Stochastic Maximum Principle for Optimal Advertising Models with Delay and Non-Convex Control Spaces

In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.

Research on Teaching Methods of Flight Control Principles

With the rapid development of China’s civil aviation industry,the teaching method of operating knowledge of flight principles has changed greatly,which creates a good implementation environment to improve the safety of civil aviation in our country.At present,the main training content of air route transport pilots in China is basic aviation theory,initial flight training,airline modification,etc.The principles of flight control are an important part of basic aviation theoretical knowledge training,which will involve a large number of flight technology training content,instructors will also be based on the pilot type.Teaching flight control theory and practical knowledge requires relatively high theoretical learning ability of students,and the learning effect of this part of theoretical knowledge will directly affect the quality of subsequent learning,but also directly affect the effectiveness of flight training.This paper focuses on the analysis of the basic concepts of flight control,studies the existing problems in the teaching of flight control principles,summarizes the teaching measures of flight control principles,aiming to provide a reference to teaching personnel.

A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS

A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.

Study on mechanical principle of reinforcing sidewalls and corners of roadway to control floor heave by anchors

The movement principle of sidewalls and floor of extraction opening is analyzed, it is found that floor heave not only has something to do with the floor strata, but sidewalls. The effect of sidewall anchor and corner anchor is studied, the mechanical principle of reinforcing sidewalls and corners is put forward and applied in engineering practice.

Maxi mumprinciple 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.

ANALYSIS MODEL ON GRADUAL CHANGE PRINCIPLE OF EFFECT ZONES OF LAYER FACE FOR ROLLED CONTROL CONCRETE DAM

The effect zones of layer face for RCC （rolled control concrete） dam have gradual change characteristics. Based on the analysis thought of complex material, a model was built to analyze above principle of RCC dam by use of series-wound and shunt-wound connection. Some methods were proposed to determine the instantaneous Young＇s modulus, delayed Young＇s modulus and viscosity coefficient of effect zones of layer face. Above models and methods were used to mine the principle of gradual change of key calculation parameters which can response the characteristics of effect zones. The principle of gradual change was described. A model was established to analyze the threedimensional viscoelastic problem of RCC dam. Above programs were developed. The examples show that the proposed models and methods to determine the key calculation parameters of effect zones can reflect the status of RCC dam accurately.

Maximum principle for anticipated recursive stochastic optimal control problem with delay and Lvy processes

In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes （AFBSDEDLs）, we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs＇ preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.

MAXIMUM PRINCIPLE FOR STOCHASTIC OPTIMAL CONTROL PROBLEM WITH DISTRIBUTED DELAYS

This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.

Real-Time Co-optimization of Gear Shifting and Engine Torque for Predictive Cruise Control of Heavy-Duty Trucks

Fuel consumption is one of the main concerns for heavy-duty trucks.Predictive cruise control(PCC)provides an intriguing opportunity to reduce fuel consumption by using the upcoming road information.In this study,a real-time implementable PCC,which simultaneously optimizes engine torque and gear shifting,is proposed for heavy-duty trucks.To minimize fuel consumption,the problem of the PCC is formulated as a nonlinear model predictive control(MPC),in which the upcoming road elevation information is used.Finding the solution of the nonlinear MPC is time consuming;thus,a real-time implementable solver is developed based on Pontryagin’s maximum principle and indirect shooting method.Dynamic programming(DP)algorithm,as a global optimization algorithm,is used as a performance benchmark for the proposed solver.Simulation,hardware-in-the-loop and real-truck experiments are conducted to verify the performance of the proposed controller.The results demonstrate that the MPC-based solution performs nearly as well as the DP-based solution,with less than 1%deviation for testing roads.Moreover,the proposed co-optimization controller is implementable in a real-truck,and the proposed MPC-based PCC algorithm achieves a fuel-saving rate of 7.9%without compromising the truck’s travel time.

Bandgap adjustment of a sandwich-like acoustic metamaterial plate with a frequency-displacement feedback control method

Several types of acoustic metamaterials composed of resonant units have been developed to achieve low-frequency bandgaps.In most of these structures,bandgaps are determined by their geometric configurations and material properties.This paper presents a frequency-displacement feedback control method for vibration suppression in a sandwich-like acoustic metamaterial plate.The band structure is theoretically derived using the Hamilton principle and validated by comparing the theoretical calculation results with the finite element simulation results.In this method,the feedback voltage is related to the displacement of a resonator and the excitation frequency.By applying a feedback voltage on the piezoelectric fiber-reinforced composite(PFRC)layers attached to a cantilever-mass resonator,the natural frequency of the resonator can be adjusted.It ensures that the bandgap moves in a frequency-dependent manner to keep the excitation frequency within the bandgap.Based on this frequency-displacement feedback control strategy,the bandgap of the metamaterial plate can be effectively adjusted,and the vibration of the metamaterial plate can be significantly suppressed.

The Maximum Principle for Fully Coupled Forward-backward Stochastic Control System

The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.

Optimal Control for Age Distribution and Weighted Size Competitive Species in a Polluted Environment

In the paper,we study an optimal control for a system representing a competitive species model with fertility and mortality depending on a weighted size in a polluted environment.A fixed point theorem is applied to obtain the existence and uniqueness exhibited by a non-negative solution of above mentioned model.A maximum principle helps to carefully verify the existence of the optimal control policy,and tangent-normal cone techniques help to obtain the optimal condition specific to control issue.

Research advances in enhanced coal seam gas extraction by controllable shock wave fracturing

With the continuous increase of mining in depth,the gas extraction faces the challenges of low permeability,great ground stress,high temperature and large gas pressure in coal seam.The controllable shock wave(CSW),as a new method for enhancing permeability of coal seam to improve gas extraction,features in the advantages of high efficiency,eco-friendly,and low cost.In order to better utilize the CSW into gas extraction in coal mine,the mechanism and feasibility of CSW enhanced extraction need to be studied.In this paper,the basic principles,the experimental tests,the mathematical models,and the on-site tests of CSW fracturing coal seams are reviewed,thereby its future research directions are provided.Based on the different media between electrodes,the CSW can be divided into three categories:hydraulic effect,wire explosion and excitation of energetic materials by detonating wire.During the process of propagation and attenuation of the high-energy shock wave in coal,the shock wave and bubble pulsation work together to produce an enhanced permeability effect on the coal seam.The stronger the strength of the CSW is,the more cracks created in the coal is,and the greater the length,width and area of the cracks being.The repeated shock on the coal seam is conducive to the formation of complex network fracture system as well as the reduction of coal seam strength,but excessive shock frequency will also damage the coal structure,resulting in the limited effect of the enhanced gas extraction.Under the influence of ground stress,the crack propagation in coal seam will be restrained.The difference of horizontal principal stress has a significant impact on the shape,propagation direction and connectivity of the CSW induced cracks.The permeability enhancement effect of CSW is affected by the breakage degree of coal seam.The shock wave is absorbed by the broken coal,which may hinder the propagation of CSW,resulting in a poor effect of permeability enhancement.When arranging two adjacent boreholes for CSW permeability enhancement test,the spacing of boreholes should not be too close,which may lead to negative pressure mutual pulling in the early stage of drainage.At present,the accurate method for effectively predicting the CSW permeability enhanced range should be further investigated.

THE OPTIMAL CONTROL VARIATIONAL PRINCIPLE AND FINITEELEMENTS ANALYSIS FOR VISCOPLASTIC DYNAMICS

This paper presents the optimal control variational principle for Perzyna modelwhich is one of the main constitutive relation of viscoplasticity in dynamics. And itcould also be transformed to solve the parametric quadratic programming problem.The FEM form of this problem and its implementation have also been discussed in thepaper.

RELATIVISTIC VARIATION PRINCIPLES AND EQUATION OF MOTION FOR VARIABLE MASS CONTROLLABLE MECHANICAL SYSTEM

With classical variable mass and relativistic variable mass cases being considered.the relativistic D' Alembert principles of Lagrange form Nielsen form and Appell. form for variable mass controllable mechanical system are given the relativistic Chaplygin equation. Nielsen equation and Appell equation .for variable mass controllable mechanical system in quasi-coordinates and generalized- coordinates are obtained, and the equations of motion of relativistic controllable mechanical system for holonomic system and constant mass system are diseussed

A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H_2/H_∞ CONTROL WITH RANDOM JUMPS

A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.

Controlling Chaos in Neuron Based on Lasalle Invariance Principle

A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalleinvariant principle.The control technique does not require analytical knowledge of the system dynamics and operateswithout an explicit knowledge of the desired steady-state position.The well-known modified Hodgkin-Huxley (MHH)and Hindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method.Simulationresults show the proposed control law is effective.The outcome of this study is significant since it is helpful to understandthe learning process of a human brain towards the information processing,memory and abnormal discharge of the brainneurons.

The Application of Principle of Automatic Control in the site Management of Electric Power Construction Enterprise

It is need to establish site project department during the construction of electric power project.The head office should design and build the main structure,continually improve structure of project department,meantime,positively apply principle of automatic control to improve the site management of electric power construction.In this article,the application strategy of principle of automatic control is analyzed focusing on the site work of electric power construction.

An Academic Summary of the International Conference Series on “The Role of the Proportionality Principle in the Pandemic Prevention and Control”

Against the background of a complicated global pandemic situation and normalized pandemic prevention and control in China,leading human rights scholars from China,North America and Eurasia conducted fruitful discussions on the human rights jurisprudence during pandemic through the lens of the proportionality principle at the Sixth Session of the International Seminar Series on"Global Pandemic Prevention and Control and Human Rights Protection",which was organized by the Center for Human Rights Studies of Renmin University of China,under the guidance of the China Society for Human Rights Studies.Focusing on the pandemic-related human rights conditions and legal challenges in global context,participating scholars examined the role of the proportionality principle during the containment of COVID-19 in six topical dimensions,including the normative utility,practical logic,reasonable limits,necessary measures,balancing of interests,and proportional jurisprudence in the post-pandemic era.In oder to cohere human rights jurisprudence for the development of a global community of health for all,this international seminar fostered five fundamental proportionality consensuses from five interrelated perspectives,involving human rights—rule of law—balance—contexts—trends".

Stochastic Maximum Principle for a Kind of Risk-sensitive Optimal Control Problem and Application to Portfolio Choice

在这份报纸，我们主要学习一种公事包选择问题在某些金融市场激发的一种风险敏感的最佳的控制问题。用古典凸的变化技术，我们为这种问题获得最大的原则。最大的原则的形式类似于它的风险中立的对应物。但是伴随方程和变化不平等重重地取决于风险敏感的参数。这是从风险中立的案例的主要差别之一。我们使用这结果解决一种最佳的公事包选择问题。鸣钟者获得的最佳的公事包策略当投资者仅仅投资家契约和股票时，动态编程原则是我们的结果的一种特殊情况。计算结果和图明确地说明在最大的期望的实用程序和模型的参数之间的关系。