Optimal Feedback Strategy Research Articles

Green Agricultural Products Supply Chain Subsidy Scheme with Green Traceability and Data-Driven Marketing of the Platform

Government subsidies have played an important role in the development of green agriculture. In addition, the Internet platform is becoming a new channel to realize green traceability and promote the sale of agricultural products. In this context, we consider a two-level green agricultural products supply chain (GAPSC) consisting of one supplier and one Internet platform. The supplier makes green R&D investments to produce green agricultural products along with conventional agricultural products, and the platform implements green traceability and data-driven marketing. The differential game models are established under four government subsidy scenarios: no subsidy (NS), consumer subsidy (CS), supplier subsidy (SS), and supplier subsidy with green traceability cost-sharing (TSS). Then, the optimal feedback strategies under each subsidy scenario are derived using Bellman's continuous dynamic programming theory. The comparative static analyses of key parameters are given, and the comparisons among different subsidy scenarios are conducted. Numerical examples are employed to obtain more management insights. The results show that the CS strategy is effective only if the competition intensity between two types of products is below a certain threshold. Compared to the NS scenario, the SS strategy can always improve the supplier's green R&D level, the greenness level, market demand for green agricultural products, and the system's utility. The TSS strategy can build on the SS strategy to further enhance the green traceability level of the platform and the greenness level and demand for green agricultural products due to the advantage of the cost-sharing mechanism. Accordingly, a win-win situation for both parties can be realized under the TSS strategy. However, the positive effect of the cost-sharing mechanism will be weakened as the supplier subsidy increases. Moreover, compared to three other scenarios, the increase in the environmental concern of the platform has a more significant negative impact on the TSS strategy.

Multiplayer Reach-Avoid Differential Games in 3D Space Inspired by Harris' Hawks' Cooperative Hunting Tactics.

This paper investigates a multiplayer reach-avoid differential game in 3-dimensional (3D) space, which involves multiple pursuers, multiple evaders, and a designated target region. The evaders aim to reach the target region, while the pursuers attempt to guard the target region by capturing the evaders. This class of research holds significant practical value. However, the complexity of the problem escalates substantially with the growing number of players, rendering its solution extremely challenging. In this paper, the multiplayer game is divided into many subgames considering the cooperation among pursuers, reducing the computational burden, and obtaining numerically tractable strategies for players. First, the Apollonius sphere, a fundamental geometric tool for analyzing the 3D differential game, is formulated, and its properties are proved. Based on this, the optimal interception point for the pursuer to capture the evader is derived and the winning conditions for the pursuer and evader are established. Then, based on the Apollonius sphere, the optimal state feedback strategies of players are designed, and simultaneously, the optimal one-to-one pairings are obtained. Meanwhile, the Value function of the multiplayer reach-avoid differential game is explicitly given and is proved to satisfy Hamilton-Jacobi-Isaacs (HJI) equation. Moreover, the matching algorithm for the case with pursuers outnumbered evaders is provided through constructing a weighted bipartite graph, and the cooperative tactics for multiple pursuers are proposed, inspired by the Harris' Hawks intelligent cooperative hunting tactics. Finally, numerical simulations are conducted to illustrate the effectiveness of the theoretical results for both cases where the number of adversary players is equal and unequal between the 2 groups.

Using unfolding models to identify targeted feedback strategies for student writing

Formative assessments are used to identify student strengths and weaknesses, but they frequently do not identify targeted feedback strategies for improving student achievement. Unfolding models offer an alternative measurement paradigm for connecting recommended feedback strategies with different levels of student achievement. In this study, a focus group of English teachers identified feedback strategies for the writing of middle school students. A questionnaire was constructed based on their identification of 10 feedback strategies related to organization, development and language usage. Next, classroom teachers responded to the feedback questionnaire based on a set of 20 essays selected to vary in writing quality. An unfolding model was used to analyze teacher responses and to identify recommended feedback strategies for each essay. Findings suggest that recommended feedback strategies can be used to define zones of targeted feedback for identifying optimal feedback strategies that can be used for improving student writing at different levels of achievement.

An Improved Whale Optimization Algorithm Based on Nonlinear Parameters and Feedback Mechanism

Whale optimization algorithm, as a relatively novel swarm-based intelligence optimization algorithm, has been extensively utilized in numerous scientific and engineering fields. The intent of this work was to devise a modified WOA based on multi-strategy, named MSWOA, to address somewhat deficiencies of the original WOA, such as converging slowly, stagnating at local minima and poor stability. First, a tent map function is adopted to optimize the distribution of the initial population in problem domain. Second, new iteration-based update strategies of convergence factor and inertia weight are constructed to regulate the balance between global and local search capabilities and improve the optimization ability. Additionally, an optimal feedback strategy is presented in the search for prey stage to enhance the global search ability. Numerical experimental results based on 24 test benchmark functions reveal that the proposed MSWOA significantly improves the standard WOA in terms of solution accuracy and convergence speed, and outperforms the comparison algorithms. Furthermore, the results show that the inertia weight strategy has the greatest effect on the performance of basic WOA performance, followed by the convergence factor, and then the optimal feedback strategy.

A Stochastic Model of Economic Growth in Time-Space

We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such a problem has been the object of various papers in deterministic cases when the possible presence of stochastic disturbances is ignored (see, e.g., [P. Brito, The Dynamics of Growth and Distribution in a Spatially Heterogeneous World, working paper 2004/14, ISEG-Lisbon School of Economics and Management, University of Lisbon, 2004], [R. Boucekkine, C. Camacho, and G. Fabbri, J. Econom. Theory, 148 (2013), pp. 2719--2736], [G. Fabbri, J. Econom. Theory, 162 (2016), pp. 114--136], and [R. Boucekkine, G. Fabbri, S. Federico, and F. Gozzi, J. Econom. Geography, 19 (2019), pp. 1287--1318]). Here we propose and solve a stochastic generalization of such models where the stochastic term, in line with the standard stochastic economic growth models (see, e.g., the books [A. G. Malliaris and W. A. Brock, Stochastic Methods in Economics and Finance, Advanced Textbooks in Economics 17, North Holland, 1982, Chapter 3] and [H. Morimoto, Stochastic Control and Mathematical Modeling: Applications in Economics, Cambridge Books, 2010, Chapter 9]), is a multiplicative one, driven by a cylindrical Wiener process. The problem is studied using the dynamic programming approach. We find an explicit solution of the associated HJB equation, use a verification type result to prove that such a solution is the value function, and find the optimal feedback strategies. Finally, we use this result to study the asymptotic behavior of the optimal trajectories.

Basin Eco-Compensation Strategy Considering a Cost-Sharing Contract

Based on differential game theory, this paper constructs a centralized game model, a Nash noncooperative game model and a game model with a cost-sharing contract. This paper discusses the interactive game strategy between the central government’s participation in subsidies and the upstream and downstream sharing of the cost of pollution control, and we obtain and compare the optimal feedback strategies and trajectory of pollution control with time upstream and downstream of a basin. The introduction of the game model for cost-sharing contracts not only maximizes the benefits in the basin but also increases the amount of pollution control, improves the ecological environment of the basin, and enhances its capital attractiveness. In addition, it is found that the central government’s subsidies have an impact on the decision-making behavior of local governments, especially in the case of introducing cost-sharing contracts. Central government subsidies can increase the enthusiasm of upstream and downstream local governments for long-term cooperation in pollution control and emission reduction.

Output feedback adaptive dynamic programming for linear differential zero-sum games

This paper addresses the problem of finding optimal output feedback strategies for solving linear differential zero-sum games using a model-free approach based on adaptive dynamic programming (ADP). In contrast to their discrete-time counterparts, differential games involve continuous-time dynamics and existing ADP approaches to their solutions require access to full measurement of the internal state. This difficulty is due to the fact that direct translation of the discrete-time output feedback ADP results requires derivatives of the input and output measurements, which is generally prohibitive in practice. This work aims to overcome this difficulty and presents a new embedded filtering based observer approach towards designing output feedback ADP algorithms for solving the differential zero-sum game problem. Two output feedback ADP algorithms based respectively on policy iteration and value iteration are developed. The proposed scheme is completely online in nature and works without requiring information of the system dynamics. In addition, this work also addresses the excitation bias problem encountered in output feedback ADP methods, which typically requires a discounting factor for its mitigation. We show that the proposed scheme is bias-free, and therefore, does not require a discounting factor. It is shown that the proposed algorithms converge to the solution obtained by solving the game algebraic Riccati equation. Two numerical examples are demonstrated to validate the proposed scheme.

Research on Collaborative Management Strategies of Closed-Loop Supply Chain under the Influence of Big-Data Marketing and Reference Price Effect

This paper integrates the Internet service platform with big-data marketing into the dynamic closed-loop supply chain system as an independent game subject. Considering the reference price effect of consumers, this work constructs differential games among manufacturer, retailer and Internet service platform under three business models of independent, collaborative production and collaborative marketing. Using Bellman’s continuous dynamic programming theory, this work obtains the optimal feedback strategies of price and big-data marketing effort, brand goodwill, return rate of used products and corporate profits under the three business models. Comparing the three scenarios and analyzing the sensitivity of key exogenous parameters, it can be found that the involvement of Internet service platform has a crucial impact on the sustainable profitability of supply chain enterprises. Considering the reference price effect of consumers, enterprises should adopt different strategic alliances in different periods, which can also gain new development momentum in the context of data-driven marketing, achieve the improvement of the triple-bottom line of closed-loop supply chain and even reach a win-win situation for supply chain enterprises.

Two-on-One Pursuit when the Pursuers Have the Same Speed as the Evader

A two-on-one pursuit-evasion differential game is considered. The setup is akin to Isaacs’ Two Cutters and Fugitive Ship differential game. In this paper it is however assumed that the three players have equal speeds and the two cutters/pursuers have a non-zero capture radius. The case where just one of the Pursuers is endowed with a circular capture set is also considered. The state space region where capture is guaranteed is delineated, thus providing the solution of the Game of Kind, and the players’ optimal state feedback strategies and the attendant value function are synthesized, thus providing the solution of the Game of Degree.

On a Two Cutters and Fugitive Ship Differential Game

Isaacs’ Two Cutters and Fugitive Ship differential game is revisited. In this letter, it is assumed that the three players, that is, the two cutters and the fugitive ship have equal speeds, but the cutters have a non-zero capture radius. The state space region where capture is guaranteed, notwithstanding the fact that the cutters are not faster than the fugitive ship, is delineated, and the protagonists’ optimal state feedback strategies are synthesized.

Students’ Perceptions of the Strengths and Limitations of Electronic Tests Focusing on Instant Feedback

Aim/Purpose: Students’ perceptions about feedback in e-tests have not been studied using qualitative methods. Therefore, the objective of this study was to investigate the students' attitude towards electronic tests, focusing on the feedback. Background: Despite the advantages of electronic tests, it is one of the neglected technologies in the students’ evaluation process. Based on the technology acceptance model, users' attitudes have a significant impact on the acceptance of each technology. There is a paucity of qualitative research regarding the examination of students’ attitudes towards e-testing and instant feedback. Methodology: A pilot study was used to achieve the aims of the study. Using purposeful sampling, the attitudes of 40 students from the University of Birjand who participated in the electronic test were examined. Contribution: This study suggests interventions to improve the acceptance of electronic tests and reduce resistance to them. It provides insight into understanding the nature of immediate feedback in electronic tests, puts forth suggestions for the successful implementation of e-tests in the students' evaluation process, and further provides information on the relationship between immediate feedback and student test anxiety Findings: Among the various features of electronic tests, instant feedback has attracted students' attention more than others. Students’ perceptions about instant feedback were contradictory, because some felt instant feedback is stressful, while others considered it desirable. Based on the results, feedback on electronic tests: opportunity or challenge was selected as a main theme. Recommendations for Practitioners: Practitioners should consider student attitude toward feedback in e-tests and they should personalize e-test feedback according to students’ preferences. Recommendation for Researchers: Researchers can examine quantitative and qualitative variables such as personality type, study approaches, exam anxiety and other factors in studying student’s attitudes towards feedback. Impact on Society: Teachers can use these finding in designing and developing e-tests in their formative and summative assessments, where they select the optimal feedback strategy for their assessments. Future Research: This study highlights that instant feedback is not necessarily acceptable to students. Further study is necessary to find when it is good and when it is not, for whom it is good or bad, how we can reduce the negative effects of instant feedback, and whether it increases exam anxiety or not.

Toward a Solution of the Active Target Defense Differential Game

A novel pursuit-evasion differential game involving three agents is considered. An Attacker missile is pursuing a Target aircraft. The Target aircraft is aided by a Defender missile launched by, say, the wingman, to intercept the Attacker before it reaches the Target aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the separation between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while at the same time the Attacker tries to minimize said distance. A long-range Beyond Visual Range engagement which is in line with current CONcepts of OPeration is envisaged, and it is therefore assumed that the players have simple motion kinematics a la Isaacs. Also, the speed of the Attacker is equal to the speed of the Defender and the latter is interested in point capture. It is also assumed that at all time the Attacker is aware of the Defender’s position, i.e., it is a perfect information game. The analytic/closed-form solution of the target defense pursuit-evasion differential game delineates the state space region where the Attacker can reach the Target without being intercepted by the Defender, thus disposing of the Game of Kind. The target defense Game of Degree is played in the remaining state space. The analytic solution of the Game of Degree yields the agents’ optimal state feedback strategies, that is, the instantaneous heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker at the instant of interception of the Attacker by the Defender, and also the instantaneous optimal heading for the Attacker to minimize said separation. Their calculation hinges on the real-time solution of a quartic equation. In this paper we contribute to the solution of a differential game with three states—an additional example to the, admittedly small, repertoire of pursuit-evasion differential games in 3-D which can be solved in closed form.

Discrete-Time Robust Hierarchical Linear-Quadratic Dynamic Games

In this paper, the theory of robust min–max control is extended to hierarchical and multiplayer dynamic games for linear quadratic discrete time systems. The proposed game model consists of one leader and many followers, while the performance of all players is affected by disturbance. The Stackelberg–Nash-saddle equilibrium point of the game is derived and a necessary and sufficient condition for the existence and uniqueness of such a solution is obtained. In the infinite time horizon, it is shown that the solution of the Riccati equation is upper bounded under a condition that is called individual controllability. By assuming such a condition and using a time-varying Lyapunov function the input-to-state stability of the hierarchical dynamic game is achieved, considering the optimal feedback strategies of the players and an arbitrary disturbance as the input.

Optimal feedback strategies for bacterial growth with degradation, recycling, and effect of temperature

SummaryMechanisms of bacterial adaptation to environmental changes are of great interest for both fundamental biology and engineering applications. In this work, we consider a continuous‐time dynamic problem of resource allocation between metabolic and gene expression machineries for a self‐replicating prokaryotic cell population. In compliance with evolutionary principles, the criterion is to maximize the accumulated structural biomass. In the model, we include both the degradation of proteins into amino acids and the recycling of the latter (ie, using as precursors again). On the basis of the analytical investigation of our problem by Pontryagin's maximum principle, we develop a numerical method to approximate the switching curve of the optimal feedback control strategy. The obtained field of extremal state trajectories consists of chattering arcs and 1 steady‐state singular arc. The constructed feedback control law can serve as a benchmark for comparing actual bacterial strategies of resource allocation. We also study the influence of temperature, whose increase intensifies protein degradation. While the growth rate suddenly decreases with the increase in temperature in a certain range, the optimal control synthesis appears to be essentially less sensitive.

Optimal investment of variance-swaps in jump-diffusion market with regime-switching

We consider a general jump-diffusion market with regime-switching where the jump risk is modeled as a Markov-modulated Poisson random measure. In this incomplete market, we price the variance-swaps using a combination of the Esscher transform and change of measure on time-inhomogeneous Markov chains. We study the dynamic optimal investment problem of the variance-swaps and characterize the optimal feedback strategy. Moreover, a closed-form solution to the HJB PDE associated with the stochastic control problem is established and the verification theorem is proved. The numerical analysis based on a two-state Markov chain uncovers some robust features of the optimal investment strategy.

Optimal resource allocation for biotrophic plant pathogens

A significant class of plant pathogens is constituted by biotrophic fungi. They set up long-term feeding relationships with their hosts. This kind of parasitism decreases competitive abilities of plants in natural environments and reduces yields in agricultural systems. Therefore, it is relevant to develop and validate mathematical models which can help to better understand how related disease associated traits evolve. In this paper, one-season dynamics of a within-host cohort of spore-producing biotrophic fungi is considered. Their within-host multiplication and outer transmission are implemented by the mycelial growth and free-living (spore) forms, respectively. We state and investigate a specific dynamic optimization problem in order to determine how the fungi allocate available host resources between mycelial growth and spore production. The pathogen fitness criterion is introduced as maximization of the reproductive output. The constructed optimal feedback strategy can serve as a benchmark to compare actual infection mechanisms. There is a singular control subregime which plays an important role from the biological point of view. It keeps the average mycelium size equal to a particular steady value and represents an intermediate configuration of the resource allocation. We also analyze the asymptotic behavior of this steady state when the lesion density is large.

First-passage time approach to controlling noise in the timing of intracellular events

In the noisy cellular environment, gene products are subject to inherent random fluctuations in copy numbers over time. How cells ensure precision in the timing of key intracellular events despite such stochasticity is an intriguing fundamental problem. We formulate event timing as a first-passage time problem, where an event is triggered when the level of a protein crosses a critical threshold for the first time. Analytical calculations are performed for the first-passage time distribution in stochastic models of gene expression. Derivation of these formulas motivates an interesting question: Is there an optimal feedback strategy to regulate the synthesis of a protein to ensure that an event will occur at a precise time, while minimizing deviations or noise about the mean? Counterintuitively, results show that for a stable long-lived protein, the optimal strategy is to express the protein at a constant rate without any feedback regulation, and any form of feedback (positive, negative, or any combination of them) will always amplify noise in event timing. In contrast, a positive feedback mechanism provides the highest precision in timing for an unstable protein. These theoretical results explain recent experimental observations of single-cell lysis times in bacteriophage [Formula: see text] Here, lysis of an infected bacterial cell is orchestrated by the expression and accumulation of a stable [Formula: see text] protein up to a threshold, and precision in timing is achieved via feedforward rather than feedback control. Our results have broad implications for diverse cellular processes that rely on precise temporal triggering of events.

Risk Sensitive Asset Management and Cascading Defaults

We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility of cascading defaults. Default events have an impact on the distress state of the surviving stocks in the portfolio. We study the recursive system of non-Lipschitz quasi-linear parabolic HJB-PDEs associated with the value function of the control problem in the different default states of the economy.We show the existence of a classical solution to this system via super-sub solution techniques and give an explicit characterization of the optimal feedback strategy in terms of the value function. We prove a verification theorem establishing the uniqueness of the solution.A numerical analysis indicates that the investor accounts for contagion effects when making investment decisions, reduces his risk exposure as he becomes more sensitive to risk, and that his strategy depends non-monotonically on the aggregate risk level.

A Stochastic Model of Optimal Debt Management and Bankruptcy

A problem of optimal debt management is modeled as a noncooperative interaction between a borrower and a pool of lenders, in an infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio $x(t)$ reaches a given size $x^*$, bankruptcy instantly occurs. The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of their investment. For a given bankruptcy threshold $x^*$, existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting. The paper also analyzes how the expected total cost to the borrower changes, depending on different values of $x^*$.

Risk-Sensitive Asset Management and Cascading Defaults

We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility of cascading defaults. Default events have an impact on the distress state of the surviving stocks in the portfolio. We study the recursive system of non-Lipschitz quasilinear parabolic HJB-PDEs associated with the value function of the control problem in the different default states of the economy. We show the existence of a classical solution to this system via super-sub solution techniques and give an explicit characterization of the optimal feedback strategy in terms of the value function. We prove a verification theorem establishing the uniqueness of the solution. A numerical analysis indicates that the investor significantly accounts for contagion effects when making investment decisions, and that his strategy depends nonmonotonically on the aggregate risk level.