Dynamic Optimization Theory Research Articles

Exploration of Dynamic Optimization Paths for Work Search Models under Incomplete Information Conditions

This article is based on the application exploration of dynamic optimization theory under incomplete information conditions. Based on the job search model and its extended model, this theory is analyzed in detail, explaining the relationship between unemployment rate and wages in the labor market, exploring the impact of Western labor unemployment formation, summarizing the experience of urban unemployment in the process of social construction in the new era, and developing high-quality and high-quality employment work for college students, It will have very important inspiration and reference significance.

Muscle Contributions to Take-Off Velocity in the Long Jump.

A key determinant of long jump performance is the ability to increase the vertical velocity of the center of mass (COM) while minimizing the loss in forward velocity (running speed) during the take-off phase, but exactly how this occurs is not fully understood. We combined a three-dimensional musculoskeletal model of the body with dynamic optimization theory to simulate the biomechanics of the long jump take-off and determine the contributions of the individual leg muscles to jump performance. The body was modeled as a 29-degree-of-freedom skeleton actuated by a combination of muscles and net joint torques. A dynamic optimization problem was solved to reproduce full-body motion and ground-force data recorded from experienced subelite jumpers. The optimization solution then was analyzed to determine each muscle's contribution to the ground-force impulse and hence the change in velocity of the COM during the take-off phase. The hip, knee, and ankle extensors dominated the change in velocity of the COM during take-off. Vasti (VAS) generated the highest support impulse and contributed one-third (33%) of the increase in vertical COM velocity generated by all the muscles. Soleus (SOL) and gluteus maximus (GMAX) also developed substantial support impulses and contributed 24% and 16% of the increase in vertical COM velocity, respectively. VAS also generated the highest braking impulse and contributed approximately one-half (55%) of the loss in forward COM velocity generated by all the muscles, whereas SOL and GMAX made much smaller contributions (12% and 7%, respectively). VAS, SOL, and GMAX contributed nearly three-quarters (73%) of the increase in vertical COM velocity at take-off, suggesting that these muscles ought to be prioritized in strength training programs aimed at improving long jump performance.

Dynamic Optimization of Complementarity Systems

Dynamic optimization theory is established for nonlinear complementarity systems, a class of highly nonlinear and nonsmooth dynamical systems, which find widespread use in engineering. In particular, optimal control problems involving complementarity systems are solved using a direct approach, allowing for gradient-based sequential methods (e.g., single or multiple shooting) to update a parametrically discretized control. This is accomplished via lexicographic directional differentiation, a recently developed tool in nonsmooth analysis. The computationally relevant theory is specialized to optimization-constrained ODEs and parameter estimation problems, with motivating applications.

Dynamic cognitive maps for robot route planning in complex workplaces represented by abstract mazes

Adaptive path planning and optimization for robots are a persistent challenge due to the lack of a cognitive map of the complex and dynamic environments. This paper presents a cognitive-map-based method for dynamic robot path planning by a formal maze model for workplace layouts representation. The maze model and global path trees provide a cognitive map for the robot to aware the environment. A theory of dynamic Paths Finding and Optimization (PFO) is developed. Powered by the PFO algorithm, a robot is able to autonomously explore the optimal path in a complex workplace by a single sight-read of its layout. The maze based PFO methodology provides robot for an efficient real time path cognition and optimization algorithm for dealing with dynamic workplaces. A set of experiments demonstrates the efficiency of the method, which extends traditional stepwise robot vision technologies to cognitive-map-driven global path optimization.

Optimal decision for multi-pollutants problem under ecological compensation mechanism and learning by doing

Multi-pollutants transboundary pollution is a complicated problem, for such problems, the research involves the attributes of pollutants, the degree of separability , whether the abatement cost is separable, etc. To address these challenges, this paper discusses the problem of multi-pollutant transboundary pollution based on differential game theory under the learning by doing and ecological compensation mechanism. Using the dynamic optimal control theory, we obtain the optimal equilibrium strategy under the noncooperation and cooperation model between the two regions and analyze the influence of multi-pollutants characteristics and other parameters on the optimal equilibrium strategy. In our model, the pollutants can be either technological substitutes or complements which are not necessarily separable, and the abatement costs of two pollutants are not separable. Through numerical simulation, the results show that (i) The two pollutants are substitutes or supplements which have no impact on the emission levels of these two pollutants, and as the degree of the inseparability of the two pollutants increases, the emission level decreases gradually; (ii) The abatement investment level of the two pollutants are substitutes is higher than the two pollutants are complements, and the abatement investment level increases with the degree of inseparable under the cooperation and noncooperation models; (iii) The pollution stocks of two pollutants are substitutes is higher than the two pollutants are complements. • Consider multiple pollutants and they are not necessarily separable. • The ecological compensation mechanism and learning by doing are considered. • Exploring and analyzing the optimal strategy between regions.

Predictive Simulations of Human Sprinting: Effects of Muscle-Tendon Properties on Sprint Performance.

We combined a full-body musculoskeletal model with dynamic optimization theory to predict the biomechanics of maximum-speed sprinting and evaluate the effects of changes in muscle-tendon properties on sprint performance. The body was modeled as a three-dimensional skeleton actuated by 86 muscle-tendon units. A simulation of jogging was used as an initial guess to generate a predictive dynamic optimization solution for maximum-speed sprinting. Nominal values of lower-limb muscle strength, muscle fascicle length, muscle intrinsic maximum shortening velocity (fiber-type composition), and tendon compliance were then altered incrementally to study the relative influence of each property on sprint performance. Model-predicted patterns of full-body motion, ground forces, and muscle activations were in general agreement with experimental data recorded for maximum-effort sprinting. Maximum sprinting speed was 1.3 times more sensitive to a change in muscle strength compared with the same change in muscle fascicle length, 2.0 times more sensitive to a change in muscle fascicle length compared with the same change in muscle intrinsic maximum shortening velocity, and 9.1 times more sensitive to a change in muscle intrinsic maximum shortening velocity compared with the same change in tendon compliance. A 10% increase in muscle strength increased maximum sprinting speed by 5.9%, whereas increasing muscle fascicle length, muscle intrinsic maximum shortening velocity, and tendon compliance by 10% increased maximum sprinting speed by 4.7%, 2.4%, and 0.3%, respectively. Sprint performance was most sensitive to changes in muscle strength and least affected by changes in tendon compliance. Sprint performance was also more heavily influenced by changes in muscle fascicle length than muscle intrinsic maximum shortening velocity. These results could inform training methods aimed at optimizing performance in elite sprinters.

Agent's Optimal Compensation Under Inflation Risk by Using Dynamic Contract Model.

This paper studies the problem of principal-agent with moral hazard in continuous time. The firm’s cash flow is described by geometric Brownian motion (hereafter GBM). The agent affects the drift of the firm’s cash flow by her hidden effort. Meanwhile, the firm rewards the agent with corresponding compensation and equity which depend on the output. The model extends dynamic optimal contract theory to an inflation environment. Firstly, the authors obtain the dynamic equation of the firm’s real cash flow under inflation by using the Itô formula. Then, the authors use the martingale representation theorem to obtain agent’s continuation value process. Moreover, the authors derive the Hamilton-Jacobi-Bellman (HJB) equation of investor’s value process, from which the authors derive the investors’ scaled value function by solving the second-order ordinary differential equation. Comparing with He[1], the authors find that inflation risk affects the agent’s optimal compensation depending on the firm’s position in the market.

Research on dynamic target tracking algorithm in mobile sensor networks

With the increasing complexity of networked cooperative detection environment, new targets appear and leave in the detection area, and the mobility of targets is increasing. The emergence of sensors makes the sensors in the sensor network have certain motion characteristics. These uncertainties increase the complexity of the problem. At the same time, the dynamic selection of sensor resources needs to consider the needs of different priority tasks, platform survival risk, sensor cost and other factors. In view of these problems to be solved, based on the qualitative synthesis theory of predictive control and stochastic dynamic programming optimization theory, the dynamic sensor selection decision theory and method based on multi-step forward decision are explored. This paper studies the dynamic sensor strategy based on multi-step forward decision scheduling, and carries out the research on the optimization decomposition method of sensor selection under different structural characteristics, the dynamic optimization method of sensor selection under complex and uncertain environment, and the multi-objective optimization method of dynamic sensor selection under heterogeneous targets, so as to explore a new way of dynamic sensor selection algorithm design and performance analysis under networked collaborative tracking A new way. The research of dynamic target tracking algorithm in mobile sensor networks has important theoretical and engineering significance to improve the resource efficient utilization and the overall target tracking performance of sensor networks.

｢탄소중립 2050｣ 추진전략 이행에 따른 근해어업의 온실가스 감축잠재량 추정

The purpose of this study is to estimate potential greenhouse gas(GHG) reductions of offshore fisheries following the implementation of 「2050 Carbon Neutral」 strategy and then to suggest policy alternatives based on the analysis results. To estimate the potential GHG reductions, a dynamic optimal fisheries theory was used in the analysis. As a result, the offshore fisheries" fishing effort was inputted 30% more than the optimal level. If excess fishing effort were reduced, the potential GHG reductions of offshore fisheries was estimated to 464,683tCO₂. In addition, when GHG emissions are regulated, the profit rate of offshore fisheries decreases by 0.46%, but it is analyzed that there is no significant damage. Thus, in order to reduce GHG emissions, it is necessary to expand fishing vessel buyback program and start discussion on the development of electric hybrid fishing vessels.

A Building-Material Supply Chain Sustainable Operations under Fairness Concerns and Reference Price Benefits

This paper incorporates fairness concerns and consumer reference price effects into a two-echelon building-material closed-loop supply chain consisting of a manufacturer and a retailer. By establishing four differential game models, we investigate the sustainable operations and cooperation of this supply chain. The four game models are a Nash noncooperative game, Stackelberg game with cost sharing, Stackelberg game with fairness concerns and cost sharing, and centralized decision model. By using dynamic models and optimal control theory, we obtain the two members’ optimal equilibrium strategies in the supply chain. Analytical results show that the consumer reference price effect has a positive impact on the manufacturer’s effort level, retailer’s publicity level, and product brand goodwill, which can improve the supply chain performance. The retailer’s partial commitment to cost sharing can enhance the production enthusiasm of the manufacturer, improve the brand reputation of the product, and enhance the two members’ individual profitability. The distributional fairness concerns of the manufacturer not only prevent the manufacturer and retailer from achieving Pareto improvement but also lead to the decline of the manufacturer’s effort level and profitability. The research conclusions of this paper can provide some insights into the cooperation and sustainable development of the supply chain.

An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

One of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

A Reinforcement Learning-Based Adaptive Path Tracking Approach for Autonomous Driving

The path tracking system is a crucial component in fully autonomous vehicles. While many methods provide state-of-the-art tracking performance, they tend to emphasize tracking accuracy for safety, at the price of ride quality. Although methods based on a dynamic model and optimization theory guarantee improved tracking performance, a high-fidelity model is unavailable in most autonomous systems, and the complex optimization process may increase the computational burden. Therefore, for practical, real-life systems, it is urgent to develop a tracking method with a simple, effective control framework for real-time implementation. Moreover, the tracking approach should adaptively balance between tracking accuracy and the passenger experience. With that in mind, a simple tracking scheme with adaptive lateral and longitudinal control approaches is proposed. For lateral control, a pure pursuit (PP) geometric controller is used as a basic tracking framework to design the steering method. A detailed analysis shows that PP inefficiently reduces the lateral error. A PID controller is integrated with PP by a customized reinforcement learning model to better deal with tracking error by trading off between PP and PID. Moreover, a rough-to-fine velocity adaptation method is proposed to adjust the speed according to the geometry of the predefined path and the real-time tracking feedback. The proposed controlling approach is tested in different path tracking scenarios. The results show that the approach can adaptively change the weights of PP and PID to maintain a balance between tracking error (within $\pm \text{0.5}\;\text{m}$ ) and jerk (within $\pm 0.5\;\text{m}{\tt /} \text{s}^3$ ), and can adapt to high-speed scenarios (up to $\text{80}\;\text{km/h}$ ). Finally, a field test is carried out to validate the practicability.

Selling Passes to Strategic Customers

Many service providers offer a prepaid package of credits that can be redeemed for future use, often called passes, in conjunction with regular individual sales. In dynamic pricing situations, customers can strategize on the purchase, redemption, and renewal of the pass by optimizing the timing and choices between passes and individual items based on future prices and their own changing needs. In “Selling Passes to Strategic Customers,” Wang, Levin, and Nediak integrate dynamic choice modeling and optimal control theory to study how to jointly price the passes and individual items in a dynamic setting. They endogenize an individual customer’s purchase/redemption decisions in their model and find that the seemingly complex problem has a simple (approximate) solution. The optimal prices remain nearly constant most of the time, except near the beginning and end of the sales horizon, exhibiting so-called turnpike properties. The pass, as a form of advance purchase, allows the seller to capitalize on the customer’s forward-looking behavior by exploiting the uncertainty of customer valuations.

Dynamic Optimal Control of Transboundary Pollution Abatement under Learning-by-Doing Depreciation

This paper analyzes a dynamic Stackelberg differential game model of watershed transboundary water pollution abatement and discusses the optimal decision-making problem under non-cooperative and cooperative differential game, in which the accumulation effect and depreciation effect of learning-by-doing pollution abatement investment are taken into account. We use dynamic optimization theory to solve the equilibrium solution of models. Through numerical simulation analysis, the path simulation and analysis of the optimal trajectory curves of each variable under finite-planning horizon and long-term steady state were carried out. Under the finite-planning horizon, the longer the planning period is, the lower the optimal emission rate is in equilibrium. The long-term steady-state game under cooperative decision can effectively reduce the amount of pollution emission. The investment intensity of pollution abatement in the implementation of non-cooperative game is higher than that of cooperative game. Under the long-term steady state, the pollution abatement investment trajectory of the cooperative game is relatively stable and there is no obvious crowding out effect. Investment continues to rise, and the optimal equilibrium level at steady state is higher than that under non-cooperative decision making. The level of decline in pollution stock under finite-planning horizon is not significant. Under the condition of long-term steady state, the trajectories of upstream and downstream pollution in the non-cooperative model and cooperative model are similar, but cooperative decision-making model is superior to the non-cooperative model in terms of the period of stabilization and steady state.

How Could We Prevent Spread of the Coronavirus without Deteriorating Economy?

In the present paper, we attempt to find a way of preventing the spread of the new coronavirus without deteriorating the economy, by constructing an intertemporal model based on the dynamic optimization theory. More precisely, following the procedures used in dynamic optimization, we derive the optimal intertemporal path of the contact rate among the workers in an economy where the new coronavirus is spreading widely. It is revealed that under the optimal regulation, the workers should contact with other workers less and less at first, and then contact with other workers more and more until the contact rate reaches certain point.

Preface: Advances in theory and real world applications of control and dynamic optimization

Preface: Advances in theory and real world applications of control and dynamic optimization

A novel hybrid approach based on dynamic adaptive variable-weight optimization for short-term wind speed prediction

One of the most important preconditions for guaranteeing a smooth link between wind farms and the power system is to develop an accurate model for forecasting the wind speed. This paper describes a novel wind speed prediction model based on dynamic adaptive variable-weight optimization theory that considers the relevance of historical observations. The model applies signal preprocessing to recorded wind speed observations using ensemble empirical mode decomposition. The decomposed signals are then subjected to a random noise reduction procedure, which improves the robustness of the prediction model. An autoregressive integrated moving average model, general regression neural network, and long short-term memory are used to recognize the different features of each decomposed subsequence. Brain storm optimization is then applied to further promote the forecasting performance by integrating different forecasting models with dynamically adapted variable weights. To evaluate the prediction capacity of the proposed method, three case studies are conducted. The experimental outcomes reveal that the method presented in this paper provides more satisfactory prediction ability and robustness than other models.

Optimal Strategies for Dengue Prevention and Control during Daily Commuting between Two Residential Areas

: In this paper, we report an application for the mathematical theory of dynamic optimization for design of optimal strategies that account for daily commuting of human residents, aiming to reduce vector-borne infections (dengue) among human populations. Our analysis is based on a two-patch dengue transmission model amended with control variables that represent personal protection measures aimed at reduction of the number of contacts between mosquitoes and human hosts (e.g., the use of repellents, mosquito nets, or insecticide-treated clothing). As a result, we have proposed and numerically solved an optimal control problem to minimize the costs associated with the application of control measures, while also minimizing the total number of dengue-infected people in both residential areas. Our principal goal was to identify an optimal strategy for personal protection that renders the maximal number of averted human infections per unit of invested cost, and this goal has been accomplished on the grounds of cost-effectiveness analysis.

Dynamic Economic Optimal Dispatch of Microgrid Based on Improved Differential Evolution Algorithm

Aiming at the static economical dispatch for microgrid ignoring the inherent link between the lack of each time interval, considering wind turbines, photovoltaic cells and sodium sulfur battery uncertainty factors on economic dispatch, taking the minimum micro power output and micro grid operation cost as objective function, the establishment of a micro grid dynamic economic dispatch model. Using VC + +, the dynamic economic dispatch program of microgrid is developed by using improved differential evolution algorithm. By changing the dynamic crossover factor, the convergence speed of the algorithm and the ability to avoid falling into local optimum are improved. According to the characteristics of microgrid example structure, the output principle and operation control strategy of microgrid are formulated according to the operation of microgrid isolated grid / grid connected operation. The results show that the economic dispatch of microgrid using dynamic optimization theory is more advantageous than static scheduling in cost saving, and it makes the charge and discharge of sodium sulfur battery more global and practical.

Aircraft Trajectory Control at the Motion on the Predetermined Route Based on the Global Navigation Satellite System

An algorithm to control the aircraft trajectory is proposed. This algorithm is based on the dynamic stochastic systems optimal control theory. The optimal control implementation is shown to reduce the deviation of the controlled trajectory from the predetermined one. The optimal control is based on estimating phase coordinates with the high accuracy by the global navigation satellite system.