paper, a fuzzy homogeneity and scale-space approach to color image segmentation is proposed. A color image is transformed into fuzzy domain with maximum fuzzy entropy principle. The fuzzy homogeneity histogram is employed, and both global and local informations are considered when we process fuzzy homogeneity histogram. The scale-space filter is utilized for analyzing the fuzzy homogeneity histogram to find the appropriate segments of the homogeneity histogram bounded by the local extrema of the derivatives. A fuzzy region merging process is then implemented based on color difference and cluster sizes to avoid over-segmentation. The proposed method is compared with the space domain approach, and experimental results demonstrate the effectiveness of the proposed approach.