Numerical solution of minimax problems of optimal control,part 1

This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P).For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector , as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized.In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.This research was supported by the National Science Foundation, Grant No. ENG-79-18667, and by Wright-Patterson Air Force Base, Contract No. F33615-80-C3000. This paper is a condensation of the investigations reported in Refs. 1–7. The authors are indebted to E. M. Coker and E. M. Sims for analytical and computational assistance.     

Determination of methylmercury fluxes across the air–water and air–soil interfaces by gas chromatography with electron capture detection

A method for the determination of methylmercury (MeHg) fluxes across the air–water and air–soil interfaces was developed using an in situ chamber. The MeHg in the air coming out of the chamber was captured by a column containing sulfhydryl cotton fiber adsorbent. MeHg was then desorbed from the column by using 2 mol L^–1 HCl. The MeHg in the effluent was extracted with benzene, and determined by gas chromatography with electron capture detection. Finally, the MeHg flux was calculated using the chamber. The method was applied to simulated experiments, and the results showed that the MeHg fluxes in the air–water system were higher than those in the air–soil–water system. The method was also successfully applied to the field measurements of an environment polluted by a chemical factory, and the results showed that the MeHg fluxes across the air–soil and air–water interfaces were 0.21–3.09 and 0.14–0.79 ng m^–2 h^–1, respectively. The method will be a useful tool in the environmental study of MeHg.     

Molecular Tailoring of Surfaces: Pulsed Plasma Polymerization of Bromine Containing Monomers

The use of a variable duty cycle pulsed RF plasma is shown to provide film chemistry control during polymerization of saturated (CH₂Br₂) and unsaturated (CH₂=CHCH₂Br) bromine containing monomers. With both monomers, the degree of bromine atom retention in the films is observed to increase in a progressive fashion as the RF duty cycle employed during plasma polymerization is decreased. The film deposition rates, when expressed in terms of thickness per Joule of RF energy input, increase rapidly as the RF duty cycles are reduced. Additionally, the film morphology is observed to become increasingly smooth with decreasing RF duty cycles during deposition, as illustrated with the allyl bromide monomer. The film chemistry controllability of this study is demonstrated with monomers possessing the relatively weak C-Br bond. As such, the present work represents an important extension of the pulsed plasma polymerization approach to include retention of a labile bond during film formation. The introduction of reactive surface functional groups, at controlled densities, provides additional molecular tailoring possibilities via subsequent chemical derivatization processes.     

Polypyrrole-based sensor for hydrazine and ammonia

An ultra-thin layer of polypyrrole can be coated on non-conducting substrates, e.g., acrylic, by dip coating into a colloidal suspension of polypyrrole. This thin coating reversibly combines with low concentrations of ammonia or hydrazine with a concomitant reversible increase in resistance; 0.1 μg cm^?3 of ammonia can readily be detected with a 1 cm² area of sensor.     

混合控制下腐蚀过程的电化学动力学参数测定

通过恒电量脉冲技术测定Q235碳钢在天然海水中腐蚀过程的电化学动力学参数. 分别利用不同极化幅度的恒电量瞬态响应分析获得极化电阻和Tafel斜率, 进而计算腐蚀电流icorr. 并对比了恒电量方法和考虑扩散影响的稳态极化曲线方法的测量结果. 结果表明, 采用恒电量强极化积分算法(CPSI)获得的Tafel斜率与极化曲线方法有很好的相关性. 同时, CPSI测定的阴极Tafel斜率符合氧还原反应的理论Tafel斜率值. 因此, 采用恒电量瞬态响应测量大大减小了浓差极化的影响, 有利于快速测定电荷传递和扩散传质混合控制下腐蚀过程的电化学动力学参数.     

电爆炸箔断路开关的理论和实验研究

 采用金属箔电爆炸过程的二维数值计算模型，对含电爆炸金属箔断路开关的电感储能脉冲功率调节系统进行了数值计算。以此为基础，研制出了一种低电感型的电爆炸箔断路开关，并以4μF/75kV脉冲电容器组作为初级能源，13Ω电阻作为负载进行实验研究。研究结果表明：在负载上可获得约250kV，脉宽大于400ns的脉冲电压。     

Seed‐Mediated Synthesis of Gold Tetrahedra in High Purity and with Tunable,Well‐Controlled Sizes

We report a facile synthesis of Au tetrahedra in high purity and with tunable, well‐controlled sizes via seed‐mediated growth. The success of this synthesis relies on the use of single‐crystal, spherical Au nanocrystals as the seeds and manipulation of the reaction kinetics to induce an unsymmetrical growth pattern for the seeds. In particular, the dropwise addition of a precursor solution with a syringe pump, assisted by cetyltrimethylammonium chloride and bromide at appropriate concentrations, was found to be critical to the formation of Au tetrahedra in high purity. Their sizes could be readily tuned in the range of 30–60 nm by simply varying the amount of precursor added to the reaction solution. The current strategy not only enables the synthesis of Au tetrahedra with tunable and controlled sizes but also provides a facile and versatile approach to reducing the symmetry of nanocrystals made of a face‐centered cubic lattice.     

Kriging‐based optimization applied to flow control

The automatic optimization of flow control devices is a delicate issue because of the drastic computational time related to unsteady high‐fidelity flow analyses and the possible multimodality of the objective function. Thus, we experiment in this article the use of kriging‐based algorithms to optimize flow control parameters because these methods have shown their efficiency for global optimization at moderate cost. Navier–Stokes simulations, carried out for different control parameters, are used to build iteratively a kriging model. At each step, a statistical analysis is performed to enrich the model with new simulation results by exploring the most promising areas, until optimal flow control parameters are found. This approach is validated and demonstrated on two problems, including comparisons with similar studies: the control of the flow around an oscillatory rotating cylinder and the reduction of the intensity of a shock wave for a transonic airfoil by adding a bump to the airfoil profile. Copyright © 2011 John Wiley & Sons, Ltd.     

Impulsive generalized function synchronization of complex dynamical networks

This Letter investigates generalized function synchronization of continuous and discrete complex networks by impulsive control. By constructing the reasonable corresponding impulsively controlled response networks, some criteria and corollaries are derived for the generalized function synchronization between the impulsively controlled complex networks, continuous and discrete networks are both included. Furthermore, the generalized linear synchronization and nonlinear synchronization are respectively illustrated by several examples. All the numerical simulations demonstrate the correctness of the theoretical results.     

Active transient elasto-acoustic response damping of a thick-walled liquid-coupled piezolaminated cylindrical vessel

The linear 3D piezoelasticity theory in conjunction with the versatile transfer matrix approach and the wave equation for the internal acoustic domain are employed for active non-stationary vibroacoustic response control of an arbitrarily thick, tri-laminate, fluid-filled, simply supported, piezocomposite cylindrical tank, excited by arbitrary (non-axisymmetric) time-dependent on-surface mechanical loads. The smart structure is composed of a supporting core layer of functionally graded orthotropic material perfectly bonded to inner and outer spatially distributed radially polarized functionally graded piezoceramic sensor and uniform force actuator (FGPM) layers. Active vibration damping is implemented by transferring the accumulated voltage on the sensor layer to the piezoelectric actuator layer in context of proportional and derivative control laws. Durbin's numerical inverse Laplace transform scheme is utilized to calculate the time response histories of the relevant interface displacement/stress components, center-point acoustic pressure, and actuator voltage, for selected loading configurations (i.e., concentrated step, impulse, and moving external loads). Numerical simulations demonstrate the effectiveness of the adopted distributed sensing/actuation configuration together with the active damping control strategy in suppressing the vibroacoustic response of a three-layered (Ba₂NaNb₅O₁₅/Al/PZT4) water-filled piezoelastic cylindrical tank. Limiting cases are considered and the validity of results is established by comparison with the available data as well as with the aid of a commercial finite element package.